%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:47:30 AM UTC 2026
% Result : Theorem 92.69s 15.79s
% Output : CNFRefutation 15.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 269
% Syntax : Number of formulae : 4969 (1781 unt; 0 typ; 268 def)
% Number of atoms : 41711 (16274 equ; 0 cnn)
% Maximal formula atoms : 269 ( 8 avg)
% Number of connectives : 84640 (16524 ~;15994 |; 52 &;50997 @)
% ( 14 <=>;1059 =>; 0 <=; 0 <~>)
% Maximal formula depth : 277 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2508 (2508 >; 0 *; 0 +; 0 <<)
% Number of symbols : 465 ( 462 usr; 272 con; 0-4 aty)
% Number of variables : 17904 (1228 ^;16641 !; 35 ?;17904 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_ap2apEq1,type,
ap2apEq1: $o ).
thf(tp_ap2apEq2,type,
ap2apEq2: $o ).
thf(tp_ap2p,type,
ap2p: $o ).
thf(tp_apProp,type,
apProp: $o ).
thf(tp_app,type,
app: $o ).
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_beta1,type,
beta1: $o ).
thf(tp_beta2,type,
beta2: $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_binintersectTELcontra,type,
binintersectTELcontra: $o ).
thf(tp_binintersectTERcontra,type,
binintersectTERcontra: $o ).
thf(tp_binintersectT_lem,type,
binintersectT_lem: $o ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionE,type,
binunionE: $o ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_binunionIR,type,
binunionIR: $o ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_binunionRsub,type,
binunionRsub: $o ).
thf(tp_binunionTE,type,
binunionTE: $o ).
thf(tp_binunionTEcontra,type,
binunionTEcontra: $o ).
thf(tp_binunionTILcontra,type,
binunionTILcontra: $o ).
thf(tp_binunionTIRcontra,type,
binunionTIRcontra: $o ).
thf(tp_binunionT_lem,type,
binunionT_lem: $o ).
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_brelnall2,type,
brelnall2: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_cartprodpairmemEL,type,
cartprodpairmemEL: $o ).
thf(tp_cartprodpairmemER,type,
cartprodpairmemER: $o ).
thf(tp_cartprodpairsurjEq,type,
cartprodpairsurjEq: $o ).
thf(tp_cartprodsndin,type,
cartprodsndin: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $o ).
thf(tp_complementImpComplementIntersect,type,
complementImpComplementIntersect: $o ).
thf(tp_complementInPowersetComplementIntersect,type,
complementInPowersetComplementIntersect: $o ).
thf(tp_complementSubsetComplementIntersect,type,
complementSubsetComplementIntersect: $o ).
thf(tp_complementTE1,type,
complementTE1: $o ).
thf(tp_complementTI1,type,
complementTI1: $o ).
thf(tp_complementT_lem,type,
complementT_lem: $o ).
thf(tp_complementTcontraSubset,type,
complementTcontraSubset: $o ).
thf(tp_complementTnotintersectT,type,
complementTnotintersectT: $o ).
thf(tp_contraSubsetComplement,type,
contraSubsetComplement: $o ).
thf(tp_contrasubsetT,type,
contrasubsetT: $o ).
thf(tp_contrasubsetT1,type,
contrasubsetT1: $o ).
thf(tp_contrasubsetT2,type,
contrasubsetT2: $o ).
thf(tp_contrasubsetT3,type,
contrasubsetT3: $o ).
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descr__Cong,type,
descr__Cong: $o ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_disjointsetsI1,type,
disjointsetsI1: $o ).
thf(tp_doubleComplementE1,type,
doubleComplementE1: $o ).
thf(tp_doubleComplementEq,type,
doubleComplementEq: $o ).
thf(tp_doubleComplementI1,type,
doubleComplementI1: $o ).
thf(tp_doubleComplementSub1,type,
doubleComplementSub1: $o ).
thf(tp_doubleComplementSub2,type,
doubleComplementSub2: $o ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrEL1,type,
dpsetconstrEL1: $o ).
thf(tp_dpsetconstrEL2,type,
dpsetconstrEL2: $o ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $o ).
thf(tp_dpsetconstrERa,type,
dpsetconstrERa: $o ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_dpsetconstrSub,type,
dpsetconstrSub: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_dsetconstr__Cong,type,
dsetconstr__Cong: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptyset__Cong,type,
emptyset__Cong: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqbreln,type,
eqbreln: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_eta1,type,
eta1: $o ).
thf(tp_eta2,type,
eta2: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1E2,type,
ex1E2: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_exuE3u,type,
exuE3u: $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $o ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_ifSingleton,type,
ifSingleton: $o ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iffalseProp1,type,
iffalseProp1: $o ).
thf(tp_iffalseProp2,type,
iffalseProp2: $o ).
thf(tp_ifp,type,
ifp: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_iftrueProp1,type,
iftrueProp1: $o ).
thf(tp_iftrueProp2,type,
iftrueProp2: $o ).
thf(tp_iftrueorfalse,type,
iftrueorfalse: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inComplementUnionImpInComplement1,type,
inComplementUnionImpInComplement1: $o ).
thf(tp_inComplementUnionImpNotIn1,type,
inComplementUnionImpNotIn1: $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inIntersectImpInIntersectUnions,type,
inIntersectImpInIntersectUnions: $o ).
thf(tp_inIntersectImpInUnion,type,
inIntersectImpInUnion: $o ).
thf(tp_inIntersectImpInUnion2,type,
inIntersectImpInUnion2: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_intersectInPowersetIntersectUnions,type,
intersectInPowersetIntersectUnions: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2lamEq,type,
lam2lamEq: $o ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powersetTE1,type,
powersetTE1: $o ).
thf(tp_powersetTI1,type,
powersetTI1: $o ).
thf(tp_powersetT_lem,type,
powersetT_lem: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY1375,type,
sK100_SY1375: $i > $i > $i > $i > $i ).
thf(tp_sK101_SY1279,type,
sK101_SY1279: $i > $i > $i > $i > $i ).
thf(tp_sK102_SY1279,type,
sK102_SY1279: $i > $i > $i > $i > $i ).
thf(tp_sK103_SY1344,type,
sK103_SY1344: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK104_SY736,type,
sK104_SY736: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK105_SY1352,type,
sK105_SY1352: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK106_SY1279,type,
sK106_SY1279: $i > $i > $i > $i > $i ).
thf(tp_sK107_SY1383,type,
sK107_SY1383: $i > $i > $i > $i > $i ).
thf(tp_sK108_SY1384,type,
sK108_SY1384: $i > $i > $i > $i > $i ).
thf(tp_sK109_SY1390,type,
sK109_SY1390: $i > $i > $i > $i > $i ).
thf(tp_sK10_SY733,type,
sK10_SY733: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK110_SY1369,type,
sK110_SY1369: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK111_SY1370,type,
sK111_SY1370: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY1329,type,
sK112_SY1329: $i > $i > $i > $i ).
thf(tp_sK113_SY1329,type,
sK113_SY1329: $i > $i > $i > $i ).
thf(tp_sK114_SY1382,type,
sK114_SY1382: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK115_SY689,type,
sK115_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK116_SY58,type,
sK116_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK117_SY1373,type,
sK117_SY1373: $i > $i > $i > $i ).
thf(tp_sK118_SY1402,type,
sK118_SY1402: $i > $i > $i > $i ).
thf(tp_sK119_SY1388,type,
sK119_SY1388: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK11_SY768,type,
sK11_SY768: $i > $i > $i ).
thf(tp_sK120_SY1389,type,
sK120_SY1389: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK121_SY689,type,
sK121_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK122_SY58,type,
sK122_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK123_SY1408,type,
sK123_SY1408: $i > $i > $i > $i ).
thf(tp_sK124_SY1393,type,
sK124_SY1393: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK125_SY1394,type,
sK125_SY1394: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK126_SY1395,type,
sK126_SY1395: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK127_SY1391,type,
sK127_SY1391: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK128_SY1398,type,
sK128_SY1398: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK129_SY1399,type,
sK129_SY1399: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK12_SY769,type,
sK12_SY769: ( $i > $o ) > $i > $i ).
thf(tp_sK130_SY1400,type,
sK130_SY1400: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK131_SY1401,type,
sK131_SY1401: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK132_SY1396,type,
sK132_SY1396: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK133_SY1406,type,
sK133_SY1406: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK134_SY1407,type,
sK134_SY1407: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK135_SY689,type,
sK135_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK136_SY58,type,
sK136_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK137_SY1412,type,
sK137_SY1412: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK138_SY689,type,
sK138_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK139_SY58,type,
sK139_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK13_SY818,type,
sK13_SY818: $i > $i > $i ).
thf(tp_sK140_SY689,type,
sK140_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK141_SY58,type,
sK141_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK142_SY689,type,
sK142_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK143_SY58,type,
sK143_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK144_SY1418,type,
sK144_SY1418: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK145_SY689,type,
sK145_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK146_SY58,type,
sK146_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK147_SY689,type,
sK147_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK148_SY58,type,
sK148_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK149_SY689,type,
sK149_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY824,type,
sK14_SY824: ( $i > $o ) > $i > $i ).
thf(tp_sK150_SY58,type,
sK150_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK151_SY689,type,
sK151_SY689: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY58,type,
sK152_SY58: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK153_SY1424,type,
sK153_SY1424: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK154_SY1428,type,
sK154_SY1428: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK155_SY1429,type,
sK155_SY1429: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK156_SY1430,type,
sK156_SY1430: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK157_SY1438,type,
sK157_SY1438: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK158_SY1439,type,
sK158_SY1439: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK159_SY1440,type,
sK159_SY1440: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK15_SY834,type,
sK15_SY834: $i > $i > $i ).
thf(tp_sK160_SY1447,type,
sK160_SY1447: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY848,type,
sK16_SY848: ( $i > $o ) > $i > $i ).
thf(tp_sK17_SY946,type,
sK17_SY946: $i > $i > $i ).
thf(tp_sK18_SY995,type,
sK18_SY995: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK19_SY1221,type,
sK19_SY1221: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY1059,type,
sK20_SY1059: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK21_SY1061,type,
sK21_SY1061: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK22_SY170,type,
sK22_SY170: $i > $i ).
thf(tp_sK23_SY262,type,
sK23_SY262: $i > $i ).
thf(tp_sK24_SY1107,type,
sK24_SY1107: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK25_SY1125,type,
sK25_SY1125: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK26_SY909,type,
sK26_SY909: ( $i > $o ) > $i > $i ).
thf(tp_sK27_SY1133,type,
sK27_SY1133: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK28_SY952,type,
sK28_SY952: $i > $i > $i ).
thf(tp_sK29_SY1174,type,
sK29_SY1174: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK30_SY1267,type,
sK30_SY1267: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK31_SY1220,type,
sK31_SY1220: $i > ( $i > $o ) > $i ).
thf(tp_sK32_SY746,type,
sK32_SY746: ( $i > $o ) > $i > $i ).
thf(tp_sK33_SY1232,type,
sK33_SY1232: ( $i > $o ) > $i > $i ).
thf(tp_sK34_SY1241,type,
sK34_SY1241: ( $i > $o ) > $i > $i ).
thf(tp_sK35_SY905,type,
sK35_SY905: ( $i > $o ) > $i > $i ).
thf(tp_sK36_SY974,type,
sK36_SY974: $i > $i > $i ).
thf(tp_sK37_SY1201,type,
sK37_SY1201: $i > $i > $i > $i ).
thf(tp_sK38_SY30,type,
sK38_SY30: $i > $i > $i ).
thf(tp_sK39_SY1219,type,
sK39_SY1219: $o > $i > $i > $i ).
thf(tp_sK3_SY3,type,
sK3_SY3: $i ).
thf(tp_sK40_SX0,type,
sK40_SX0: $i > $i > $i ).
thf(tp_sK41_SX0,type,
sK41_SX0: $i > $i > $i ).
thf(tp_sK42_SY778,type,
sK42_SY778: $i > $i > $i ).
thf(tp_sK43_SY395,type,
sK43_SY395: $i > $i ).
thf(tp_sK44_SY1274,type,
sK44_SY1274: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK45_SY42,type,
sK45_SY42: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY736,type,
sK46_SY736: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK47_SY1295,type,
sK47_SY1295: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK48_SY1303,type,
sK48_SY1303: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK49_SY947,type,
sK49_SY947: $i > $i > $i ).
thf(tp_sK4_SY5,type,
sK4_SY5: $i ).
thf(tp_sK50_SY972,type,
sK50_SY972: $i > $i > $i ).
thf(tp_sK51_SY1335,type,
sK51_SY1335: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY1231,type,
sK52_SY1231: $i > $i > $i > $i ).
thf(tp_sK53_SY1250,type,
sK53_SY1250: $i > $i > $i > $i ).
thf(tp_sK54_SY930,type,
sK54_SY930: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK55_SY941,type,
sK55_SY941: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK56_SY1161,type,
sK56_SY1161: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK57_SY947,type,
sK57_SY947: $i > $i > $i ).
thf(tp_sK58_SY1272,type,
sK58_SY1272: $i > $i > $i > $i ).
thf(tp_sK59_SY1334,type,
sK59_SY1334: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY484,type,
sK5_SY484: $i > $i ).
thf(tp_sK60_SY1277,type,
sK60_SY1277: $i > $i > $i > $i > $i ).
thf(tp_sK61_SY1222,type,
sK61_SY1222: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY1234,type,
sK62_SY1234: $i > ( $i > $o ) > $i ).
thf(tp_sK63_SY1290,type,
sK63_SY1290: $i > $i > $i > $i > $i ).
thf(tp_sK64_SY1293,type,
sK64_SY1293: $i > $i > $i > $i > $i ).
thf(tp_sK65_SY1340,type,
sK65_SY1340: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK66_SY1248,type,
sK66_SY1248: $i > ( $i > $o ) > $i ).
thf(tp_sK67_SY1302,type,
sK67_SY1302: $i > $i > $i > $i > $i ).
thf(tp_sK68_SY1258,type,
sK68_SY1258: $i > ( $i > $o ) > $i ).
thf(tp_sK69_SY1342,type,
sK69_SY1342: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK6_SY25,type,
sK6_SY25: $i > $i ).
thf(tp_sK70_SY1259,type,
sK70_SY1259: $i > ( $i > $o ) > $i ).
thf(tp_sK71_SY1260,type,
sK71_SY1260: $i > ( $i > $o ) > $i ).
thf(tp_sK72_SY1265,type,
sK72_SY1265: $i > ( $i > $o ) > $i ).
thf(tp_sK73_SY1313,type,
sK73_SY1313: $i > $i > $i > $i > $i ).
thf(tp_sK74_SY1343,type,
sK74_SY1343: $i > $i > $i > $i > $i ).
thf(tp_sK75_SY1346,type,
sK75_SY1346: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY1318,type,
sK76_SY1318: $i > $i > $i > $i ).
thf(tp_sK77_SY44,type,
sK77_SY44: $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY44,type,
sK78_SY44: $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY64,type,
sK79_SY64: $i > ( $i > $o ) > $i ).
thf(tp_sK7_SY302,type,
sK7_SY302: $i > $i ).
thf(tp_sK80_SY1321,type,
sK80_SY1321: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK81_SY758,type,
sK81_SY758: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK82_SY225,type,
sK82_SY225: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY451,type,
sK83_SY451: $i > ( $i > $o ) > $i ).
thf(tp_sK84_SY1327,type,
sK84_SY1327: $i > $i > $i ).
thf(tp_sK85_SY579,type,
sK85_SY579: $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY39,type,
sK86_SY39: $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY44,type,
sK87_SY44: $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY64,type,
sK88_SY64: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY225,type,
sK89_SY225: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY679,type,
sK8_SY679: $i > $i > $i ).
thf(tp_sK90_SY451,type,
sK90_SY451: $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY579,type,
sK91_SY579: $i > ( $i > $o ) > $i ).
thf(tp_sK92_SY1273,type,
sK92_SY1273: $i > $i > $i > $i ).
thf(tp_sK93_SY1273,type,
sK93_SY1273: $i > $i > $i > $i ).
thf(tp_sK94_SY1279,type,
sK94_SY1279: $i > $i > $i > $i > $i ).
thf(tp_sK95_SY39,type,
sK95_SY39: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY39,type,
sK96_SY39: $i > ( $i > $o ) > $i ).
thf(tp_sK97_SY1273,type,
sK97_SY1273: $i > $i > $i > $i ).
thf(tp_sK98_SY39,type,
sK98_SY39: $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY736,type,
sK99_SY736: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK9_SY685,type,
sK9_SY685: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinAx,type,
setadjoinAx: $o ).
thf(tp_setadjoinE,type,
setadjoinE: $o ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_setadjoinOr,type,
setadjoinOr: $o ).
thf(tp_setadjoinSub,type,
setadjoinSub: $o ).
thf(tp_setadjoinSub2,type,
setadjoinSub2: $o ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setbeta,type,
setbeta: $o ).
thf(tp_setext,type,
setext: $o ).
thf(tp_setextAx,type,
setextAx: $o ).
thf(tp_setextT,type,
setextT: $o ).
thf(tp_setextsub,type,
setextsub: $o ).
thf(tp_setminus,type,
setminus: $i > $i > $i ).
thf(tp_setminusEL,type,
setminusEL: $o ).
thf(tp_setminusELneg,type,
setminusELneg: $o ).
thf(tp_setminusER,type,
setminusER: $o ).
thf(tp_setminusERneg,type,
setminusERneg: $o ).
thf(tp_setminusI,type,
setminusI: $o ).
thf(tp_setminusILneg,type,
setminusILneg: $o ).
thf(tp_setminusIRneg,type,
setminusIRneg: $o ).
thf(tp_setminusLsub,type,
setminusLsub: $o ).
thf(tp_setminusSubset1,type,
setminusSubset1: $o ).
thf(tp_setminusSubset2,type,
setminusSubset2: $o ).
thf(tp_setminusT_lem,type,
setminusT_lem: $o ).
thf(tp_setoftrueEq,type,
setoftrueEq: $o ).
thf(tp_setsmeet,type,
setsmeet: $i > $i > $o ).
thf(tp_setukpairIL,type,
setukpairIL: $o ).
thf(tp_setukpairIR,type,
setukpairIR: $o ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_subbreln,type,
subbreln: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTI,type,
subsetTI: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theeq,type,
theeq: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,definition,
( ap2apEq2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(beta1,definition,
( beta1
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(beta2,definition,
( beta2
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectTELcontra,definition,
( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,definition,
( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binunionTE,definition,
( binunionTE
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionTEcontra,definition,
( binunionTEcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(binunionTILcontra,definition,
( binunionTILcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,definition,
( binunionTIRcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(binunionT_lem,definition,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,definition,
( brelnall2
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairsurjEq,definition,
( cartprodpairsurjEq
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(complementImpComplementIntersect,definition,
( 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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementImpComplementIntersect) ).
thf(complementInPowersetComplementIntersect,definition,
( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementInPowersetComplementIntersect) ).
thf(complementSubsetComplementIntersect,definition,
( complementSubsetComplementIntersect
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementSubsetComplementIntersect) ).
thf(complementTE1,definition,
( complementTE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1) ).
thf(complementTI1,definition,
( complementTI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTI1) ).
thf(complementT_lem,definition,
( complementT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem) ).
thf(complementTcontraSubset,definition,
( complementTcontraSubset
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTcontraSubset) ).
thf(complementTnotintersectT,definition,
( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTnotintersectT) ).
thf(contraSubsetComplement,definition,
( contraSubsetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contraSubsetComplement) ).
thf(contrasubsetT,definition,
( contrasubsetT
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( ( in @ Xx @ Y )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT) ).
thf(contrasubsetT1,definition,
( 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 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT1) ).
thf(contrasubsetT2,definition,
( contrasubsetT2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT2) ).
thf(contrasubsetT3,definition,
( contrasubsetT3
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contrasubsetT3) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(doubleComplementE1,definition,
( doubleComplementE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementE1) ).
thf(doubleComplementEq,definition,
( doubleComplementEq
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementEq) ).
thf(doubleComplementI1,definition,
( doubleComplementI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementI1) ).
thf(doubleComplementSub1,definition,
( doubleComplementSub1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub1) ).
thf(doubleComplementSub2,definition,
( doubleComplementSub2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',doubleComplementSub2) ).
thf(dpsetconstrEL1,definition,
( dpsetconstrEL1
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,definition,
( dpsetconstrEL2
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrERa,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,definition,
( dpsetconstrSub
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqbreln,definition,
( eqbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(eta1,definition,
( eta1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta1) ).
thf(eta2,definition,
( eta2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eta2) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1E2,definition,
( ex1E2
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(funcGraphProp1,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcGraphProp3,definition,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp4,definition,
( funcGraphProp4
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,definition,
( funcext2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(funcextLem,definition,
( funcextLem
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(ifSingleton,definition,
( ifSingleton
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iffalseProp1,definition,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,definition,
( iffalseProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(ifp,definition,
( ifp
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iftrueProp1,definition,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,definition,
( iftrueProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(iftrueorfalse,definition,
( iftrueorfalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(inComplementUnionImpInComplement1,definition,
( inComplementUnionImpInComplement1
= ( ! [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 @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(inComplementUnionImpNotIn1,definition,
( inComplementUnionImpNotIn1
= ( ! [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 @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inIntersectImpInIntersectUnions,definition,
( 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 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(inIntersectImpInUnion,definition,
( 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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,definition,
( 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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(intersectInPowersetIntersectUnions,definition,
( 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 ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam2lamEq,definition,
( lam2lamEq
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetTE1,definition,
( powersetTE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(powersetTI1,definition,
( powersetTI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetT_lem,definition,
( powersetT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setextT,definition,
( setextT
= ( ! [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 ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ Y )
=> ( in @ Xx @ X ) ) )
=> ( X = Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextT) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setminusT_lem,definition,
( setminusT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusT_lem) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(subbreln,definition,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTI,definition,
( 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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTI) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theeq,definition,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,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
=> ! [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 @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1) ).
thf(2,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
=> ( 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
=> ! [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 @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setextAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
emptysetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
setadjoinAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
powersetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
setunionAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
omega0Ax = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(9,plain,
omegaSAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(10,plain,
omegaIndAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(11,plain,
replAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(12,plain,
foundationAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(13,plain,
wellorderingAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(14,plain,
descrp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(15,plain,
dsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(16,plain,
dsetconstrEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(17,plain,
dsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(18,plain,
exuE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(19,plain,
prop2setE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(20,plain,
emptysetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(21,plain,
emptysetimpfalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(22,plain,
notinemptyset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(23,plain,
exuE3e = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(24,plain,
setext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(25,plain,
emptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(26,plain,
noeltsimpempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(27,plain,
setbeta = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(28,plain,
nonemptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(29,plain,
nonemptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(30,plain,
nonemptyI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(31,plain,
setadjoinIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(32,plain,
emptyinunitempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(33,plain,
setadjoinIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(34,plain,
setadjoinE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(35,plain,
setadjoinOr = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(36,plain,
setoftrueEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(37,plain,
powersetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(38,plain,
emptyinPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(39,plain,
emptyInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(40,plain,
powersetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(41,plain,
setunionI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(42,plain,
setunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(43,plain,
subPowSU = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(44,plain,
exuE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(45,plain,
nonemptyImpWitness = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(46,plain,
uniqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(47,plain,
notinsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(48,plain,
eqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(49,plain,
singletonsswitch = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(50,plain,
upairsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(51,plain,
upairsetIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(52,plain,
upairsetIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(53,plain,
emptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(54,plain,
vacuousDall = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(55,plain,
quantDeMorgan1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(56,plain,
quantDeMorgan2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(57,plain,
quantDeMorgan3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(58,plain,
quantDeMorgan4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(59,plain,
prop2setI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(60,plain,
prop2set2propI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(61,plain,
notdexE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(62,plain,
notdallE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(63,plain,
exuI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(64,plain,
exuI3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(65,plain,
exuI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(66,plain,
inCongP = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(67,plain,
in__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(68,plain,
exuE3u = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(69,plain,
exu__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(70,plain,
emptyset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(71,plain,
setadjoin__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(72,plain,
powerset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(73,plain,
setunion__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(74,plain,
omega__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(75,plain,
exuEu = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(76,plain,
descr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(77,plain,
dsetconstr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(78,plain,
subsetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(79,plain,
eqimpsubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(80,plain,
eqimpsubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(81,plain,
subsetI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(82,plain,
emptysetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(83,plain,
subsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(84,plain,
subsetE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(85,plain,
notsubsetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(86,plain,
notequalI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(87,plain,
notequalI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(88,plain,
subsetRefl = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(89,plain,
subsetTrans = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(90,plain,
setadjoinSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(91,plain,
setadjoinSub2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(92,plain,
subset2powerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(93,plain,
setextsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(94,plain,
subsetemptysetimpeq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(95,plain,
powersetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(96,plain,
powersetE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(97,plain,
inPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(98,plain,
powersetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(99,plain,
sepInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(100,plain,
sepSubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(101,plain,
binunionIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(102,plain,
upairset2IR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(103,plain,
binunionIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(104,plain,
binunionEcases = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(105,plain,
binunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(106,plain,
binunionLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(107,plain,
binunionRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(108,plain,
binintersectI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(109,plain,
binintersectSubset5 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(110,plain,
binintersectEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(111,plain,
binintersectLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(112,plain,
binintersectSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(113,plain,
binintersectSubset3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(114,plain,
binintersectER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(115,plain,
disjointsetsI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(116,plain,
binintersectRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(117,plain,
binintersectSubset4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(118,plain,
binintersectSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(119,plain,
bs114d = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(120,plain,
setminusI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(121,plain,
setminusEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(122,plain,
setminusER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(123,plain,
setminusSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(124,plain,
setminusERneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(125,plain,
setminusELneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(126,plain,
setminusILneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(127,plain,
setminusIRneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(128,plain,
setminusLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(129,plain,
setminusSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(130,plain,
symdiffE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(131,plain,
symdiffI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(132,plain,
symdiffI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(133,plain,
symdiffIneg1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(134,plain,
symdiffIneg2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(135,plain,
secondinupair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(136,plain,
setukpairIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(137,plain,
setukpairIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(138,plain,
kpairiskpair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(139,plain,
kpairp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(140,plain,
singletonsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(141,plain,
singletoninpowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(142,plain,
singletoninpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(143,plain,
upairset2E = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(144,plain,
upairsubunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(145,plain,
upairinpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(146,plain,
ubforcartprodlem1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(147,plain,
ubforcartprodlem2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(148,plain,
ubforcartprodlem3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(149,plain,
cartprodpairin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(150,plain,
cartprodmempair1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(151,plain,
cartprodmempair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(152,plain,
setunionE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(153,plain,
setunionsingleton1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(154,plain,
setunionsingleton2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(155,plain,
setunionsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(156,plain,
singletonprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(157,plain,
ex1E1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(158,plain,
ex1I = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(159,plain,
ex1I2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(160,plain,
singletonsuniq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(161,plain,
setukpairinjL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(162,plain,
kfstsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(163,plain,
theprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(164,plain,
kfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(165,plain,
cartprodfstin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(166,plain,
setukpairinjL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(167,plain,
setukpairinjL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(168,plain,
setukpairinjR11 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(169,plain,
setukpairinjR12 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(170,plain,
setukpairinjR1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(171,plain,
upairequniteq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(172,plain,
setukpairinjR2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(173,plain,
setukpairinjR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(174,plain,
ksndsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(175,plain,
ksndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(176,plain,
kpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(177,plain,
cartprodsndin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(178,plain,
cartprodpairmemEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(179,plain,
cartprodpairmemER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(180,plain,
cartprodmempaircEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(181,plain,
cartprodfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(182,plain,
cartprodsndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(183,plain,
cartprodpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(184,plain,
dpsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(185,plain,
dpsetconstrSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(186,plain,
setOfPairsIsBReln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(187,plain,
dpsetconstrERa = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(188,plain,
dpsetconstrEL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(189,plain,
dpsetconstrEL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(190,plain,
dpsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(191,plain,
funcImageSingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(192,plain,
apProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(193,plain,
app = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(194,plain,
infuncsetfunc = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(195,plain,
ap2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(196,plain,
funcinfuncset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(197,plain,
lamProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(198,plain,
lamp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(199,plain,
lam2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(200,plain,
brelnall1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(201,plain,
brelnall2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(202,plain,
ex1E2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(203,plain,
funcGraphProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(204,plain,
funcGraphProp3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(205,plain,
funcGraphProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(206,plain,
funcextLem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(207,plain,
funcGraphProp4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(208,plain,
subbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(209,plain,
eqbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(210,plain,
funcext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(211,plain,
funcext2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(212,plain,
ap2apEq1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(213,plain,
ap2apEq2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(214,plain,
beta1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(215,plain,
eta1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(216,plain,
lam2lamEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(217,plain,
beta2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(218,plain,
eta2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(219,plain,
iffalseProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(220,plain,
iffalseProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(221,plain,
iftrueProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(222,plain,
iftrueProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(223,plain,
ifSingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(224,plain,
ifp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(225,plain,
theeq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(226,plain,
iftrue = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(227,plain,
iffalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(228,plain,
iftrueorfalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(229,plain,
binintersectT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(230,plain,
binunionT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(231,plain,
powersetT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(232,plain,
setminusT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(233,plain,
complementT_lem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(234,plain,
setextT = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(235,plain,
subsetTI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(236,plain,
powersetTI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(237,plain,
powersetTE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(238,plain,
complementTI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(239,plain,
complementTE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(240,plain,
binintersectTELcontra = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(241,plain,
binintersectTERcontra = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(242,plain,
contrasubsetT = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(243,plain,
contrasubsetT1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(244,plain,
contrasubsetT2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(245,plain,
contrasubsetT3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(246,plain,
doubleComplementI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(247,plain,
doubleComplementE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(248,plain,
doubleComplementSub1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(249,plain,
doubleComplementSub2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(250,plain,
doubleComplementEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(251,plain,
complementTnotintersectT = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(252,plain,
complementImpComplementIntersect = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(253,plain,
complementSubsetComplementIntersect = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(254,plain,
complementInPowersetComplementIntersect = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(255,plain,
contraSubsetComplement = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(256,plain,
complementTcontraSubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(257,plain,
binunionTILcontra = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(258,plain,
binunionTIRcontra = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(259,plain,
inIntersectImpInUnion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(260,plain,
inIntersectImpInUnion2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(261,plain,
inIntersectImpInIntersectUnions = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(262,plain,
intersectInPowersetIntersectUnions = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(263,plain,
inComplementUnionImpNotIn1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(264,plain,
inComplementUnionImpInComplement1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(265,plain,
binunionTE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(266,plain,
binunionTEcontra = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(267,plain,
( ( ! [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 @ ( setminus @ A @ X ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(268,plain,
( ( ~ ! [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 @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[267]) ).
thf(269,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY5 @ sK1_A )
& ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
& ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[268]) ).
thf(270,plain,
binunionTEcontra = $true,
inference(copy,[status(thm)],[266]) ).
thf(271,plain,
binunionTE = $true,
inference(copy,[status(thm)],[265]) ).
thf(272,plain,
inComplementUnionImpInComplement1 = $true,
inference(copy,[status(thm)],[264]) ).
thf(273,plain,
inComplementUnionImpNotIn1 = $true,
inference(copy,[status(thm)],[263]) ).
thf(274,plain,
intersectInPowersetIntersectUnions = $true,
inference(copy,[status(thm)],[262]) ).
thf(275,plain,
inIntersectImpInIntersectUnions = $true,
inference(copy,[status(thm)],[261]) ).
thf(276,plain,
inIntersectImpInUnion2 = $true,
inference(copy,[status(thm)],[260]) ).
thf(277,plain,
inIntersectImpInUnion = $true,
inference(copy,[status(thm)],[259]) ).
thf(278,plain,
binunionTIRcontra = $true,
inference(copy,[status(thm)],[258]) ).
thf(279,plain,
binunionTILcontra = $true,
inference(copy,[status(thm)],[257]) ).
thf(280,plain,
complementTcontraSubset = $true,
inference(copy,[status(thm)],[256]) ).
thf(281,plain,
contraSubsetComplement = $true,
inference(copy,[status(thm)],[255]) ).
thf(282,plain,
complementInPowersetComplementIntersect = $true,
inference(copy,[status(thm)],[254]) ).
thf(283,plain,
complementSubsetComplementIntersect = $true,
inference(copy,[status(thm)],[253]) ).
thf(284,plain,
complementImpComplementIntersect = $true,
inference(copy,[status(thm)],[252]) ).
thf(285,plain,
complementTnotintersectT = $true,
inference(copy,[status(thm)],[251]) ).
thf(286,plain,
doubleComplementEq = $true,
inference(copy,[status(thm)],[250]) ).
thf(287,plain,
doubleComplementSub2 = $true,
inference(copy,[status(thm)],[249]) ).
thf(288,plain,
doubleComplementSub1 = $true,
inference(copy,[status(thm)],[248]) ).
thf(289,plain,
doubleComplementE1 = $true,
inference(copy,[status(thm)],[247]) ).
thf(290,plain,
doubleComplementI1 = $true,
inference(copy,[status(thm)],[246]) ).
thf(291,plain,
contrasubsetT3 = $true,
inference(copy,[status(thm)],[245]) ).
thf(292,plain,
contrasubsetT2 = $true,
inference(copy,[status(thm)],[244]) ).
thf(293,plain,
contrasubsetT1 = $true,
inference(copy,[status(thm)],[243]) ).
thf(294,plain,
contrasubsetT = $true,
inference(copy,[status(thm)],[242]) ).
thf(295,plain,
binintersectTERcontra = $true,
inference(copy,[status(thm)],[241]) ).
thf(296,plain,
binintersectTELcontra = $true,
inference(copy,[status(thm)],[240]) ).
thf(297,plain,
complementTE1 = $true,
inference(copy,[status(thm)],[239]) ).
thf(298,plain,
complementTI1 = $true,
inference(copy,[status(thm)],[238]) ).
thf(299,plain,
powersetTE1 = $true,
inference(copy,[status(thm)],[237]) ).
thf(300,plain,
powersetTI1 = $true,
inference(copy,[status(thm)],[236]) ).
thf(301,plain,
subsetTI = $true,
inference(copy,[status(thm)],[235]) ).
thf(302,plain,
setextT = $true,
inference(copy,[status(thm)],[234]) ).
thf(303,plain,
complementT_lem = $true,
inference(copy,[status(thm)],[233]) ).
thf(304,plain,
setminusT_lem = $true,
inference(copy,[status(thm)],[232]) ).
thf(305,plain,
powersetT_lem = $true,
inference(copy,[status(thm)],[231]) ).
thf(306,plain,
binunionT_lem = $true,
inference(copy,[status(thm)],[230]) ).
thf(307,plain,
binintersectT_lem = $true,
inference(copy,[status(thm)],[229]) ).
thf(308,plain,
iftrueorfalse = $true,
inference(copy,[status(thm)],[228]) ).
thf(309,plain,
iffalse = $true,
inference(copy,[status(thm)],[227]) ).
thf(310,plain,
iftrue = $true,
inference(copy,[status(thm)],[226]) ).
thf(311,plain,
theeq = $true,
inference(copy,[status(thm)],[225]) ).
thf(312,plain,
ifp = $true,
inference(copy,[status(thm)],[224]) ).
thf(313,plain,
ifSingleton = $true,
inference(copy,[status(thm)],[223]) ).
thf(314,plain,
iftrueProp2 = $true,
inference(copy,[status(thm)],[222]) ).
thf(315,plain,
iftrueProp1 = $true,
inference(copy,[status(thm)],[221]) ).
thf(316,plain,
iffalseProp2 = $true,
inference(copy,[status(thm)],[220]) ).
thf(317,plain,
iffalseProp1 = $true,
inference(copy,[status(thm)],[219]) ).
thf(318,plain,
eta2 = $true,
inference(copy,[status(thm)],[218]) ).
thf(319,plain,
beta2 = $true,
inference(copy,[status(thm)],[217]) ).
thf(320,plain,
lam2lamEq = $true,
inference(copy,[status(thm)],[216]) ).
thf(321,plain,
eta1 = $true,
inference(copy,[status(thm)],[215]) ).
thf(322,plain,
beta1 = $true,
inference(copy,[status(thm)],[214]) ).
thf(323,plain,
ap2apEq2 = $true,
inference(copy,[status(thm)],[213]) ).
thf(324,plain,
ap2apEq1 = $true,
inference(copy,[status(thm)],[212]) ).
thf(325,plain,
funcext2 = $true,
inference(copy,[status(thm)],[211]) ).
thf(326,plain,
funcext = $true,
inference(copy,[status(thm)],[210]) ).
thf(327,plain,
eqbreln = $true,
inference(copy,[status(thm)],[209]) ).
thf(328,plain,
subbreln = $true,
inference(copy,[status(thm)],[208]) ).
thf(329,plain,
funcGraphProp4 = $true,
inference(copy,[status(thm)],[207]) ).
thf(330,plain,
funcextLem = $true,
inference(copy,[status(thm)],[206]) ).
thf(331,plain,
funcGraphProp2 = $true,
inference(copy,[status(thm)],[205]) ).
thf(332,plain,
funcGraphProp3 = $true,
inference(copy,[status(thm)],[204]) ).
thf(333,plain,
funcGraphProp1 = $true,
inference(copy,[status(thm)],[203]) ).
thf(334,plain,
ex1E2 = $true,
inference(copy,[status(thm)],[202]) ).
thf(335,plain,
brelnall2 = $true,
inference(copy,[status(thm)],[201]) ).
thf(336,plain,
brelnall1 = $true,
inference(copy,[status(thm)],[200]) ).
thf(337,plain,
lam2p = $true,
inference(copy,[status(thm)],[199]) ).
thf(338,plain,
lamp = $true,
inference(copy,[status(thm)],[198]) ).
thf(339,plain,
lamProp = $true,
inference(copy,[status(thm)],[197]) ).
thf(340,plain,
funcinfuncset = $true,
inference(copy,[status(thm)],[196]) ).
thf(341,plain,
ap2p = $true,
inference(copy,[status(thm)],[195]) ).
thf(342,plain,
infuncsetfunc = $true,
inference(copy,[status(thm)],[194]) ).
thf(343,plain,
app = $true,
inference(copy,[status(thm)],[193]) ).
thf(344,plain,
apProp = $true,
inference(copy,[status(thm)],[192]) ).
thf(345,plain,
funcImageSingleton = $true,
inference(copy,[status(thm)],[191]) ).
thf(346,plain,
dpsetconstrER = $true,
inference(copy,[status(thm)],[190]) ).
thf(347,plain,
dpsetconstrEL2 = $true,
inference(copy,[status(thm)],[189]) ).
thf(348,plain,
dpsetconstrEL1 = $true,
inference(copy,[status(thm)],[188]) ).
thf(349,plain,
dpsetconstrERa = $true,
inference(copy,[status(thm)],[187]) ).
thf(350,plain,
setOfPairsIsBReln = $true,
inference(copy,[status(thm)],[186]) ).
thf(351,plain,
dpsetconstrSub = $true,
inference(copy,[status(thm)],[185]) ).
thf(352,plain,
dpsetconstrI = $true,
inference(copy,[status(thm)],[184]) ).
thf(353,plain,
cartprodpairsurjEq = $true,
inference(copy,[status(thm)],[183]) ).
thf(354,plain,
cartprodsndpairEq = $true,
inference(copy,[status(thm)],[182]) ).
thf(355,plain,
cartprodfstpairEq = $true,
inference(copy,[status(thm)],[181]) ).
thf(356,plain,
cartprodmempaircEq = $true,
inference(copy,[status(thm)],[180]) ).
thf(357,plain,
cartprodpairmemER = $true,
inference(copy,[status(thm)],[179]) ).
thf(358,plain,
cartprodpairmemEL = $true,
inference(copy,[status(thm)],[178]) ).
thf(359,plain,
cartprodsndin = $true,
inference(copy,[status(thm)],[177]) ).
thf(360,plain,
kpairsurjEq = $true,
inference(copy,[status(thm)],[176]) ).
thf(361,plain,
ksndpairEq = $true,
inference(copy,[status(thm)],[175]) ).
thf(362,plain,
ksndsingleton = $true,
inference(copy,[status(thm)],[174]) ).
thf(363,plain,
setukpairinjR = $true,
inference(copy,[status(thm)],[173]) ).
thf(364,plain,
setukpairinjR2 = $true,
inference(copy,[status(thm)],[172]) ).
thf(365,plain,
upairequniteq = $true,
inference(copy,[status(thm)],[171]) ).
thf(366,plain,
setukpairinjR1 = $true,
inference(copy,[status(thm)],[170]) ).
thf(367,plain,
setukpairinjR12 = $true,
inference(copy,[status(thm)],[169]) ).
thf(368,plain,
setukpairinjR11 = $true,
inference(copy,[status(thm)],[168]) ).
thf(369,plain,
setukpairinjL = $true,
inference(copy,[status(thm)],[167]) ).
thf(370,plain,
setukpairinjL2 = $true,
inference(copy,[status(thm)],[166]) ).
thf(371,plain,
cartprodfstin = $true,
inference(copy,[status(thm)],[165]) ).
thf(372,plain,
kfstpairEq = $true,
inference(copy,[status(thm)],[164]) ).
thf(373,plain,
theprop = $true,
inference(copy,[status(thm)],[163]) ).
thf(374,plain,
kfstsingleton = $true,
inference(copy,[status(thm)],[162]) ).
thf(375,plain,
setukpairinjL1 = $true,
inference(copy,[status(thm)],[161]) ).
thf(376,plain,
singletonsuniq = $true,
inference(copy,[status(thm)],[160]) ).
thf(377,plain,
ex1I2 = $true,
inference(copy,[status(thm)],[159]) ).
thf(378,plain,
ex1I = $true,
inference(copy,[status(thm)],[158]) ).
thf(379,plain,
ex1E1 = $true,
inference(copy,[status(thm)],[157]) ).
thf(380,plain,
singletonprop = $true,
inference(copy,[status(thm)],[156]) ).
thf(381,plain,
setunionsingleton = $true,
inference(copy,[status(thm)],[155]) ).
thf(382,plain,
setunionsingleton2 = $true,
inference(copy,[status(thm)],[154]) ).
thf(383,plain,
setunionsingleton1 = $true,
inference(copy,[status(thm)],[153]) ).
thf(384,plain,
setunionE2 = $true,
inference(copy,[status(thm)],[152]) ).
thf(385,plain,
cartprodmempair = $true,
inference(copy,[status(thm)],[151]) ).
thf(386,plain,
cartprodmempair1 = $true,
inference(copy,[status(thm)],[150]) ).
thf(387,plain,
cartprodpairin = $true,
inference(copy,[status(thm)],[149]) ).
thf(388,plain,
ubforcartprodlem3 = $true,
inference(copy,[status(thm)],[148]) ).
thf(389,plain,
ubforcartprodlem2 = $true,
inference(copy,[status(thm)],[147]) ).
thf(390,plain,
ubforcartprodlem1 = $true,
inference(copy,[status(thm)],[146]) ).
thf(391,plain,
upairinpowunion = $true,
inference(copy,[status(thm)],[145]) ).
thf(392,plain,
upairsubunion = $true,
inference(copy,[status(thm)],[144]) ).
thf(393,plain,
upairset2E = $true,
inference(copy,[status(thm)],[143]) ).
thf(394,plain,
singletoninpowunion = $true,
inference(copy,[status(thm)],[142]) ).
thf(395,plain,
singletoninpowerset = $true,
inference(copy,[status(thm)],[141]) ).
thf(396,plain,
singletonsubset = $true,
inference(copy,[status(thm)],[140]) ).
thf(397,plain,
kpairp = $true,
inference(copy,[status(thm)],[139]) ).
thf(398,plain,
kpairiskpair = $true,
inference(copy,[status(thm)],[138]) ).
thf(399,plain,
setukpairIR = $true,
inference(copy,[status(thm)],[137]) ).
thf(400,plain,
setukpairIL = $true,
inference(copy,[status(thm)],[136]) ).
thf(401,plain,
secondinupair = $true,
inference(copy,[status(thm)],[135]) ).
thf(402,plain,
symdiffIneg2 = $true,
inference(copy,[status(thm)],[134]) ).
thf(403,plain,
symdiffIneg1 = $true,
inference(copy,[status(thm)],[133]) ).
thf(404,plain,
symdiffI2 = $true,
inference(copy,[status(thm)],[132]) ).
thf(405,plain,
symdiffI1 = $true,
inference(copy,[status(thm)],[131]) ).
thf(406,plain,
symdiffE = $true,
inference(copy,[status(thm)],[130]) ).
thf(407,plain,
setminusSubset1 = $true,
inference(copy,[status(thm)],[129]) ).
thf(408,plain,
setminusLsub = $true,
inference(copy,[status(thm)],[128]) ).
thf(409,plain,
setminusIRneg = $true,
inference(copy,[status(thm)],[127]) ).
thf(410,plain,
setminusILneg = $true,
inference(copy,[status(thm)],[126]) ).
thf(411,plain,
setminusELneg = $true,
inference(copy,[status(thm)],[125]) ).
thf(412,plain,
setminusERneg = $true,
inference(copy,[status(thm)],[124]) ).
thf(413,plain,
setminusSubset2 = $true,
inference(copy,[status(thm)],[123]) ).
thf(414,plain,
setminusER = $true,
inference(copy,[status(thm)],[122]) ).
thf(415,plain,
setminusEL = $true,
inference(copy,[status(thm)],[121]) ).
thf(416,plain,
setminusI = $true,
inference(copy,[status(thm)],[120]) ).
thf(417,plain,
bs114d = $true,
inference(copy,[status(thm)],[119]) ).
thf(418,plain,
binintersectSubset1 = $true,
inference(copy,[status(thm)],[118]) ).
thf(419,plain,
binintersectSubset4 = $true,
inference(copy,[status(thm)],[117]) ).
thf(420,plain,
binintersectRsub = $true,
inference(copy,[status(thm)],[116]) ).
thf(421,plain,
disjointsetsI1 = $true,
inference(copy,[status(thm)],[115]) ).
thf(422,plain,
binintersectER = $true,
inference(copy,[status(thm)],[114]) ).
thf(423,plain,
binintersectSubset3 = $true,
inference(copy,[status(thm)],[113]) ).
thf(424,plain,
binintersectSubset2 = $true,
inference(copy,[status(thm)],[112]) ).
thf(425,plain,
binintersectLsub = $true,
inference(copy,[status(thm)],[111]) ).
thf(426,plain,
binintersectEL = $true,
inference(copy,[status(thm)],[110]) ).
thf(427,plain,
binintersectSubset5 = $true,
inference(copy,[status(thm)],[109]) ).
thf(428,plain,
binintersectI = $true,
inference(copy,[status(thm)],[108]) ).
thf(429,plain,
binunionRsub = $true,
inference(copy,[status(thm)],[107]) ).
thf(430,plain,
binunionLsub = $true,
inference(copy,[status(thm)],[106]) ).
thf(431,plain,
binunionE = $true,
inference(copy,[status(thm)],[105]) ).
thf(432,plain,
binunionEcases = $true,
inference(copy,[status(thm)],[104]) ).
thf(433,plain,
binunionIR = $true,
inference(copy,[status(thm)],[103]) ).
thf(434,plain,
upairset2IR = $true,
inference(copy,[status(thm)],[102]) ).
thf(435,plain,
binunionIL = $true,
inference(copy,[status(thm)],[101]) ).
thf(436,plain,
sepSubset = $true,
inference(copy,[status(thm)],[100]) ).
thf(437,plain,
sepInPowerset = $true,
inference(copy,[status(thm)],[99]) ).
thf(438,plain,
powersetsubset = $true,
inference(copy,[status(thm)],[98]) ).
thf(439,plain,
inPowerset = $true,
inference(copy,[status(thm)],[97]) ).
thf(440,plain,
powersetE1 = $true,
inference(copy,[status(thm)],[96]) ).
thf(441,plain,
powersetI1 = $true,
inference(copy,[status(thm)],[95]) ).
thf(442,plain,
subsetemptysetimpeq = $true,
inference(copy,[status(thm)],[94]) ).
thf(443,plain,
setextsub = $true,
inference(copy,[status(thm)],[93]) ).
thf(444,plain,
subset2powerset = $true,
inference(copy,[status(thm)],[92]) ).
thf(445,plain,
setadjoinSub2 = $true,
inference(copy,[status(thm)],[91]) ).
thf(446,plain,
setadjoinSub = $true,
inference(copy,[status(thm)],[90]) ).
thf(447,plain,
subsetTrans = $true,
inference(copy,[status(thm)],[89]) ).
thf(448,plain,
subsetRefl = $true,
inference(copy,[status(thm)],[88]) ).
thf(449,plain,
notequalI2 = $true,
inference(copy,[status(thm)],[87]) ).
thf(450,plain,
notequalI1 = $true,
inference(copy,[status(thm)],[86]) ).
thf(451,plain,
notsubsetI = $true,
inference(copy,[status(thm)],[85]) ).
thf(452,plain,
subsetE2 = $true,
inference(copy,[status(thm)],[84]) ).
thf(453,plain,
subsetE = $true,
inference(copy,[status(thm)],[83]) ).
thf(454,plain,
emptysetsubset = $true,
inference(copy,[status(thm)],[82]) ).
thf(455,plain,
subsetI2 = $true,
inference(copy,[status(thm)],[81]) ).
thf(456,plain,
eqimpsubset1 = $true,
inference(copy,[status(thm)],[80]) ).
thf(457,plain,
eqimpsubset2 = $true,
inference(copy,[status(thm)],[79]) ).
thf(458,plain,
subsetI1 = $true,
inference(copy,[status(thm)],[78]) ).
thf(459,plain,
dsetconstr__Cong = $true,
inference(copy,[status(thm)],[77]) ).
thf(460,plain,
descr__Cong = $true,
inference(copy,[status(thm)],[76]) ).
thf(461,plain,
exuEu = $true,
inference(copy,[status(thm)],[75]) ).
thf(462,plain,
omega__Cong = $true,
inference(copy,[status(thm)],[74]) ).
thf(463,plain,
setunion__Cong = $true,
inference(copy,[status(thm)],[73]) ).
thf(464,plain,
powerset__Cong = $true,
inference(copy,[status(thm)],[72]) ).
thf(465,plain,
setadjoin__Cong = $true,
inference(copy,[status(thm)],[71]) ).
thf(466,plain,
emptyset__Cong = $true,
inference(copy,[status(thm)],[70]) ).
thf(467,plain,
exu__Cong = $true,
inference(copy,[status(thm)],[69]) ).
thf(468,plain,
exuE3u = $true,
inference(copy,[status(thm)],[68]) ).
thf(469,plain,
in__Cong = $true,
inference(copy,[status(thm)],[67]) ).
thf(470,plain,
inCongP = $true,
inference(copy,[status(thm)],[66]) ).
thf(471,plain,
exuI2 = $true,
inference(copy,[status(thm)],[65]) ).
thf(472,plain,
exuI3 = $true,
inference(copy,[status(thm)],[64]) ).
thf(473,plain,
exuI1 = $true,
inference(copy,[status(thm)],[63]) ).
thf(474,plain,
notdallE = $true,
inference(copy,[status(thm)],[62]) ).
thf(475,plain,
notdexE = $true,
inference(copy,[status(thm)],[61]) ).
thf(476,plain,
prop2set2propI = $true,
inference(copy,[status(thm)],[60]) ).
thf(477,plain,
prop2setI = $true,
inference(copy,[status(thm)],[59]) ).
thf(478,plain,
quantDeMorgan4 = $true,
inference(copy,[status(thm)],[58]) ).
thf(479,plain,
quantDeMorgan3 = $true,
inference(copy,[status(thm)],[57]) ).
thf(480,plain,
quantDeMorgan2 = $true,
inference(copy,[status(thm)],[56]) ).
thf(481,plain,
quantDeMorgan1 = $true,
inference(copy,[status(thm)],[55]) ).
thf(482,plain,
vacuousDall = $true,
inference(copy,[status(thm)],[54]) ).
thf(483,plain,
emptyE1 = $true,
inference(copy,[status(thm)],[53]) ).
thf(484,plain,
upairsetIR = $true,
inference(copy,[status(thm)],[52]) ).
thf(485,plain,
upairsetIL = $true,
inference(copy,[status(thm)],[51]) ).
thf(486,plain,
upairsetE = $true,
inference(copy,[status(thm)],[50]) ).
thf(487,plain,
singletonsswitch = $true,
inference(copy,[status(thm)],[49]) ).
thf(488,plain,
eqinunit = $true,
inference(copy,[status(thm)],[48]) ).
thf(489,plain,
notinsingleton = $true,
inference(copy,[status(thm)],[47]) ).
thf(490,plain,
uniqinunit = $true,
inference(copy,[status(thm)],[46]) ).
thf(491,plain,
nonemptyImpWitness = $true,
inference(copy,[status(thm)],[45]) ).
thf(492,plain,
exuE2 = $true,
inference(copy,[status(thm)],[44]) ).
thf(493,plain,
subPowSU = $true,
inference(copy,[status(thm)],[43]) ).
thf(494,plain,
setunionE = $true,
inference(copy,[status(thm)],[42]) ).
thf(495,plain,
setunionI = $true,
inference(copy,[status(thm)],[41]) ).
thf(496,plain,
powersetE = $true,
inference(copy,[status(thm)],[40]) ).
thf(497,plain,
emptyInPowerset = $true,
inference(copy,[status(thm)],[39]) ).
thf(498,plain,
emptyinPowerset = $true,
inference(copy,[status(thm)],[38]) ).
thf(499,plain,
powersetI = $true,
inference(copy,[status(thm)],[37]) ).
thf(500,plain,
setoftrueEq = $true,
inference(copy,[status(thm)],[36]) ).
thf(501,plain,
setadjoinOr = $true,
inference(copy,[status(thm)],[35]) ).
thf(502,plain,
setadjoinE = $true,
inference(copy,[status(thm)],[34]) ).
thf(503,plain,
setadjoinIR = $true,
inference(copy,[status(thm)],[33]) ).
thf(504,plain,
emptyinunitempty = $true,
inference(copy,[status(thm)],[32]) ).
thf(505,plain,
setadjoinIL = $true,
inference(copy,[status(thm)],[31]) ).
thf(506,plain,
nonemptyI1 = $true,
inference(copy,[status(thm)],[30]) ).
thf(507,plain,
nonemptyI = $true,
inference(copy,[status(thm)],[29]) ).
thf(508,plain,
nonemptyE1 = $true,
inference(copy,[status(thm)],[28]) ).
thf(509,plain,
setbeta = $true,
inference(copy,[status(thm)],[27]) ).
thf(510,plain,
noeltsimpempty = $true,
inference(copy,[status(thm)],[26]) ).
thf(511,plain,
emptyI = $true,
inference(copy,[status(thm)],[25]) ).
thf(512,plain,
setext = $true,
inference(copy,[status(thm)],[24]) ).
thf(513,plain,
exuE3e = $true,
inference(copy,[status(thm)],[23]) ).
thf(514,plain,
notinemptyset = $true,
inference(copy,[status(thm)],[22]) ).
thf(515,plain,
emptysetimpfalse = $true,
inference(copy,[status(thm)],[21]) ).
thf(516,plain,
emptysetE = $true,
inference(copy,[status(thm)],[20]) ).
thf(517,plain,
prop2setE = $true,
inference(copy,[status(thm)],[19]) ).
thf(518,plain,
exuE1 = $true,
inference(copy,[status(thm)],[18]) ).
thf(519,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[17]) ).
thf(520,plain,
dsetconstrEL = $true,
inference(copy,[status(thm)],[16]) ).
thf(521,plain,
dsetconstrI = $true,
inference(copy,[status(thm)],[15]) ).
thf(522,plain,
descrp = $true,
inference(copy,[status(thm)],[14]) ).
thf(523,plain,
wellorderingAx = $true,
inference(copy,[status(thm)],[13]) ).
thf(524,plain,
foundationAx = $true,
inference(copy,[status(thm)],[12]) ).
thf(525,plain,
replAx = $true,
inference(copy,[status(thm)],[11]) ).
thf(526,plain,
omegaIndAx = $true,
inference(copy,[status(thm)],[10]) ).
thf(527,plain,
omegaSAx = $true,
inference(copy,[status(thm)],[9]) ).
thf(528,plain,
omega0Ax = $true,
inference(copy,[status(thm)],[8]) ).
thf(529,plain,
setunionAx = $true,
inference(copy,[status(thm)],[7]) ).
thf(530,plain,
powersetAx = $true,
inference(copy,[status(thm)],[6]) ).
thf(531,plain,
setadjoinAx = $true,
inference(copy,[status(thm)],[5]) ).
thf(532,plain,
emptysetAx = $true,
inference(copy,[status(thm)],[4]) ).
thf(533,plain,
setextAx = $true,
inference(copy,[status(thm)],[3]) ).
thf(534,plain,
( ( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
& ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
& ( in @ sK4_SY5 @ sK1_A )
& ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
& ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(536,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(537,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(538,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(539,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(540,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(541,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(543,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(544,plain,
( ( omega = omega )
= $true ),
inference(unfold_def,[status(thm)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(545,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX1 @ SX3 )
| ~ ( in @ SX3 @ SX0 )
| SX2 )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(546,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[531,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(547,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(548,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(549,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| SX3 )
| ~ ( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(550,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX1 @ SX3 ) )
| ~ ( ~ ( SX1 @ SX3 )
| ( SX0 @ SX2 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(552,plain,
( ( ! [SX0: $i] : ( subset @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(553,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(554,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(555,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX1 @ ( powerset @ SX2 ) )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(557,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(558,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(559,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(560,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( subset
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(561,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(562,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(563,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( kpair @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(564,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( SX2 @ SX3 @ SX4 )
| ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(565,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(567,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(569,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ksnd @ ( kpair @ SX0 @ SX1 ) )
= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[361,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(570,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(572,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(574,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[423,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(575,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(576,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[281,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(578,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ ( binintersect @ ( binunion @ SX1 @ SX3 ) @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(579,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( ( ap @ SX0 @ SX1
@ ( lam @ SX0 @ SX1
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
@ SX3 )
= ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(580,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(581,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( SX0 @ SX2 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( SX0 @ SX2 @ SX4 )
| ( SX3 = SX4 ) ) ) )
| ~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX0 @ SX4 @ SX3 ) )
| ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(582,plain,
( ( ! [SX0: $i] : ( subset @ emptyset @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(583,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[515,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(586,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[402,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(587,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(588,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(590,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(593,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[489,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[520,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(597,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(unfold_def,[status(thm)],[528,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[428,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
| ( in @ SX4 @ ( binintersect @ ( binunion @ SX1 @ SX3 ) @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[478,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(601,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(602,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(603,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[532,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(604,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(605,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(609,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(612,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(614,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( subset @ SX1 @ SX2 )
| ~ ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(617,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(618,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[483,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] :
( ~ ( ~ SX1
| ( SX4 != SX2 ) )
| ~ ( ~ ~ SX1
| ( SX4 != SX3 ) ) ) )
= ( setadjoin @ SX2 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(624,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(625,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[517,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(626,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[518,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in
@ ( setunion
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
@ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(628,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(630,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[273,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kpair @ SX2 @ SX3 )
= ( kpair @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(635,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(636,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(637,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(638,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ ( setminus @ SX0 @ SX2 ) @ ( setminus @ SX0 @ SX1 ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
| ( in @ SX4 @ ( binunion @ SX1 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(640,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(641,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(642,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(643,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(644,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(645,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(646,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(647,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX4 @ ( binintersect @ SX1 @ SX2 ) )
| ( in @ SX4 @ ( binunion @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(648,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ ( setminus @ SX0 @ SX2 ) @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(649,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ( subset @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[280,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(650,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(651,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(652,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( SX1
= ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( in @ SX3
@ ( dsetconstr @ SX0
@ ^ [SX4: $i] :
( ~ ( ~ SX1
| ( SX4 != SX2 ) )
| ~ ( ~ ~ SX1
| ( SX4 != SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(654,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[480,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(655,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(656,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(658,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(659,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(660,plain,
( ( ! [SX0: $i] :
( ( setunion @ ( setadjoin @ SX0 @ emptyset ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(661,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(662,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(663,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(665,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(666,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(669,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(670,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(671,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( in
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(672,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(673,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(674,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ( SX4 != SX5 )
| ~ ( ~ ( ~ ( SX2 @ SX4 )
| ( SX3 @ SX5 ) )
| ~ ( ~ ( SX3 @ SX5 )
| ( SX2 @ SX4 ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(676,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(677,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(678,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(679,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[516,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( setminus @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(681,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[282,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(682,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[442,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(683,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(684,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
| ~ ( in @ SX3 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ( in @ SX1 @ ( powerset @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(688,plain,
( ( emptyset = emptyset )
= $true ),
inference(unfold_def,[status(thm)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(689,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( ( ap @ SX0 @ SX1
@ ( lam @ SX0 @ SX1
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
@ SX3 )
= ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(691,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ SX1
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] :
( ~ ( ~ SX1
| ( SX4 != SX2 ) )
| ~ ( ~ ~ SX1
| ( SX4 != SX3 ) ) ) )
= ( setadjoin @ SX3 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(693,plain,
( ( ! [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : $true )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[500,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(694,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( in @ SX4 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(695,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(696,plain,
( ( ! [SX0: $i] :
( ~ ~ ( ~ ( in @ emptyset @ SX0 )
| ~ ! [SX1: $i] :
( ~ ~ ( ~ ( in @ SX1 @ omega )
| ~ ( in @ SX1 @ SX0 ) )
| ( in @ ( setadjoin @ SX1 @ SX1 ) @ SX0 ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(697,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(698,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(699,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( in
@ ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) )
@ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(702,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( SX2 @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(704,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(707,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(711,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(713,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(715,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[514,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(717,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) )
= ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $o,SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ SX4 @ ( binunion @ SX1 @ SX2 ) )
| ~ ( ~ ( in @ SX4 @ SX1 )
| SX3 )
| ~ ( ~ ( in @ SX4 @ SX2 )
| SX3 )
| SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[271,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(720,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(722,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binintersect @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(723,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(724,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(725,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( binunion @ SX1 @ SX2 ) @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ ( ( SX2 != SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[502,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(734,plain,
( ( ! [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX3 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX4 )
| ( in @ SX3 @ SX4 ) )
| ~ ( ~ ( in @ SX3 @ SX4 )
| ( in @ SX2 @ SX4 ) ) ) )
| ( SX2 = SX3 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX3 @ SX1 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SX2: $i] :
( ~ ~ ( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX0 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SX1 )
| ~ ( in @ SX4 @ SX2 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SX2 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(736,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(738,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(739,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(740,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(741,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(743,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ! [SX1: $i,SX2: $i] :
( ~ ( SX0 @ SX1 )
| ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(744,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( kfst @ ( kpair @ SX0 @ SX1 ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[372,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(746,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(747,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( in @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(750,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( if @ SX0 @ SX1 @ SX2 @ SX3 ) @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( ( lam @ SX0 @ SX1
@ ^ [SX3: $i] : ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(752,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( singleton
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(756,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(757,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(758,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(759,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(760,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(761,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX2 != SX3 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(762,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 )
| ~ ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[270,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(763,plain,
( ( ~ ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(764,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(765,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( ( if @ SX0 @ SX1 @ SX2 @ SX3 )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(766,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ! [SX2: $i] :
~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX2 = SX1 ) )
| ~ ( ( SX2 != SX1 )
| ( SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(767,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( subset @ SX1 @ ( setminus @ SX0 @ SX2 ) )
| ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(768,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ SX1
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX4: $i] :
( ~ ( ~ SX1
| ( SX4 != SX2 ) )
| ~ ( ~ ~ SX1
| ( SX4 != SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( binintersect @ SX0 @ ( binunion @ SX1 @ SX2 ) )
= ( binunion @ ( binintersect @ SX0 @ SX1 ) @ ( binintersect @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(771,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $o] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| SX3 )
| SX3 ) )
= $true ),
inference(unfold_def,[status(thm)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(776,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( SX0 @ SX2 )
| ( SX1 @ SX3 ) )
| ~ ( ~ ( SX1 @ SX3 )
| ( SX0 @ SX2 ) ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX0 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[460,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(777,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(778,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(779,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( singleton
@ ( dsetconstr @ SX0
@ ^ [SX4: $i] :
( ~ ( ~ SX1
| ( SX4 != SX2 ) )
| ~ ( ~ ~ SX1
| ( SX4 != SX3 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(783,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(784,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[430,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(785,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( subset @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[326,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(787,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[433,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(788,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) )
| ~ ( in @ SX3 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[279,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(789,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(790,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(791,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(793,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(796,plain,
( ( ! [SX0: $i] : ( in @ SX0 @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(799,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( kpair @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(800,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ~ ( subset @ SY7 @ ( cartprod @ SV1 @ SY6 ) )
| ! [SY8: $i > $o] :
( ~ ! [SY9: $i] :
( ~ ( in @ SY9 @ SV1 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY6 )
| ~ ( in @ ( kpair @ SY9 @ SX5 ) @ SY7 )
| ( SY8 @ ( kpair @ SY9 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY7 )
| ( SY8 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(801,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
( ( SV2 != SY12 )
| ! [SY13: $i,SY14: $i] :
( ( SY13 != SY14 )
| ~ ( ~ ( ~ ( in @ SY13 @ SV2 )
| ( in @ SY14 @ SY12 ) )
| ~ ( ~ ( in @ SY14 @ SY12 )
| ( in @ SY13 @ SV2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(802,plain,
! [SV3: $i] :
( ( ! [SY15: $i] :
( ~ ( in @ SY15 @ ( powerset @ SV3 ) )
| ( subset @ ( setminus @ SV3 @ ( setminus @ SV3 @ SY15 ) ) @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(803,plain,
! [SV4: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( in @ SY17 @ ( setadjoin @ SV4 @ ( setadjoin @ SY16 @ emptyset ) ) )
| ( SY17 = SV4 )
| ( SY17 = SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(804,plain,
! [SV5: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( subset @ SY19 @ ( cartprod @ SV5 @ SY18 ) )
| ! [SY20: $i] :
( ~ ( subset @ SY20 @ ( cartprod @ SV5 @ SY18 ) )
| ~ ! [SY21: $i] :
( ~ ( in @ SY21 @ SV5 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY18 )
| ~ ( in @ ( kpair @ SY21 @ SX5 ) @ SY19 )
| ( in @ ( kpair @ SY21 @ SX5 ) @ SY20 ) ) )
| ~ ! [SY23: $i] :
( ~ ( in @ SY23 @ SV5 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY18 )
| ~ ( in @ ( kpair @ SY23 @ SX5 ) @ SY20 )
| ( in @ ( kpair @ SY23 @ SX5 ) @ SY19 ) ) )
| ( SY19 = SY20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(805,plain,
! [SV6: $i] :
( ( ~ ! [SY25: $i] :
~ ( in @ SY25 @ SV6 )
| ( SV6 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(806,plain,
! [SV7: $i] :
( ( ~ ( singleton @ SV7 )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV7 )
| ( ( setunion @ SV7 )
= SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(807,plain,
! [SV8: $i] :
( ( ! [SY27: $i] :
( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ SV8 )
| ( in @ SY28 @ SY27 ) )
| ( subset @ SV8 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(808,plain,
! [SV9: $i] :
( ( ~ ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 )
| ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(809,plain,
! [SV10: $i] :
( ( ! [SY32: $i] :
( ~ ( in @ SY32 @ ( setunion @ SV10 ) )
| ! [SY33: $o] :
( ~ ! [SY34: $i] :
( ~ ( in @ SY32 @ SY34 )
| ~ ( in @ SY34 @ SV10 )
| SY33 )
| SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(810,plain,
! [SV11: $i] :
( ( ! [SY35: $i,SY36: $i] :
~ ( ~ ( ~ ( in @ SY36 @ ( setadjoin @ SV11 @ SY35 ) )
| ( SY36 = SV11 )
| ( in @ SY36 @ SY35 ) )
| ~ ( ~ ( ( SY36 = SV11 )
| ( in @ SY36 @ SY35 ) )
| ( in @ SY36 @ ( setadjoin @ SV11 @ SY35 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(811,plain,
! [SV12: $i > $o] :
( ( ~ ~ ! [SY37: $i] :
~ ! [SY38: $i] :
~ ( ~ ( ~ ( SV12 @ SY38 )
| ( SY38 = SY37 ) )
| ~ ( ( SY38 != SY37 )
| ( SV12 @ SY38 ) ) )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(812,plain,
! [SV13: $i > $o] :
( ( ~ ~ ! [SY41: $i] :
~ ( SV13 @ SY41 )
| ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(813,plain,
! [SV14: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( in @ SY47 @ ( symdiff @ SV14 @ SY46 ) )
| ! [SY48: $o] :
( ~ ( ~ ( in @ SY47 @ SV14 )
| ~ ~ ( in @ SY47 @ SY46 )
| SY48 )
| ~ ( ~ ~ ( in @ SY47 @ SV14 )
| ~ ( in @ SY47 @ SY46 )
| SY48 )
| SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(814,plain,
! [SV15: $i > $o] :
( ( ! [SY49: $i > $o] :
( ~ ! [SY50: $i,SY51: $i] :
( ( SY50 != SY51 )
| ~ ( ~ ( ~ ( SV15 @ SY50 )
| ( SY49 @ SY51 ) )
| ~ ( ~ ( SY49 @ SY51 )
| ( SV15 @ SY50 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY49 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY49 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY49 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY49 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(815,plain,
! [SV16: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ~ ~ ( in @ SY61 @ SV16 )
| ~ ( in @ SY61 @ ( setminus @ SV16 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(816,plain,
! [SV17: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV17 @ emptyset ) ) @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(817,plain,
! [SV18: $i] :
( ( ~ ( in @ SV18 @ omega )
| ( in @ ( setadjoin @ SV18 @ SV18 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(818,plain,
! [SV19: $i > $o] :
( ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ( SV19 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( SV19 @ SY63 )
| ( SY62 = SY63 ) ) )
| ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(819,plain,
! [SV20: $i] :
( ( ! [SY66: $i] :
( ~ ~ ( subset @ SV20 @ SY66 )
| ( SV20 != SY66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(820,plain,
! [SV21: $i] :
( ( ! [SY67: $i] :
( ~ ( in @ SY67 @ ( powerset @ SV21 ) )
| ! [SY68: $i] :
( ~ ( in @ SY68 @ ( powerset @ SV21 ) )
| ! [SY69: $i] :
( ~ ( in @ SY69 @ SV21 )
| ~ ( in @ SY67 @ ( powerset @ SY68 ) )
| ~ ( in @ SY69 @ SY67 )
| ( in @ SY69 @ SY68 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(821,plain,
! [SV22: $i] :
( ( ! [SY70: $i,SY71: $i] :
( ~ ~ ( in @ SY71 @ ( setminus @ SV22 @ SY70 ) )
| ~ ~ ( in @ SY71 @ SY70 )
| ~ ( in @ SY71 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(822,plain,
! [SV23: $i] :
( ( ! [SY72: $i] :
( ~ ( in @ SY72 @ SV23 )
| ( subset @ ( setadjoin @ SY72 @ emptyset ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(823,plain,
! [SV24: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ~ ( in @ SY74 @ ( funcSet @ SV24 @ SY73 ) )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV24 )
| ( in @ ( ap @ SV24 @ SY73 @ SY74 @ SY75 ) @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(824,plain,
! [SV25: $i] :
( ( ! [SY76: $i > $o] :
( subset
@ ( dsetconstr @ SV25
@ ^ [SX2: $i] : ( SY76 @ SX2 ) )
@ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(825,plain,
! [SV26: $i] :
( ( ! [SY78: $i,SY79: $i,SY80: $i] :
( ( ( kpair @ SV26 @ SY78 )
!= ( kpair @ SY79 @ SY80 ) )
| ( SV26 = SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(826,plain,
! [SV27: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i] :
( ~ ( in @ ( kpair @ SY82 @ SY83 ) @ ( cartprod @ SV27 @ SY81 ) )
| ( in @ SY82 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(827,plain,
! [SV28: $i] :
( ( ! [SY84: $i] : ( iskpair @ ( kpair @ SV28 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(828,plain,
! [SV29: $i] :
( ( ! [SY85: $i,SY86: $i > $i > $o,SY87: $i] :
( ~ ( in @ SY87 @ SV29 )
| ! [SY88: $i] :
( ~ ( in @ SY88 @ SY85 )
| ~ ( SY86 @ SY87 @ SY88 )
| ( in @ ( kpair @ SY87 @ SY88 )
@ ( dpsetconstr @ SV29 @ SY85
@ ^ [SX5: $i,SX6: $i] : ( SY86 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(829,plain,
! [SV30: $i] :
( ( ! [SY91: $i,SY92: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV30 @ SY91
@ ^ [SX3: $i,SX4: $i] : ( SY92 @ SX3 @ SX4 ) )
@ ( cartprod @ SV30 @ SY91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(830,plain,
! [SV31: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( in @ SY96 @ ( funcSet @ SV31 @ SY95 ) )
| ! [SY97: $i] :
( ~ ( in @ SY97 @ SV31 )
| ! [SY98: $i] :
( ~ ( in @ SY98 @ SY95 )
| ~ ( in @ ( kpair @ SY97 @ SY98 ) @ SY96 )
| ( ( ap @ SV31 @ SY95 @ SY96 @ SY97 )
= SY98 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(831,plain,
! [SV32: $i] :
( ( ! [SY99: $i] :
( ( SV32 != SY99 )
| ( ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV32 @ ( setadjoin @ SY99 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(832,plain,
! [SV33: $i] :
( ( ! [SY100: $i,SY101: $i] :
( ~ ( in @ SY101 @ ( setadjoin @ SV33 @ SY100 ) )
| ( SY101 = SV33 )
| ( in @ SY101 @ SY100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(833,plain,
! [SV34: $i] :
( ( ! [SY102: $i] :
( ( ksnd @ ( kpair @ SV34 @ SY102 ) )
= SY102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(834,plain,
! [SV35: $i] :
( ( ! [SY103: $o,SY104: $i] :
( ~ ( in @ SY104 @ SV35 )
| ! [SY105: $i] :
( ~ ( in @ SY105 @ SV35 )
| ~ ~ SY103
| ( ( if @ SV35 @ SY103 @ SY104 @ SY105 )
= SY105 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(835,plain,
! [SV36: $i] :
( ( ! [SY106: $i,SY107: $i > $i] :
( ~ ! [SY108: $i] :
( ~ ( in @ SY108 @ SV36 )
| ( in @ ( SY107 @ SY108 ) @ SY106 ) )
| ( func @ SV36 @ SY106
@ ( lam @ SV36 @ SY106
@ ^ [SX3: $i] : ( SY107 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(836,plain,
! [SV37: $i] :
( ( ! [SY110: $i,SY111: $i] :
( ~ ( in @ SY111 @ SV37 )
| ( in @ ( setadjoin @ SY111 @ emptyset ) @ ( powerset @ ( binunion @ SV37 @ SY110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(837,plain,
! [SV38: $i] :
( ( ! [SY112: $i] :
( ~ ( subset @ SV38 @ SY112 )
| ( ( binintersect @ SV38 @ SY112 )
= SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(838,plain,
! [SV39: $i] :
( ( ! [SY113: $i] :
( ( ( binintersect @ SV39 @ SY113 )
!= SY113 )
| ( subset @ SY113 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(839,plain,
! [SV40: $i] :
( ( ! [SY114: $i] :
( ~ ( subset @ SV40 @ SY114 )
| ( ( setminus @ SV40 @ SY114 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(840,plain,
! [SV41: $i] :
( ( ! [SY115: $i] :
( ~ ( in @ SY115 @ ( powerset @ SV41 ) )
| ! [SY116: $i] :
( ~ ( in @ SY116 @ ( powerset @ SV41 ) )
| ~ ( subset @ SY115 @ ( setminus @ SV41 @ SY116 ) )
| ! [SY117: $i] :
( ~ ( in @ SY117 @ SV41 )
| ~ ( in @ SY117 @ SY116 )
| ( in @ SY117 @ ( setminus @ SV41 @ SY115 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(841,plain,
! [SV42: $i] :
( ( ! [SY118: $i] :
( ( ( binintersect @ SV42 @ SY118 )
!= SV42 )
| ( subset @ SV42 @ SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(842,plain,
! [SV43: $i] :
( ( ! [SY119: $i] :
( ~ ( in @ SY119 @ ( powerset @ SV43 ) )
| ! [SY120: $i] :
( ~ ( in @ SY120 @ ( powerset @ SV43 ) )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SY119 @ SY120 ) @ ( powerset @ ( binintersect @ ( binunion @ SY119 @ SY121 ) @ ( binunion @ SY120 @ SY121 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(843,plain,
! [SV44: $i] :
( ( ! [SY122: $i,SY123: $i > $i] :
( ~ ! [SY124: $i] :
( ~ ( in @ SY124 @ SV44 )
| ( in @ ( SY123 @ SY124 ) @ SY122 ) )
| ! [SY125: $i] :
( ~ ( in @ SY125 @ SV44 )
| ( ( ap @ SV44 @ SY122
@ ( lam @ SV44 @ SY122
@ ^ [SX4: $i] : ( SY123 @ SX4 ) )
@ SY125 )
= ( SY123 @ SY125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(844,plain,
! [SV45: $i] :
( ( ! [SY127: $i,SY128: $i] :
( ~ ( in @ SY128 @ SV45 )
| ~ ~ ( in @ SY128 @ SY127 )
| ( in @ SY128 @ ( symdiff @ SV45 @ SY127 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(845,plain,
! [SV46: $i > $i > $o] :
( ( ! [SY129: $i] :
( ~ ! [SY130: $i] :
( ~ ( in @ SY130 @ SY129 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( SV46 @ SY130 @ SY131 )
| ~ ! [SY132: $i] :
( ~ ( SV46 @ SY130 @ SY132 )
| ( SY131 = SY132 ) ) ) )
| ~ ! [SY133: $i] :
~ ! [SY134: $i] :
~ ( ~ ( ~ ( in @ SY134 @ SY133 )
| ~ ! [SY135: $i] :
~ ~ ( ~ ( in @ SY135 @ SY129 )
| ~ ( SV46 @ SY135 @ SY134 ) ) )
| ~ ( ~ ~ ! [SY136: $i] :
~ ~ ( ~ ( in @ SY136 @ SY129 )
| ~ ( SV46 @ SY136 @ SY134 ) )
| ( in @ SY134 @ SY133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(846,plain,
! [SV47: $i] :
( ( subset @ emptyset @ SV47 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(847,plain,
! [SV48: $i] :
( ( ~ ( in @ SV48 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(848,plain,
! [SV49: $i] :
( ( ! [SY137: $i,SY138: $i] :
( ~ ( in @ SY138 @ SV49 )
| ( in @ SY138 @ ( binunion @ SV49 @ SY137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(849,plain,
! [SV50: $i] :
( ( ! [SY139: $i] :
( ~ ( in @ SY139 @ ( powerset @ SV50 ) )
| ! [SY140: $i] :
( ~ ( in @ SY140 @ ( powerset @ SV50 ) )
| ! [SY141: $i] :
( ~ ( in @ SY141 @ SV50 )
| ~ ~ ( in @ SY141 @ SY139 )
| ~ ( in @ SY141 @ ( binintersect @ SY139 @ SY140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(850,plain,
! [SV51: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ~ ( in @ SY143 @ SV51 )
| ~ ~ ( in @ SY143 @ SY142 )
| ~ ( in @ SY143 @ ( symdiff @ SV51 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(851,plain,
! [SV52: $i] :
( ( ~ ~ ! [SY144: $i] :
~ ( in @ SY144 @ SV52 )
| ( SV52 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(852,plain,
! [SV53: $i] :
( ( subset @ SV53 @ SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(853,plain,
! [SV54: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( func @ SV54 @ SY145 @ SY146 )
| ! [SY147: $i] :
( ~ ( in @ SY147 @ SV54 )
| ( in @ ( ap @ SV54 @ SY145 @ SY146 @ SY147 ) @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(854,plain,
! [SV55: $i] :
( ( ! [SY148: $i > $o] :
( ~ ~ ~ ! [SY149: $i] :
~ ~ ( ~ ( in @ SY149 @ SV55 )
| ~ ( SY148 @ SY149 ) )
| ! [SY150: $i] :
( ~ ( in @ SY150 @ SV55 )
| ~ ( SY148 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(855,plain,
! [SV56: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( in @ SY152 @ ( binunion @ SV56 @ SY151 ) )
| ( in @ SY152 @ SV56 )
| ( in @ SY152 @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(856,plain,
! [SV57: $i] :
( ( ! [SY153: $i,SY154: $i] :
( ~ ( in @ SY154 @ ( binintersect @ SV57 @ SY153 ) )
| ( in @ SY154 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(857,plain,
! [SV58: $i] :
( ( ! [SY155: $i] :
( ~ ( ( SV58 != SY155 ) )
| ~ ( in @ SY155 @ ( setadjoin @ SV58 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(858,plain,
! [SV59: $i] :
( ( ! [SY156: $i > $o,SY157: $i] :
( ~ ( in @ SY157
@ ( dsetconstr @ SV59
@ ^ [SX3: $i] : ( SY156 @ SX3 ) ) )
| ( in @ SY157 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(859,plain,
! [SV60: $i] :
( ( ! [SY159: $i,SY160: $i] :
( ~ ( in @ SY160 @ ( setminus @ SV60 @ SY159 ) )
| ~ ( in @ SY160 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(860,plain,
! [SV61: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ~ ( in @ SY162 @ SV61 )
| ~ ( in @ SY162 @ SY161 )
| ( in @ SY162 @ ( binintersect @ SV61 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(861,plain,
! [SV62: $i] :
( ( ! [SY163: $i] :
( ~ ( in @ SY163 @ ( powerset @ SV62 ) )
| ! [SY164: $i] :
( ~ ( in @ SY164 @ ( powerset @ SV62 ) )
| ! [SY165: $i] :
( ~ ( in @ SY165 @ ( powerset @ SV62 ) )
| ! [SY166: $i] :
( ~ ( in @ SY166 @ SV62 )
| ~ ( in @ SY166 @ ( binintersect @ SY163 @ SY164 ) )
| ( in @ SY166 @ ( binintersect @ ( binunion @ SY163 @ SY165 ) @ ( binunion @ SY164 @ SY165 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(862,plain,
! [SV63: $i] :
( ( ! [SY167: $i > $o] :
( ~ ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV63 )
| ~ ~ ( SY167 @ SY168 ) )
| ~ ! [SY169: $i] :
( ~ ( in @ SY169 @ SV63 )
| ( SY167 @ SY169 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(863,plain,
! [SV64: $o] :
( ( ~ SV64
| ( in @ emptyset @ ( prop2set @ SV64 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(864,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(865,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[601]) ).
thf(866,plain,
! [SV65: $i] :
( ( ~ ( ( SV65 != emptyset ) )
| ~ ! [SY170: $i] :
~ ( in @ SY170 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(867,plain,
! [SV66: $i] :
( ( ~ ( in @ SV66 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(868,plain,
! [SV67: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ( subset @ SV67 @ SY171 )
| ~ ~ ( in @ SY172 @ SY171 )
| ~ ( in @ SY172 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(869,plain,
! [SV68: $i] :
( ( ! [SY173: $i] :
( ~ ( in @ SY173 @ ( powerset @ SV68 ) )
| ! [SY174: $i] :
( ~ ( in @ SY174 @ ( powerset @ SV68 ) )
| ~ ! [SY175: $i] :
( ~ ( in @ SY175 @ SV68 )
| ~ ( in @ SY175 @ SY173 )
| ( in @ SY175 @ SY174 ) )
| ( subset @ SY173 @ SY174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(870,plain,
! [SV69: $i] :
( ( ! [SY176: $i] :
( ( SV69 != SY176 )
| ( ( powerset @ SV69 )
= ( powerset @ SY176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(871,plain,
! [SV70: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( func @ SV70 @ SY177 @ SY178 )
| ( in @ SY178 @ ( funcSet @ SV70 @ SY177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(872,plain,
! [SV71: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ( ( kpair @ SV71 @ SY179 )
!= ( kpair @ SY180 @ SY181 ) )
| ( SY179 = SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(873,plain,
! [SV72: $i] :
( ( ! [SY182: $i,SY183: $i] :
( ~ ( subset @ SV72 @ SY182 )
| ~ ( subset @ SY182 @ SY183 )
| ( subset @ SV72 @ SY183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(874,plain,
! [SV73: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( in @ SY185 @ ( funcSet @ SV73 @ SY184 ) )
| ! [SY186: $i] :
( ~ ( in @ SY186 @ SV73 )
| ( ( ap @ SV73 @ SY184 @ SY185 @ SY186 )
= ( ap @ SV73 @ SY184 @ SY185 @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(875,plain,
! [SV74: $i] :
( ( ! [SY187: $i] :
( ~ ! [SY188: $i] :
~ ( ~ ( ~ ( in @ SY188 @ SV74 )
| ( in @ SY188 @ SY187 ) )
| ~ ( ~ ( in @ SY188 @ SY187 )
| ( in @ SY188 @ SV74 ) ) )
| ( SV74 = SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(876,plain,
! [SV75: $i] :
( ( ! [SY189: $i] :
( ( SV75 != SY189 )
| ( ( setadjoin @ SV75 @ ( setadjoin @ SY189 @ emptyset ) )
= ( setadjoin @ SV75 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(877,plain,
! [SV76: $i] :
( ( ! [SY190: $i > $o] :
( ~ ! [SY191: $i] :
( ~ ( in @ SY191 @ SV76 )
| ! [SY192: $i] :
( ~ ( in @ SY192 @ SV76 )
| ~ ( SY190 @ SY191 )
| ~ ( SY190 @ SY192 )
| ( SY191 = SY192 ) ) )
| ~ ~ ! [SY193: $i] :
~ ~ ( ~ ( in @ SY193 @ SV76 )
| ~ ( SY190 @ SY193 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SX2: $i] : ( SY190 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(878,plain,
! [SV77: $i] :
( ( ! [SY195: $i] :
( ~ ( in @ SY195 @ ( powerset @ SV77 ) )
| ! [SY196: $i] :
( ~ ( in @ SY196 @ ( powerset @ SV77 ) )
| ! [SY197: $i] :
( ~ ( in @ SY197 @ SV77 )
| ~ ( subset @ SY195 @ SY196 )
| ~ ~ ( in @ SY197 @ SY196 )
| ~ ( in @ SY197 @ SY195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(879,plain,
! [SV78: $i] :
( ( ! [SY198: $i] : ( in @ SV78 @ ( setadjoin @ SV78 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(880,plain,
! [SV79: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( in @ SY199 @ SY200 )
| ~ ( in @ SY200 @ SV79 )
| ( in @ SY199 @ ( setunion @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(881,plain,
! [SV80: $i] :
( ( ~ ( iskpair @ SV80 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV80 )
@ ^ [SY201: $i] : ( in @ ( setadjoin @ SY201 @ emptyset ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(882,plain,
! [SV81: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ~ ( in @ SY203 @ ( funcSet @ SV81 @ SY202 ) )
| ( func @ SV81 @ SY202 @ SY203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(883,plain,
! [SV82: $i] :
( ( ! [SY204: $i] :
~ ( ~ ( ~ ( in @ SY204 @ ( powerset @ SV82 ) )
| ! [SY205: $i] :
( ~ ( in @ SY205 @ SY204 )
| ( in @ SY205 @ SV82 ) ) )
| ~ ( ~ ! [SY206: $i] :
( ~ ( in @ SY206 @ SY204 )
| ( in @ SY206 @ SV82 ) )
| ( in @ SY204 @ ( powerset @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(884,plain,
! [SV83: $i] :
( ( ! [SY207: $i > $o] :
( ~ ~ ! [SY208: $i] :
~ ~ ( ~ ( in @ SY208 @ SV83 )
| ~ ( SY207 @ SY208 ) )
| ( ( dsetconstr @ SV83
@ ^ [SX2: $i] : ( SY207 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(885,plain,
! [SV84: $i] :
( ( ! [SY210: $o,SY211: $i] :
( ~ ( in @ SY211 @ SV84 )
| ! [SY212: $i] :
( ~ ( in @ SY212 @ SV84 )
| ~ SY210
| ( ( dsetconstr @ SV84
@ ^ [SX4: $i] :
( ~ ( ~ SY210
| ( SX4 != SY211 ) )
| ~ ( ~ ~ SY210
| ( SX4 != SY212 ) ) ) )
= ( setadjoin @ SY211 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(886,plain,
! [SV85: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ( in @ SY215 @ SV85 )
| ! [SY216: $i] :
( ~ ( in @ SY216 @ SY214 )
| ( in @ ( kpair @ SY215 @ SY216 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SY214 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(887,plain,
! [SV86: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( func @ SV86 @ SY217 @ SY218 )
| ! [SY219: $i] :
( ~ ( in @ SY219 @ SV86 )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SY217 )
| ~ ( in @ ( kpair @ SY219 @ SY220 ) @ SY218 )
| ( ( ap @ SV86 @ SY217 @ SY218 @ SY219 )
= SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(888,plain,
! [SV87: $i] :
( ( ! [SY221: $i] :
( ( SV87 != SY221 )
| ( subset @ SY221 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(889,plain,
! [SV88: $o] :
( ( ! [SY222: $i] :
( ~ ( in @ SY222 @ ( prop2set @ SV88 ) )
| SV88 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[625]) ).
thf(890,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[625]) ).
thf(891,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[625]) ).
thf(892,plain,
! [SV89: $i > $o] :
( ( ~ ~ ! [SY223: $i] :
~ ~ ( ~ ( SV89 @ SY223 )
| ~ ! [SY224: $i] :
( ~ ( SV89 @ SY224 )
| ( SY223 = SY224 ) ) )
| ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(893,plain,
! [SV90: $i] :
( ( ! [SY227: $i,SY228: $i] :
( ~ ( func @ SV90 @ SY227 @ SY228 )
| ! [SY229: $i] :
( ~ ( in @ SY229 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY227
@ ^ [SX4: $i] : ( in @ ( kpair @ SY229 @ SX4 ) @ SY228 ) ) )
@ SY227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(894,plain,
! [SV91: $i] :
( ( ! [SY231: $i] : ( subset @ ( binintersect @ SV91 @ SY231 ) @ SY231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(895,plain,
! [SV92: $i] :
( ( ! [SY232: $i > $o,SY233: $i] :
( ~ ( in @ SY233 @ SV92 )
| ~ ( SY232 @ SY233 )
| ( ( dsetconstr @ SV92
@ ^ [SX3: $i] : ( SY232 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(896,plain,
! [SV93: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( in @ SY236 @ ( setminus @ SV93 @ SY235 ) )
| ( in @ SY236 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(897,plain,
! [SV94: $i] :
( ( ! [SY237: $i] :
( ( ( setminus @ SV94 @ SY237 )
!= emptyset )
| ( subset @ SV94 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(898,plain,
! [SV95: $i] :
( ( ! [SY238: $i > $o,SY239: $i] :
( ~ ( in @ SY239 @ SV95 )
| ~ ( ~ ( ~ ( in @ SY239
@ ( dsetconstr @ SV95
@ ^ [SX3: $i] : ( SY238 @ SX3 ) ) )
| ( SY238 @ SY239 ) )
| ~ ( ~ ( SY238 @ SY239 )
| ( in @ SY239
@ ( dsetconstr @ SV95
@ ^ [SX3: $i] : ( SY238 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(899,plain,
! [SV96: $i] :
( ( ! [SY242: $i] :
( ~ ( in @ SY242 @ ( powerset @ SV96 ) )
| ! [SY243: $i] :
( ~ ( in @ SY243 @ ( powerset @ SV96 ) )
| ! [SY244: $i] :
( ~ ( in @ SY244 @ SV96 )
| ~ ( in @ SY244 @ ( setminus @ SV96 @ ( binunion @ SY242 @ SY243 ) ) )
| ~ ( in @ SY244 @ SY242 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(900,plain,
! [SV97: $i] :
( ( ! [SY245: $i,SY246: $i] :
( ~ ( in @ SY246 @ SV97 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY245 )
| ( ( kpair @ SY246 @ SX3 )
= ( kpair @ SY246 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(901,plain,
! [SV98: $i] :
( ( ! [SY248: $i] :
( ~ ( in @ SY248 @ ( powerset @ SV98 ) )
| ( in @ ( setminus @ SV98 @ SY248 ) @ ( powerset @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(902,plain,
! [SV99: $o] :
( ( ~ SV99
| ( set2prop @ ( prop2set @ SV99 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[636]) ).
thf(903,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[636]) ).
thf(904,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[636]) ).
thf(905,plain,
! [SV100: $i] :
( ( ! [SY249: $i] :
( ( SV100 != SY249 )
| ! [SY250: $i,SY251: $i] :
( ( SY250 != SY251 )
| ~ ( in @ SY250 @ SV100 )
| ( in @ SY251 @ SY249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(906,plain,
! [SV101: $i] :
( ( ! [SY252: $i] :
( ~ ( in @ SY252 @ ( powerset @ SV101 ) )
| ! [SY253: $i] :
( ~ ( in @ SY253 @ ( powerset @ SV101 ) )
| ~ ( subset @ ( setminus @ SV101 @ SY253 ) @ ( setminus @ SV101 @ SY252 ) )
| ( subset @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(907,plain,
! [SV102: $i] :
( ( ! [SY254: $i] :
( ~ ( in @ SY254 @ ( powerset @ SV102 ) )
| ! [SY255: $i] :
( ~ ( in @ SY255 @ ( powerset @ SV102 ) )
| ! [SY256: $i] :
( ~ ( in @ SY256 @ ( powerset @ SV102 ) )
| ! [SY257: $i] :
( ~ ( in @ SY257 @ SV102 )
| ~ ( in @ SY257 @ ( binintersect @ SY254 @ SY255 ) )
| ( in @ SY257 @ ( binunion @ SY254 @ SY256 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(908,plain,
! [SV103: $i] :
( ( ! [SY258: $i] : ( subset @ SY258 @ ( setadjoin @ SV103 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(909,plain,
! [SV104: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( func @ SV104 @ SY259 @ SY260 )
| ! [SY261: $i] :
( ~ ( in @ SY261 @ SV104 )
| ( in @ ( kpair @ SY261 @ ( ap @ SV104 @ SY259 @ SY260 @ SY261 ) ) @ SY260 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(910,plain,
! [SV105: $i] :
( ( ~ ( ( SV105 != emptyset ) )
| ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV105 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(911,plain,
! [SV106: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( in @ SY264 @ ( cartprod @ SV106 @ SY263 ) )
| ( in @ ( kfst @ SY264 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(912,plain,
! [SV107: $i] :
( ( in @ emptyset @ ( powerset @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(913,plain,
! [SV108: $i] :
( ( ! [SY265: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV108 @ ( setadjoin @ SY265 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(914,plain,
! [SV109: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( in @ SY267 @ SV109 )
| ! [SY268: $i] :
( ~ ( in @ SY268 @ SY266 )
| ( in @ ( kpair @ SY267 @ SY268 ) @ ( cartprod @ SV109 @ SY266 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(915,plain,
! [SV110: $i] :
( ( ! [SY269: $i] :
( ~ ( in @ SY269 @ ( powerset @ SV110 ) )
| ! [SY270: $i] :
( ~ ( in @ SY270 @ ( powerset @ SV110 ) )
| ! [SY271: $i] :
( ~ ( in @ SY271 @ ( powerset @ SV110 ) )
| ! [SY272: $i] :
( ~ ( in @ SY272 @ SV110 )
| ~ ( in @ SY272 @ ( binintersect @ SY269 @ SY270 ) )
| ( in @ SY272 @ ( binunion @ SY270 @ SY271 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(916,plain,
! [SV111: $i] :
( ( ! [SY273: $i] :
( ~ ( in @ SY273 @ ( powerset @ SV111 ) )
| ! [SY274: $i] :
( ~ ( in @ SY274 @ ( powerset @ SV111 ) )
| ~ ( subset @ SY273 @ SY274 )
| ( subset @ ( setminus @ SV111 @ SY274 ) @ ( setminus @ SV111 @ SY273 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(917,plain,
! [SV112: $i] :
( ( ! [SY275: $i] :
( ~ ( in @ SY275 @ ( powerset @ SV112 ) )
| ! [SY276: $i] :
( ~ ( in @ SY276 @ ( powerset @ SV112 ) )
| ~ ( subset @ SY275 @ ( setminus @ SV112 @ SY276 ) )
| ( subset @ SY276 @ ( setminus @ SV112 @ SY275 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(918,plain,
! [SV113: $i] :
( ( ! [SY277: $i] :
( ~ ! [SY278: $i] :
( ~ ( in @ SY278 @ SV113 )
| ( in @ SY278 @ SY277 ) )
| ( subset @ SV113 @ SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(919,plain,
! [SV114: $i] :
( ( ! [SY279: $i,SY280: $i] :
( ~ ( in @ SY280 @ SV114 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY279 )
| ( ( kfst @ ( kpair @ SY280 @ SX3 ) )
= SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(920,plain,
! [SV115: $i] :
( ( ! [SY282: $i] :
( ~ ( in @ SY282 @ ( powerset @ SV115 ) )
| ( SY282
= ( setminus @ SV115 @ ( setminus @ SV115 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(921,plain,
! [SV116: $i] :
( ( ! [SY283: $o,SY284: $i] :
( ~ ( in @ SY284 @ SV116 )
| ! [SY285: $i] :
( ~ ( in @ SY285 @ SV116 )
| ~ ~ SY283
| ( in @ SY285
@ ( dsetconstr @ SV116
@ ^ [SX4: $i] :
( ~ ( ~ SY283
| ( SX4 != SY284 ) )
| ~ ( ~ ~ SY283
| ( SX4 != SY285 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(922,plain,
! [SV117: $i] :
( ( ! [SY287: $i > $o] :
( ~ ! [SY288: $i] :
( ~ ( in @ SY288 @ SV117 )
| ~ ( SY287 @ SY288 ) )
| ~ ~ ! [SY289: $i] :
~ ~ ( ~ ( in @ SY289 @ SV117 )
| ~ ( SY287 @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(923,plain,
! [SV118: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ~ ( func @ SV118 @ SY290 @ SY291 )
| ! [SY292: $i] :
( ~ ( func @ SV118 @ SY290 @ SY292 )
| ~ ! [SY293: $i] :
( ~ ( in @ SY293 @ SV118 )
| ( ( ap @ SV118 @ SY290 @ SY291 @ SY293 )
= ( ap @ SV118 @ SY290 @ SY292 @ SY293 ) ) )
| ! [SY294: $i] :
( ~ ( in @ SY294 @ SV118 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY290 )
| ~ ( in @ ( kpair @ SY294 @ SX5 ) @ SY292 )
| ( in @ ( kpair @ SY294 @ SX5 ) @ SY291 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(924,plain,
! [SV119: $i] :
( ( ! [SY296: $i] :
( ~ ( in @ SV119 @ ( setadjoin @ SY296 @ emptyset ) )
| ( SV119 = SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(925,plain,
! [SV120: $i] :
( ( ! [SY297: $i] :
( ~ ( in @ SY297 @ ( powerset @ SV120 ) )
| ! [SY298: $i] :
( ~ ( in @ SY298 @ SV120 )
| ~ ( in @ SY298 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SY297 ) ) )
| ( in @ SY298 @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(926,plain,
! [SV121: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( in @ SY300 @ SV121 )
| ! [SY301: $i] :
( ~ ( in @ SY301 @ SY299 )
| ( in @ ( setadjoin @ ( setadjoin @ SY300 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY300 @ ( setadjoin @ SY301 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SY299 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(927,plain,
! [SV122: $i] :
( ( ~ ! [SY302: $i] :
~ ( in @ SY302 @ SV122 )
| ( SV122 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(928,plain,
! [SV123: $i] :
( ( ( setunion @ ( setadjoin @ SV123 @ emptyset ) )
= SV123 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(929,plain,
! [SV124: $i] :
( ( ! [SY303: $i] :
( ~ ! [SY304: $i] :
( ~ ( in @ SY304 @ SY303 )
| ( in @ SY304 @ SV124 ) )
| ( in @ SY303 @ ( powerset @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(930,plain,
! [SV125: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( in @ SY306 @ ( cartprod @ SV125 @ SY305 ) )
| ( ( kpair @ ( kfst @ SY306 ) @ ( ksnd @ SY306 ) )
= SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(931,plain,
! [SV126: $i] :
( ( ! [SY307: $i,SY308: $i] :
( ~ ( subset @ SY308 @ ( cartprod @ SV126 @ SY307 ) )
| ! [SY309: $i] :
( ~ ( subset @ SY309 @ ( cartprod @ SV126 @ SY307 ) )
| ~ ! [SY310: $i] :
( ~ ( in @ SY310 @ SV126 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY307 )
| ~ ( in @ ( kpair @ SY310 @ SX5 ) @ SY308 )
| ( in @ ( kpair @ SY310 @ SX5 ) @ SY309 ) ) )
| ( subset @ SY308 @ SY309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(932,plain,
! [SV127: $i] :
( ( ! [SY312: $i] : ( in @ SY312 @ ( setadjoin @ SV127 @ ( setadjoin @ SY312 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(933,plain,
! [SV128: $i] :
( ( ! [SY313: $i,SY314: $i > $i > $o,SY315: $i] :
( ~ ( in @ SY315 @ SV128 )
| ! [SY316: $i] :
( ~ ( in @ SY316 @ SY313 )
| ~ ( in @ ( kpair @ SY315 @ SY316 )
@ ( dpsetconstr @ SV128 @ SY313
@ ^ [SX5: $i,SX6: $i] : ( SY314 @ SX5 @ SX6 ) ) )
| ( SY314 @ SY315 @ SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(934,plain,
! [SV129: $i] :
( ( ! [SY319: $i] :
( ~ ( in @ SY319 @ ( powerset @ SV129 ) )
| ! [SY320: $i] :
( ~ ( in @ SY320 @ SV129 )
| ~ ~ ( in @ SY320 @ ( setminus @ SV129 @ SY319 ) )
| ( in @ SY320 @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(935,plain,
! [SV130: $i] :
( ( ! [SY321: $i,SY322: $i,SY323: $i] :
( ~ ( in @ ( kpair @ SY322 @ SY323 ) @ ( cartprod @ SV130 @ SY321 ) )
| ( in @ SY323 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(936,plain,
! [SV131: $i] :
( ( ! [SY324: $i > $o] :
( ~ ! [SY325: $i] :
( ~ ( in @ SY325 @ SV131 )
| ! [SY326: $i] :
( ~ ( in @ SY326 @ SV131 )
| ~ ( SY324 @ SY325 )
| ~ ( SY324 @ SY326 )
| ( SY325 = SY326 ) ) )
| ~ ~ ! [SY327: $i] :
~ ~ ( ~ ( in @ SY327 @ SV131 )
| ~ ( SY324 @ SY327 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SX2: $i] : ( SY324 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(937,plain,
! [SV132: $i] :
( ( ! [SY329: $i > $o,SY330: $i] :
( ~ ( in @ SY330
@ ( dsetconstr @ SV132
@ ^ [SX3: $i] : ( SY329 @ SX3 ) ) )
| ( SY329 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(938,plain,
! [SV133: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( in @ SY333 @ SV133 )
| ~ ~ ( in @ SY333 @ SY332 )
| ( SV133 != SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(939,plain,
! [SV134: $i] :
( ( ! [SY334: $i > $o] :
( in
@ ( dsetconstr @ SV134
@ ^ [SX2: $i] : ( SY334 @ SX2 ) )
@ ( powerset @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(940,plain,
! [SV135: $i] :
( ( ! [SY336: $i] : ( subset @ SY336 @ ( binunion @ SV135 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(941,plain,
! [SV136: $i] :
( ( ! [SY337: $i] :
( ~ ( in @ SY337 @ ( powerset @ SV136 ) )
| ! [SY338: $i] :
( ~ ( in @ SY338 @ ( powerset @ SV136 ) )
| ! [SY339: $i] :
( ~ ( in @ SY339 @ SV136 )
| ~ ( in @ SY339 @ ( setminus @ SV136 @ ( binunion @ SY337 @ SY338 ) ) )
| ( in @ SY339 @ ( setminus @ SV136 @ SY337 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(942,plain,
! [SV137: $i] :
( ( ! [SY340: $i] :
( ( SV137 != SY340 )
| ! [SY341: $i > $o,SY342: $i > $o] :
( ~ ! [SY343: $i] :
( ~ ( in @ SY343 @ SV137 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY340 )
| ( SY343 != SX5 )
| ~ ( ~ ( ~ ( SY341 @ SY343 )
| ( SY342 @ SX5 ) )
| ~ ( ~ ( SY342 @ SX5 )
| ( SY341 @ SY343 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SX4: $i] : ( SY341 @ SX4 ) )
= ( dsetconstr @ SY340
@ ^ [SX4: $i] : ( SY342 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(943,plain,
! [SV138: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ( in @ SY348 @ SV138 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY347 )
| ( ( ksnd @ ( kpair @ SY348 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(944,plain,
! [SV139: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( subset @ SY351 @ SV139 )
| ~ ( subset @ SY351 @ SY350 )
| ( subset @ SY351 @ ( binintersect @ SV139 @ SY350 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(945,plain,
! [SV140: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( in @ SY353 @ SV140 )
| ~ ~ ( in @ SY353 @ SY352 )
| ~ ( subset @ SV140 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(946,plain,
! [SV141: $i] :
( ( ! [SY354: $i] :
( ~ ( in @ SY354 @ ( powerset @ SV141 ) )
| ! [SY355: $i] :
( ~ ( in @ SY355 @ SV141 )
| ~ ( in @ SY355 @ SY354 )
| ( in @ SY355 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SY354 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(947,plain,
! [SV142: $i] :
( ( ~ ( in @ SV142 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(948,plain,
! [SV143: $i] :
( ( ! [SY357: $i] : ( subset @ ( setminus @ SV143 @ SY357 ) @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(949,plain,
! [SV144: $i] :
( ( ! [SY358: $i] :
( ~ ( in @ SY358 @ ( powerset @ SV144 ) )
| ! [SY359: $i] :
( ~ ( in @ SY359 @ ( powerset @ SV144 ) )
| ( in @ ( setminus @ SV144 @ SY358 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SY358 @ SY359 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(950,plain,
! [SV145: $i] :
( ( ~ ( subset @ SV145 @ emptyset )
| ( SV145 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(951,plain,
! [SV146: $i > $o] :
( ( ~ ~ ! [SY360: $i] :
~ ~ ( ~ ( SV146 @ SY360 )
| ~ ! [SY361: $i] :
( ~ ( SV146 @ SY361 )
| ( SY360 = SY361 ) ) )
| ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(952,plain,
! [SV147: $i] :
( ( ! [SY364: $i] :
( ~ ( in @ SY364 @ ( powerset @ SV147 ) )
| ! [SY365: $i] :
( ~ ( in @ SY365 @ ( powerset @ SV147 ) )
| ! [SY366: $i] :
( ~ ( in @ SY366 @ SV147 )
| ~ ~ ( in @ SY366 @ ( binunion @ SY364 @ SY365 ) )
| ~ ( in @ SY366 @ SY365 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(953,plain,
! [SV148: $i] :
( ( ! [SY367: $i] :
( ~ ( in @ SY367 @ ( powerset @ SV148 ) )
| ! [SY368: $i] :
( ~ ( in @ SY368 @ ( powerset @ SV148 ) )
| ~ ! [SY369: $i] :
( ~ ( in @ SY369 @ SV148 )
| ~ ( in @ SY369 @ SY367 )
| ( in @ SY369 @ SY368 ) )
| ( in @ SY367 @ ( powerset @ SY368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(954,plain,
! [SV149: $i] :
( ( ! [SY370: $i] :
( ~ ( subset @ SV149 @ SY370 )
| ( subset @ ( powerset @ SV149 ) @ ( powerset @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(955,plain,
! [SV150: $i] :
( ( ! [SY371: $i] : ( in @ SY371 @ ( setadjoin @ SV150 @ ( setadjoin @ SY371 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(956,plain,
! [SV151: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( subset @ SV151 @ SY373 )
| ( subset @ SV151 @ ( setadjoin @ SY372 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(957,plain,
! [SV152: $i] :
( ( ! [SY374: $i,SY375: $i > $i] :
( ~ ! [SY376: $i] :
( ~ ( in @ SY376 @ SV152 )
| ( in @ ( SY375 @ SY376 ) @ SY374 ) )
| ! [SY377: $i] :
( ~ ( in @ SY377 @ SV152 )
| ( ( ap @ SV152 @ SY374
@ ( lam @ SV152 @ SY374
@ ^ [SX4: $i] : ( SY375 @ SX4 ) )
@ SY377 )
= ( SY375 @ SY377 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(958,plain,
! [SV153: $i] :
( ( ! [SY379: $i] :
( ~ ( in @ SY379 @ ( powerset @ SV153 ) )
| ! [SY380: $i] :
( ~ ( in @ SY380 @ ( powerset @ SV153 ) )
| ( in @ ( setminus @ SY379 @ SY380 ) @ ( powerset @ SV153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(959,plain,
! [SV154: $i] :
( ( ! [SY381: $o,SY382: $i] :
( ~ ( in @ SY382 @ SV154 )
| ! [SY383: $i] :
( ~ ( in @ SY383 @ SV154 )
| ~ ~ SY381
| ( ( dsetconstr @ SV154
@ ^ [SX4: $i] :
( ~ ( ~ SY381
| ( SX4 != SY382 ) )
| ~ ( ~ ~ SY381
| ( SX4 != SY383 ) ) ) )
= ( setadjoin @ SY383 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(960,plain,
! [SV155: $i] :
( ( ( dsetconstr @ SV155
@ ^ [SX1: $i] : $true )
= SV155 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(961,plain,
! [SV156: $i] :
( ( ! [SY386: $i,SY387: $i > $i > $o,SY388: $i,SY389: $i] :
( ~ ( in @ ( kpair @ SY388 @ SY389 )
@ ( dpsetconstr @ SV156 @ SY386
@ ^ [SX5: $i,SX6: $i] : ( SY387 @ SX5 @ SX6 ) ) )
| ( in @ SY389 @ SY386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(962,plain,
! [SV157: $i] :
( ( ! [SY392: $o,SY393: $i] :
( ~ ( in @ SY393 @ SV157 )
| ! [SY394: $i] :
( ~ ( in @ SY394 @ SV157 )
| ( in @ ( if @ SV157 @ SY392 @ SY393 @ SY394 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(963,plain,
! [SV158: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV158 )
| ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) )
| ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(964,plain,
! [SV159: $i] :
( ( ~ ( iskpair @ SV159 )
| ( ( kpair @ ( kfst @ SV159 ) @ ( ksnd @ SV159 ) )
= SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(965,plain,
! [SV160: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ( in @ SY398 @ ( setadjoin @ SV160 @ ( setadjoin @ SY397 @ emptyset ) ) )
| ( SY398 = SV160 )
| ( SY398 = SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(966,plain,
! [SV161: $i] :
( ( ! [SY399: $i,SY400: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV161 @ SY399
@ ^ [SX3: $i,SX4: $i] : ( SY400 @ SX3 @ SX4 ) )
@ ( cartprod @ SV161 @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(967,plain,
! [SV162: $i] :
( ( ! [SY403: $i,SY404: $i > $i] :
( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV162 )
| ( in @ ( SY404 @ SY405 ) @ SY403 ) )
| ( in
@ ( lam @ SV162 @ SY403
@ ^ [SX3: $i] : ( SY404 @ SX3 ) )
@ ( funcSet @ SV162 @ SY403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(968,plain,
! [SV163: $i] :
( ( ! [SY407: $i] :
( ~ ( in @ SY407 @ ( powerset @ SV163 ) )
| ( subset @ SY407 @ ( setminus @ SV163 @ ( setminus @ SV163 @ SY407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(969,plain,
! [SV164: $i] :
( ( ! [SY408: $i,SY409: $i > $i > $o,SY410: $i,SY411: $i] :
( ~ ( in @ ( kpair @ SY410 @ SY411 )
@ ( dpsetconstr @ SV164 @ SY408
@ ^ [SX5: $i,SX6: $i] : ( SY409 @ SX5 @ SX6 ) ) )
| ( SY409 @ SY410 @ SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(970,plain,
! [SV165: $i] :
( ( ! [SY414: $i] :
( ~ ( subset @ SV165 @ SY414 )
| ~ ( subset @ SY414 @ SV165 )
| ( SV165 = SY414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(971,plain,
! [SV166: $i] :
( ( ! [SY415: $i,SY416: $i] :
( ~ ( in @ SY416 @ ( binintersect @ SV166 @ SY415 ) )
| ( in @ SY416 @ SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(972,plain,
! [SV167: $i] :
( ( ! [SY417: $i] :
( ~ ( in @ SY417 @ SV167 )
| ( in @ SY417 @ ( powerset @ ( setunion @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(973,plain,
! [SV168: $i] :
( ( ! [SY418: $i] :
( ~ ( in @ SY418 @ ( powerset @ SV168 ) )
| ! [SY419: $i] :
( ~ ( in @ SY419 @ ( powerset @ SV168 ) )
| ! [SY420: $i] :
( ~ ( in @ SY420 @ SV168 )
| ~ ( in @ SY420 @ ( setminus @ SV168 @ SY418 ) )
| ( in @ SY420 @ ( setminus @ SV168 @ ( binintersect @ SY418 @ SY419 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(974,plain,
! [SV169: $i] :
( ( ! [SY421: $i > $o] :
( ~ ~ ~ ! [SY422: $i] :
~ ~ ( ~ ( in @ SY422 @ SV169 )
| ~ ( SY421 @ SY422 ) )
| ! [SY423: $i] :
( ~ ( in @ SY423 @ SV169 )
| ~ ( SY421 @ SY423 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(975,plain,
! [SV170: $i] :
( ( ! [SY424: $i] :
( ( ( setadjoin @ SV170 @ emptyset )
!= ( setadjoin @ SY424 @ emptyset ) )
| ( SV170 = SY424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(976,plain,
! [SV171: $i] :
( ( ! [SY425: $i,SY426: $i] :
( ~ ( in @ SY426 @ SY425 )
| ~ ( in @ SY426 @ ( setminus @ SV171 @ SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(977,plain,
! [SV172: $i] :
( ( ! [SY427: $i] :
( ( SV172 != SY427 )
| ( subset @ SV172 @ SY427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(978,plain,
! [SV173: $i] :
( ( ! [SY428: $i] :
( ~ ( in @ SY428 @ ( powerset @ SV173 ) )
| ( subset @ SY428 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(979,plain,
! [SV174: $i] :
( ( ! [SY429: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV174
@ ^ [SX2: $i] : ( SY429 @ SX2 ) ) )
| ~ ! [SY431: $i] :
~ ~ ( ~ ( in @ SY431 @ SV174 )
| ~ ( SY429 @ SY431 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(980,plain,
! [SV175: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( in @ SY433 @ ( funcSet @ SV175 @ SY432 ) )
| ! [SY434: $i] :
( ~ ( in @ SY434 @ ( funcSet @ SV175 @ SY432 ) )
| ~ ! [SY435: $i] :
( ~ ( in @ SY435 @ SV175 )
| ( ( ap @ SV175 @ SY432 @ SY433 @ SY435 )
= ( ap @ SV175 @ SY432 @ SY434 @ SY435 ) ) )
| ( SY433 = SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(981,plain,
! [SV176: $i] :
( ( ! [SY436: $i] :
( ~ ( in @ SY436 @ ( powerset @ SV176 ) )
| ! [SY437: $i] :
( ~ ( in @ SY437 @ SV176 )
| ~ ( in @ SY437 @ SY436 )
| ~ ( in @ SY437 @ ( setminus @ SV176 @ SY436 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(982,plain,
! [SV177: $i] :
( ( ~ ( in @ SV177 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(983,plain,
! [SV178: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( in @ SY439 @ SY438 )
| ( in @ SY439 @ ( setadjoin @ SV178 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(984,plain,
! [SV179: $i] :
( ( in @ emptyset @ ( powerset @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(985,plain,
! [SV180: $i] :
( ( ! [SY440: $i,SY441: $i > $i] :
( ~ ! [SY442: $i] :
( ~ ( in @ SY442 @ SV180 )
| ( in @ ( SY441 @ SY442 ) @ SY440 ) )
| ( ( lam @ SV180 @ SY440
@ ^ [SX3: $i] : ( SY441 @ SX3 ) )
= ( lam @ SV180 @ SY440
@ ^ [SX3: $i] : ( SY441 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(986,plain,
! [SV181: $i] :
( ( ! [SY445: $i] :
( ~ ( in @ SY445 @ ( powerset @ SV181 ) )
| ! [SY446: $i] :
( ~ ( in @ SY446 @ ( powerset @ SV181 ) )
| ! [SY447: $o,SY448: $i] :
( ~ ( in @ SY448 @ SV181 )
| ~ ( in @ SY448 @ ( binunion @ SY445 @ SY446 ) )
| ~ ( ~ ( in @ SY448 @ SY445 )
| SY447 )
| ~ ( ~ ( in @ SY448 @ SY446 )
| SY447 )
| SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(987,plain,
! [SV182: $i > $o] :
( ( ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( SV182 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV182 @ SY450 )
| ( SY449 = SY450 ) ) )
| ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(988,plain,
! [SV183: $i] :
( ( ! [SY452: $i] :
( ( SV183 != SY452 )
| ( ( setunion @ SV183 )
= ( setunion @ SY452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(989,plain,
! [SV184: $i] :
( ( ! [SY453: $i] :
( ~ ( in @ SY453 @ ( powerset @ SV184 ) )
| ! [SY454: $i] :
( ~ ( in @ SY454 @ ( powerset @ SV184 ) )
| ( in @ ( binintersect @ SY453 @ SY454 ) @ ( powerset @ SV184 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(990,plain,
! [SV185: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ~ ( in @ SY456 @ ( setminus @ SV185 @ SY455 ) )
| ~ ( in @ SY456 @ SV185 )
| ( in @ SY456 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(991,plain,
! [SV186: $i] :
( ( subset @ SV186 @ ( setunion @ ( setadjoin @ SV186 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(992,plain,
! [SV187: $i] :
( ( ! [SY457: $i] :
( ~ ( in @ SY457 @ ( powerset @ SV187 ) )
| ! [SY458: $i] :
( ~ ( in @ SY458 @ ( powerset @ SV187 ) )
| ( in @ ( binunion @ SY457 @ SY458 ) @ ( powerset @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(993,plain,
! [SV188: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( func @ SV188 @ SY459 @ SY460 )
| ! [SY461: $i] :
( ~ ( in @ SY461 @ SV188 )
| ( ( ap @ SV188 @ SY459 @ SY460 @ SY461 )
= ( ap @ SV188 @ SY459 @ SY460 @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(994,plain,
! [SV189: $i] :
( ( ! [SY462: $i] :
( ~ ( subset @ SY462 @ SV189 )
| ( ( binintersect @ SV189 @ SY462 )
= SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(995,plain,
! [SV190: $i] :
( ( ! [SY463: $i,SY464: $i] :
( ~ ( in @ SY464 @ ( funcSet @ SV190 @ SY463 ) )
| ! [SY465: $i] :
( ~ ( in @ SY465 @ SV190 )
| ( in @ ( kpair @ SY465 @ ( ap @ SV190 @ SY463 @ SY464 @ SY465 ) ) @ SY464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(996,plain,
! [SV191: $i] :
( ( ! [SY466: $i > $o] :
( ~ ~ ! [SY467: $i] :
( ~ ( in @ SY467 @ SV191 )
| ( SY466 @ SY467 ) )
| ~ ! [SY468: $i] :
~ ~ ( ~ ( in @ SY468 @ SV191 )
| ~ ~ ( SY466 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(997,plain,
! [SV192: $i] :
( ( ! [SY469: $i,SY470: $i,SY471: $i] :
( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SY469 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY470 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY470 @ ( setadjoin @ SY471 @ emptyset ) ) @ emptyset ) ) )
| ( SV192 = SY470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(998,plain,
! [SV193: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ~ ( subset @ SY473 @ ( cartprod @ SV193 @ SY472 ) )
| ! [SY474: $i > $o] :
( ~ ! [SY475: $i] :
( ~ ( in @ SY475 @ SV193 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY472 )
| ~ ( in @ ( kpair @ SY475 @ SX5 ) @ SY473 )
| ( SY474 @ ( kpair @ SY475 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY473 )
| ( SY474 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(999,plain,
! [SV194: $i] :
( ( ! [SY478: $i,SY479: $i] :
( ~ ( in @ SY479 @ ( setadjoin @ SV194 @ SY478 ) )
| ! [SY480: $o] :
( ~ ( ( SY479 != SV194 )
| SY480 )
| ~ ( ~ ( in @ SY479 @ SY478 )
| SY480 )
| SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1000,plain,
! [SV195: $i] :
( ( ! [SY481: $i > $o] :
( ~ ~ ! [SY482: $i] :
( ~ ( in @ SY482 @ SV195 )
| ( SY481 @ SY482 ) )
| ~ ! [SY483: $i] :
~ ~ ( ~ ( in @ SY483 @ SV195 )
| ~ ~ ( SY481 @ SY483 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1001,plain,
! [SV196: $i] :
( ( ~ ! [SY484: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY485 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ~ ( ~ ( in @ SY487 @ SV196 )
| ~ ( in @ SY488 @ SV196 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY484 )
| ~ ( ~ ( ~ ( in @ SY487 @ SX4 )
| ( in @ SY488 @ SX4 ) )
| ~ ( ~ ( in @ SY488 @ SX4 )
| ( in @ SY487 @ SX4 ) ) ) )
| ( SY487 = SY488 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY484 )
| ~ ( in @ SX3 @ SY484 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY494: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY494 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY494 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY484 )
| ~ ( in @ SX4 @ SY494 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY494 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY484 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1002,plain,
! [SV197: $i] :
( ( ! [SY502: $i] : ( in @ SV197 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV197 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV197 @ ( setadjoin @ SY502 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1003,plain,
! [SV198: $i] :
( ( ! [SY503: $i] :
( ~ ( subset @ SV198 @ SY503 )
| ( in @ SV198 @ ( powerset @ SY503 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1004,plain,
! [SV199: $i] :
( ( ! [SY504: $i > $o,SY505: $i] :
( ~ ( in @ SY505 @ SV199 )
| ~ ( SY504 @ SY505 )
| ~ ! [SY506: $i] :
( ~ ( in @ SY506 @ SV199 )
| ~ ( SY504 @ SY506 )
| ( SY506 = SY505 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SX3: $i] : ( SY504 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1005,plain,
! [SV200: $i] :
( ( ! [SY508: $i,SY509: $i] :
( ~ ( subset @ SV200 @ SY508 )
| ~ ( in @ SY509 @ SV200 )
| ( in @ SY509 @ SY508 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1006,plain,
! [SV201: $i] :
( ( ! [SY510: $i] :
( ~ ! [SY511: $i] :
( ~ ( in @ SY511 @ SV201 )
| ( in @ SY511 @ SY510 ) )
| ~ ! [SY512: $i] :
( ~ ( in @ SY512 @ SY510 )
| ( in @ SY512 @ SV201 ) )
| ( SV201 = SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1007,plain,
! [SV202: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ( in @ SY513 @ ( powerset @ SV202 ) )
| ~ ( in @ SY514 @ SY513 )
| ( in @ SY514 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1008,plain,
! [SV203: $i] :
( ( ! [SY515: $i,SY516: $i] :
( ~ ( in @ SY516 @ ( funcSet @ SV203 @ SY515 ) )
| ( ( lam @ SV203 @ SY515
@ ^ [SY517: $i] : ( ap @ SV203 @ SY515 @ SY516 @ SY517 ) )
= SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1009,plain,
! [SV204: $i] :
( ( ! [SY518: $i] :
( ~ ( in @ SY518 @ ( powerset @ SV204 ) )
| ! [SY519: $i] :
( ~ ( in @ SY519 @ ( powerset @ SV204 ) )
| ( subset @ ( setminus @ SV204 @ SY518 ) @ ( setminus @ SV204 @ ( binintersect @ SY518 @ SY519 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1010,plain,
! [SV205: $i > $o] :
( ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( SV205 @ SY520 )
| ~ ! [SY521: $i] :
( ~ ( SV205 @ SY521 )
| ( SY520 = SY521 ) ) )
| ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1011,plain,
! [SV206: $i] :
( ( ~ ( singleton @ SV206 )
| ( in @ ( setunion @ SV206 ) @ SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1012,plain,
! [SV207: $i] :
( ( ! [SY524: $i] :
( ( kfst @ ( kpair @ SV207 @ SY524 ) )
= SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1013,plain,
! [SV208: $i] :
( ( ~ ( iskpair @ SV208 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV208 )
@ ^ [SY525: $i] :
( SV208
= ( kpair @ ( kfst @ SV208 ) @ SY525 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1014,plain,
! [SV209: $i > $o] :
( ( ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( SV209 @ SY526 )
| ~ ! [SY527: $i] :
( ~ ( SV209 @ SY527 )
| ( SY526 = SY527 ) ) )
| ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1015,plain,
! [SV210: $i] :
( ( ! [SY529: $i] :
( ~ ( in @ SY529 @ ( setunion @ SV210 ) )
| ~ ! [SY530: $i] :
~ ~ ( ~ ( in @ SY530 @ SV210 )
| ~ ( in @ SY529 @ SY530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1016,plain,
! [SV211: $i] :
( ( ! [SY531: $i,SY532: $i > $i > $o,SY533: $i,SY534: $i] :
( ~ ( in @ ( kpair @ SY533 @ SY534 )
@ ( dpsetconstr @ SV211 @ SY531
@ ^ [SX5: $i,SX6: $i] : ( SY532 @ SX5 @ SX6 ) ) )
| ( in @ SY533 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1017,plain,
! [SV212: $i] :
( ( ! [SY537: $o,SY538: $i] :
( ~ ( in @ SY538 @ SV212 )
| ! [SY539: $i] :
( ~ ( in @ SY539 @ SV212 )
| ( in @ ( if @ SV212 @ SY537 @ SY538 @ SY539 ) @ ( setadjoin @ SY538 @ ( setadjoin @ SY539 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1018,plain,
! [SV213: $i] :
( ( ! [SY540: $i,SY541: $i] :
( ~ ( func @ SV213 @ SY540 @ SY541 )
| ( ( lam @ SV213 @ SY540
@ ^ [SY542: $i] : ( ap @ SV213 @ SY540 @ SY541 @ SY542 ) )
= SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1019,plain,
! [SV214: $i] :
( ( ! [SY543: $i,SY544: $i] :
( ~ ( func @ SV214 @ SY543 @ SY544 )
| ! [SY545: $i] :
( ~ ( in @ SY545 @ SV214 )
| ( singleton
@ ( dsetconstr @ SY543
@ ^ [SX4: $i] : ( in @ ( kpair @ SY545 @ SX4 ) @ SY544 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1020,plain,
! [SV215: $i] :
( ( ! [SY547: $i,SY548: $i > $i] :
( ~ ! [SY549: $i] :
( ~ ( in @ SY549 @ SV215 )
| ( in @ ( SY548 @ SY549 ) @ SY547 ) )
| ( func @ SV215 @ SY547
@ ( dpsetconstr @ SV215 @ SY547
@ ^ [SX3: $i,SX4: $i] :
( ( SY548 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1021,plain,
! [SV216: $i] :
( ( ! [SY552: $i,SY553: $i] :
( ~ ( in @ SY553 @ SV216 )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ SY552 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY553 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY553 @ ( setadjoin @ SY554 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SY552 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1022,plain,
! [SV217: $i] :
( ( ! [SY555: $i,SY556: $i] :
( ~ ( in @ ( setadjoin @ SY556 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ ( setadjoin @ SY555 @ emptyset ) ) @ emptyset ) ) )
| ( SV217 = SY556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1023,plain,
! [SV218: $i] :
( ( ! [SY557: $i] : ( in @ SV218 @ ( setadjoin @ SV218 @ ( setadjoin @ SY557 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1024,plain,
! [SV219: $i] :
( ( ! [SY558: $i] :
~ ( ~ ( ~ ( in @ SY558 @ ( setunion @ SV219 ) )
| ~ ! [SY559: $i] :
~ ~ ( ~ ( in @ SY558 @ SY559 )
| ~ ( in @ SY559 @ SV219 ) ) )
| ~ ( ~ ~ ! [SY560: $i] :
~ ~ ( ~ ( in @ SY558 @ SY560 )
| ~ ( in @ SY560 @ SV219 ) )
| ( in @ SY558 @ ( setunion @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1025,plain,
! [SV220: $i] :
( ( ! [SY561: $i] :
( ~ ~ ~ ! [SY562: $i] :
~ ~ ( ~ ( in @ SY562 @ SV220 )
| ~ ( in @ SY562 @ SY561 ) )
| ( ( binintersect @ SV220 @ SY561 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1026,plain,
! [SV221: $i] :
( ( ! [SY563: $i] : ( in @ SY563 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV221 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV221 @ ( setadjoin @ SY563 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1027,plain,
! [SV222: $i] :
( ( ! [SY564: $i] :
( ~ ( in @ SY564 @ ( powerset @ SV222 ) )
| ! [SY565: $i] :
( ~ ( in @ SY565 @ ( powerset @ SV222 ) )
| ! [SY566: $i] :
( ~ ( in @ SY566 @ SV222 )
| ~ ( in @ SY566 @ ( setminus @ SV222 @ SY564 ) )
| ~ ( in @ SY566 @ ( binintersect @ SY564 @ SY565 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1028,plain,
! [SV223: $i] :
( ( ! [SY567: $i,SY568: $i,SY569: $i] :
( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SY567 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY568 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY568 @ ( setadjoin @ SY569 @ emptyset ) ) @ emptyset ) ) )
| ( SY568 != SY569 )
| ( SY567 = SY569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1029,plain,
! [SV224: $i] :
( ( ! [SY570: $i] :
( ~ ( in @ SY570 @ ( powerset @ SV224 ) )
| ! [SY571: $i] :
( ~ ( in @ SY571 @ ( powerset @ SV224 ) )
| ! [SY572: $i] :
( ~ ( in @ SY572 @ SV224 )
| ~ ~ ( in @ SY572 @ SY570 )
| ~ ~ ( in @ SY572 @ SY571 )
| ~ ( in @ SY572 @ ( binunion @ SY570 @ SY571 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1030,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(1031,plain,
! [SV225: $i] :
( ( ! [SY573: $i] :
( ~ ( in @ SV225 @ ( setadjoin @ SY573 @ emptyset ) )
| ( in @ SY573 @ ( setadjoin @ SV225 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1032,plain,
! [SV226: $i] :
( ( ! [SY574: $o,SY575: $i] :
( ~ ( in @ SY575 @ SV226 )
| ! [SY576: $i] :
( ~ ( in @ SY576 @ SV226 )
| ~ SY574
| ( ( if @ SV226 @ SY574 @ SY575 @ SY576 )
= SY575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1033,plain,
! [SV227: $i > $o] :
( ( ~ ~ ! [SY577: $i] :
~ ~ ( ~ ( SV227 @ SY577 )
| ~ ! [SY578: $i] :
( ~ ( SV227 @ SY578 )
| ( SY577 = SY578 ) ) )
| ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1034,plain,
! [SV228: $i] :
( ( ! [SY581: $i] :
( ~ ( in @ SY581 @ ( powerset @ SV228 ) )
| ! [SY582: $i] :
( ~ ( in @ SY582 @ ( powerset @ SV228 ) )
| ! [SY583: $i] :
( ~ ( in @ SY583 @ SV228 )
| ~ ( subset @ SY581 @ ( setminus @ SV228 @ SY582 ) )
| ~ ( in @ SY583 @ SY582 )
| ~ ( in @ SY583 @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1035,plain,
! [SV229: $i] :
( ( ! [SY584: $o,SY585: $i] :
( ~ ( in @ SY585 @ SV229 )
| ! [SY586: $i] :
( ~ ( in @ SY586 @ SV229 )
| ~ SY584
| ( in @ SY585
@ ( dsetconstr @ SV229
@ ^ [SX4: $i] :
( ~ ( ~ SY584
| ( SX4 != SY585 ) )
| ~ ( ~ ~ SY584
| ( SX4 != SY586 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1036,plain,
! [SV230: $i] :
( ( ! [SY588: $i,SY589: $i] :
( ( binintersect @ SV230 @ ( binunion @ SY588 @ SY589 ) )
= ( binunion @ ( binintersect @ SV230 @ SY588 ) @ ( binintersect @ SV230 @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1037,plain,
! [SV231: $i] :
( ( ! [SY590: $i,SY591: $i] :
( ( ( setadjoin @ SV231 @ ( setadjoin @ SY590 @ emptyset ) )
!= ( setadjoin @ SY591 @ emptyset ) )
| ( SV231 = SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1038,plain,
! [SV232: $i > $o] :
( ( ! [SY592: $i] :
( ~ ( in @ SY592 @ emptyset )
| ( SV232 @ SY592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1039,plain,
! [SV233: $i] :
( ( ! [SY593: $i] :
( ~ ( subset @ SY593 @ SV233 )
| ( in @ SY593 @ ( powerset @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1040,plain,
! [SV234: $i] :
( ( ! [SY594: $i,SY595: $i] :
( ~ ( in @ SY595 @ ( cartprod @ SV234 @ SY594 ) )
| ( in @ ( ksnd @ SY595 ) @ SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1041,plain,
! [SV235: $i] :
( ( ! [SY596: $i,SY597: $i,SY598: $o] :
( ~ ( in @ SY597 @ ( binunion @ SV235 @ SY596 ) )
| ~ ( ~ ( in @ SY597 @ SV235 )
| SY598 )
| ~ ( ~ ( in @ SY597 @ SY596 )
| SY598 )
| SY598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1042,plain,
! [SV236: $i] :
( ( ! [SY599: $i,SY600: $i,SY601: $i] :
( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SY599 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY600 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY600 @ ( setadjoin @ SY601 @ emptyset ) ) @ emptyset ) ) )
| ( SY599 = SY601 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1043,plain,
! [SV237: $i > $o] :
( ( ! [SY602: $i > $o] :
( ~ ! [SY603: $i,SY604: $i] :
( ( SY603 != SY604 )
| ~ ( ~ ( ~ ( SV237 @ SY603 )
| ( SY602 @ SY604 ) )
| ~ ( ~ ( SY602 @ SY604 )
| ( SV237 @ SY603 ) ) ) )
| ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY602 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY602 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SX2: $i] : ( SY602 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1044,plain,
! [SV238: $i] :
( ( ! [SY611: $i] :
( ~ ( in @ SY611 @ SV238 )
| ( in @ ( setadjoin @ SY611 @ emptyset ) @ ( powerset @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1045,plain,
! [SV239: $i] :
( ( ! [SY612: $i > $o] :
( ~ ( singleton
@ ( dsetconstr @ SV239
@ ^ [SX2: $i] : ( SY612 @ SX2 ) ) )
| ! [SY614: $i] :
( ~ ( in @ SY614 @ SV239 )
| ! [SY615: $i] :
( ~ ( in @ SY615 @ SV239 )
| ~ ( SY612 @ SY614 )
| ~ ( SY612 @ SY615 )
| ( SY614 = SY615 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1046,plain,
! [SV240: $i] :
( ( ! [SY616: $i,SY617: $i] :
( ~ ( in @ SY617 @ SV240 )
| ~ ~ ( in @ SY617 @ SY616 )
| ( in @ SY617 @ ( setminus @ SV240 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1047,plain,
! [SV241: $i] :
( ( ! [SY618: $i,SY619: $i] :
( ~ ~ ( in @ SY619 @ SV241 )
| ~ ( in @ SY619 @ SY618 )
| ( in @ SY619 @ ( symdiff @ SV241 @ SY618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1048,plain,
! [SV242: $i] :
( ( ! [SY620: $i] :
( ~ ( in @ SY620 @ ( powerset @ SV242 ) )
| ! [SY621: $i] :
( ~ ( in @ SY621 @ ( powerset @ SV242 ) )
| ! [SY622: $i] :
( ~ ( in @ SY622 @ SV242 )
| ~ ~ ( in @ SY622 @ SY621 )
| ~ ( in @ SY622 @ ( binintersect @ SY620 @ SY621 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1049,plain,
! [SV243: $i] :
( ( ! [SY623: $o,SY624: $i] :
( ~ ( in @ SY624 @ SV243 )
| ! [SY625: $i] :
( ~ ( in @ SY625 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SX4: $i] :
( ~ ( ~ SY623
| ( SX4 != SY624 ) )
| ~ ( ~ ~ SY623
| ( SX4 != SY625 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1050,plain,
! [SV244: $i] :
( ( ! [SY627: $i,SY628: $i] :
( ~ ( in @ SY628 @ SV244 )
| ! [SY629: $i] :
( ~ ( in @ SY629 @ SY627 )
| ( in @ ( setadjoin @ SY628 @ ( setadjoin @ SY629 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SY627 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1051,plain,
! [SV245: $i] :
( ( ! [SY630: $i] : ( subset @ SV245 @ ( binunion @ SV245 @ SY630 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1052,plain,
! [SV246: $i] :
( ( ! [SY631: $i,SY632: $i] :
( ~ ( in @ SY632 @ SV246 )
| ! [SY633: $i] :
( ~ ( in @ SY633 @ SY631 )
| ( subset @ ( setadjoin @ SY632 @ ( setadjoin @ SY633 @ emptyset ) ) @ ( binunion @ SV246 @ SY631 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1053,plain,
! [SV247: $i] :
( ( ! [SY634: $i,SY635: $i] :
( ~ ( func @ SV247 @ SY634 @ SY635 )
| ! [SY636: $i] :
( ~ ( func @ SV247 @ SY634 @ SY636 )
| ~ ! [SY637: $i] :
( ~ ( in @ SY637 @ SV247 )
| ( ( ap @ SV247 @ SY634 @ SY635 @ SY637 )
= ( ap @ SV247 @ SY634 @ SY636 @ SY637 ) ) )
| ( SY635 = SY636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1054,plain,
! [SV248: $i] :
( ( ! [SY638: $i,SY639: $i] :
( ~ ( in @ SY639 @ SY638 )
| ( in @ SY639 @ ( binunion @ SV248 @ SY638 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1055,plain,
! [SV249: $i] :
( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ ( powerset @ SV249 ) )
| ! [SY641: $i] :
( ~ ( in @ SY641 @ ( powerset @ SV249 ) )
| ! [SY642: $i] :
( ~ ( in @ SY642 @ SV249 )
| ~ ~ ( in @ SY642 @ ( binunion @ SY640 @ SY641 ) )
| ~ ( in @ SY642 @ SY640 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1056,plain,
! [SV250: $i] :
( ( ! [SY643: $i > $o,SY644: $i] :
( ~ ( in @ SY644 @ SV250 )
| ~ ( SY643 @ SY644 )
| ( in @ SY644
@ ( dsetconstr @ SV250
@ ^ [SX3: $i] : ( SY643 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1057,plain,
! [SV251: $i] :
( ( ! [SY646: $i] : ( in @ SY646 @ ( setadjoin @ SV251 @ ( setadjoin @ SY646 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1058,plain,
! [SV252: $i] :
( ( ! [SY647: $i,SY648: $i] :
( ~ ( in @ SY648 @ SV252 )
| ~ ( in @ SY648 @ SY647 )
| ~ ( in @ SY648 @ ( symdiff @ SV252 @ SY647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1059,plain,
! [SV253: $i] :
( ( ! [SY649: $i] :
( ~ ( in @ SY649 @ ( powerset @ SV253 ) )
| ( in @ ( powerset @ SY649 ) @ ( powerset @ ( powerset @ SV253 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1060,plain,
! [SV254: $i] :
( ( ! [SY650: $i,SY651: $i] :
( ~ ( in @ SY651 @ ( cartprod @ SV254 @ SY650 ) )
| ( iskpair @ SY651 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1061,plain,
! [SV255: $i] :
( ( ! [SY652: $i] : ( subset @ ( binintersect @ SV255 @ SY652 ) @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1062,plain,
! [SV256: $i] :
( ( ! [SY653: $i] :
( ( SV256 != SY653 )
| ! [SY654: $i,SY655: $i] :
( ( SY654 != SY655 )
| ( ( setadjoin @ SV256 @ SY654 )
= ( setadjoin @ SY653 @ SY655 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1063,plain,
! [SV257: $i] :
( ( in @ SV257 @ ( powerset @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1064,plain,
! [SV258: $i] :
( ( ! [SY656: $i] :
( ( SV258 != SY656 )
| ( in @ SV258 @ ( setadjoin @ SY656 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1065,plain,
! [SV259: $i] :
( ( ! [SY657: $i] :
( ~ ( in @ SY657 @ ( powerset @ SV259 ) )
| ! [SY658: $i] :
( ~ ( in @ SY658 @ ( powerset @ SV259 ) )
| ~ ! [SY659: $i] :
( ~ ( in @ SY659 @ SV259 )
| ~ ( in @ SY659 @ SY657 )
| ( in @ SY659 @ SY658 ) )
| ~ ! [SY660: $i] :
( ~ ( in @ SY660 @ SV259 )
| ~ ( in @ SY660 @ SY658 )
| ( in @ SY660 @ SY657 ) )
| ( SY657 = SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1066,plain,
! [SV260: $i] :
( ( ! [SY661: $i,SY662: $i] :
( ~ ( in @ SY662 @ ( cartprod @ SV260 @ SY661 ) )
| ~ ! [SY663: $i] :
~ ~ ( ~ ( in @ SY663 @ SV260 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY661 )
| ( SY662
!= ( kpair @ SY663 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1067,plain,
! [SV261: $i,SV1: $i] :
( ( ! [SY665: $i] :
( ~ ( subset @ SY665 @ ( cartprod @ SV1 @ SV261 ) )
| ! [SY666: $i > $o] :
( ~ ! [SY667: $i] :
( ~ ( in @ SY667 @ SV1 )
| ! [SY668: $i] :
( ~ ( in @ SY668 @ SV261 )
| ~ ( in @ ( kpair @ SY667 @ SY668 ) @ SY665 )
| ( SY666 @ ( kpair @ SY667 @ SY668 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY665 )
| ( SY666 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1068,plain,
! [SV262: $i,SV2: $i] :
( ( ( SV2 != SV262 )
| ! [SY670: $i,SY671: $i] :
( ( SY670 != SY671 )
| ~ ( ~ ( ~ ( in @ SY670 @ SV2 )
| ( in @ SY671 @ SV262 ) )
| ~ ( ~ ( in @ SY671 @ SV262 )
| ( in @ SY670 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1069,plain,
! [SV3: $i,SV263: $i] :
( ( ~ ( in @ SV263 @ ( powerset @ SV3 ) )
| ( subset @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV263 ) ) @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1070,plain,
! [SV264: $i,SV4: $i] :
( ( ! [SY672: $i] :
( ~ ( in @ SY672 @ ( setadjoin @ SV4 @ ( setadjoin @ SV264 @ emptyset ) ) )
| ( SY672 = SV4 )
| ( SY672 = SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1071,plain,
! [SV265: $i,SV5: $i] :
( ( ! [SY673: $i] :
( ~ ( subset @ SY673 @ ( cartprod @ SV5 @ SV265 ) )
| ! [SY674: $i] :
( ~ ( subset @ SY674 @ ( cartprod @ SV5 @ SV265 ) )
| ~ ! [SY675: $i] :
( ~ ( in @ SY675 @ SV5 )
| ! [SY676: $i] :
( ~ ( in @ SY676 @ SV265 )
| ~ ( in @ ( kpair @ SY675 @ SY676 ) @ SY673 )
| ( in @ ( kpair @ SY675 @ SY676 ) @ SY674 ) ) )
| ~ ! [SY677: $i] :
( ~ ( in @ SY677 @ SV5 )
| ! [SY678: $i] :
( ~ ( in @ SY678 @ SV265 )
| ~ ( in @ ( kpair @ SY677 @ SY678 ) @ SY674 )
| ( in @ ( kpair @ SY677 @ SY678 ) @ SY673 ) ) )
| ( SY673 = SY674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1072,plain,
! [SV6: $i] :
( ( ( ~ ! [SY25: $i] :
~ ( in @ SY25 @ SV6 ) )
= $true )
| ( ( SV6 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(1073,plain,
! [SV7: $i] :
( ( ( ~ ( singleton @ SV7 ) )
= $true )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ SV7 )
| ( ( setunion @ SV7 )
= SY26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[806]) ).
thf(1074,plain,
! [SV266: $i,SV8: $i] :
( ( ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV8 )
| ( in @ SY679 @ SV266 ) )
| ( subset @ SV8 @ SV266 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1075,plain,
! [SV9: $i] :
( ( ( ~ ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[808]) ).
thf(1076,plain,
! [SV10: $i,SV267: $i] :
( ( ~ ( in @ SV267 @ ( setunion @ SV10 ) )
| ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV267 @ SY681 )
| ~ ( in @ SY681 @ SV10 )
| SY680 )
| SY680 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1077,plain,
! [SV268: $i,SV11: $i] :
( ( ! [SY682: $i] :
~ ( ~ ( ~ ( in @ SY682 @ ( setadjoin @ SV11 @ SV268 ) )
| ( SY682 = SV11 )
| ( in @ SY682 @ SV268 ) )
| ~ ( ~ ( ( SY682 = SV11 )
| ( in @ SY682 @ SV268 ) )
| ( in @ SY682 @ ( setadjoin @ SV11 @ SV268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1078,plain,
! [SV12: $i > $o] :
( ( ( ~ ~ ! [SY37: $i] :
~ ! [SY38: $i] :
~ ( ~ ( ~ ( SV12 @ SY38 )
| ( SY38 = SY37 ) )
| ~ ( ( SY38 != SY37 )
| ( SV12 @ SY38 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[811]) ).
thf(1079,plain,
! [SV13: $i > $o] :
( ( ( ~ ~ ! [SY41: $i] :
~ ( SV13 @ SY41 ) )
= $true )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[812]) ).
thf(1080,plain,
! [SV269: $i,SV14: $i] :
( ( ! [SY683: $i] :
( ~ ( in @ SY683 @ ( symdiff @ SV14 @ SV269 ) )
| ! [SY684: $o] :
( ~ ( ~ ( in @ SY683 @ SV14 )
| ~ ~ ( in @ SY683 @ SV269 )
| SY684 )
| ~ ( ~ ~ ( in @ SY683 @ SV14 )
| ~ ( in @ SY683 @ SV269 )
| SY684 )
| SY684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1081,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ~ ! [SY685: $i,SY686: $i] :
( ( SY685 != SY686 )
| ~ ( ~ ( ~ ( SV15 @ SY685 )
| ( SV270 @ SY686 ) )
| ~ ( ~ ( SV270 @ SY686 )
| ( SV15 @ SY685 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1082,plain,
! [SV271: $i,SV16: $i] :
( ( ! [SY695: $i] :
( ~ ~ ( in @ SY695 @ SV16 )
| ~ ( in @ SY695 @ ( setminus @ SV16 @ SV271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1083,plain,
! [SV18: $i] :
( ( ( ~ ( in @ SV18 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV18 @ SV18 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(1084,plain,
! [SV19: $i > $o] :
( ( ( ~ ~ ! [SY62: $i] :
~ ~ ( ~ ( SV19 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( SV19 @ SY63 )
| ( SY62 = SY63 ) ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(1085,plain,
! [SV272: $i,SV20: $i] :
( ( ~ ~ ( subset @ SV20 @ SV272 )
| ( SV20 != SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1086,plain,
! [SV21: $i,SV273: $i] :
( ( ~ ( in @ SV273 @ ( powerset @ SV21 ) )
| ! [SY696: $i] :
( ~ ( in @ SY696 @ ( powerset @ SV21 ) )
| ! [SY697: $i] :
( ~ ( in @ SY697 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SY696 ) )
| ~ ( in @ SY697 @ SV273 )
| ( in @ SY697 @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1087,plain,
! [SV274: $i,SV22: $i] :
( ( ! [SY698: $i] :
( ~ ~ ( in @ SY698 @ ( setminus @ SV22 @ SV274 ) )
| ~ ~ ( in @ SY698 @ SV274 )
| ~ ( in @ SY698 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1088,plain,
! [SV23: $i,SV275: $i] :
( ( ~ ( in @ SV275 @ SV23 )
| ( subset @ ( setadjoin @ SV275 @ emptyset ) @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1089,plain,
! [SV276: $i,SV24: $i] :
( ( ! [SY699: $i] :
( ~ ( in @ SY699 @ ( funcSet @ SV24 @ SV276 ) )
| ! [SY700: $i] :
( ~ ( in @ SY700 @ SV24 )
| ( in @ ( ap @ SV24 @ SV276 @ SY699 @ SY700 ) @ SV276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1090,plain,
! [SV277: $i > $o,SV25: $i] :
( ( subset
@ ( dsetconstr @ SV25
@ ^ [SY701: $i] : ( SV277 @ SY701 ) )
@ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1091,plain,
! [SV278: $i,SV26: $i] :
( ( ! [SY702: $i,SY703: $i] :
( ( ( kpair @ SV26 @ SV278 )
!= ( kpair @ SY702 @ SY703 ) )
| ( SV26 = SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1092,plain,
! [SV279: $i,SV27: $i] :
( ( ! [SY704: $i,SY705: $i] :
( ~ ( in @ ( kpair @ SY704 @ SY705 ) @ ( cartprod @ SV27 @ SV279 ) )
| ( in @ SY704 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1093,plain,
! [SV280: $i,SV28: $i] :
( ( iskpair @ ( kpair @ SV28 @ SV280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1094,plain,
! [SV281: $i,SV29: $i] :
( ( ! [SY706: $i > $i > $o,SY707: $i] :
( ~ ( in @ SY707 @ SV29 )
| ! [SY708: $i] :
( ~ ( in @ SY708 @ SV281 )
| ~ ( SY706 @ SY707 @ SY708 )
| ( in @ ( kpair @ SY707 @ SY708 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SX5: $i,SX6: $i] : ( SY706 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1095,plain,
! [SV282: $i,SV30: $i] :
( ( ! [SY711: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV30 @ SV282
@ ^ [SX3: $i,SX4: $i] : ( SY711 @ SX3 @ SX4 ) )
@ ( cartprod @ SV30 @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1096,plain,
! [SV283: $i,SV31: $i] :
( ( ! [SY714: $i] :
( ~ ( in @ SY714 @ ( funcSet @ SV31 @ SV283 ) )
| ! [SY715: $i] :
( ~ ( in @ SY715 @ SV31 )
| ! [SY716: $i] :
( ~ ( in @ SY716 @ SV283 )
| ~ ( in @ ( kpair @ SY715 @ SY716 ) @ SY714 )
| ( ( ap @ SV31 @ SV283 @ SY714 @ SY715 )
= SY716 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1097,plain,
! [SV284: $i,SV32: $i] :
( ( ( SV32 != SV284 )
| ( ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV32 @ ( setadjoin @ SV284 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1098,plain,
! [SV285: $i,SV33: $i] :
( ( ! [SY717: $i] :
( ~ ( in @ SY717 @ ( setadjoin @ SV33 @ SV285 ) )
| ( SY717 = SV33 )
| ( in @ SY717 @ SV285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1099,plain,
! [SV286: $i,SV34: $i] :
( ( ( ksnd @ ( kpair @ SV34 @ SV286 ) )
= SV286 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1100,plain,
! [SV287: $o,SV35: $i] :
( ( ! [SY718: $i] :
( ~ ( in @ SY718 @ SV35 )
| ! [SY719: $i] :
( ~ ( in @ SY719 @ SV35 )
| ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SY718 @ SY719 )
= SY719 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[834]) ).
thf(1101,plain,
! [SV35: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV35 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV35 )
| ~ ~ $true
| ( ( if @ SV35 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[834]) ).
thf(1102,plain,
! [SV35: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV35 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV35 )
| ~ ~ $false
| ( ( if @ SV35 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[834]) ).
thf(1103,plain,
! [SV288: $i,SV36: $i] :
( ( ! [SY720: $i > $i] :
( ~ ! [SY721: $i] :
( ~ ( in @ SY721 @ SV36 )
| ( in @ ( SY720 @ SY721 ) @ SV288 ) )
| ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SX3: $i] : ( SY720 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1104,plain,
! [SV289: $i,SV37: $i] :
( ( ! [SY723: $i] :
( ~ ( in @ SY723 @ SV37 )
| ( in @ ( setadjoin @ SY723 @ emptyset ) @ ( powerset @ ( binunion @ SV37 @ SV289 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1105,plain,
! [SV290: $i,SV38: $i] :
( ( ~ ( subset @ SV38 @ SV290 )
| ( ( binintersect @ SV38 @ SV290 )
= SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1106,plain,
! [SV291: $i,SV39: $i] :
( ( ( ( binintersect @ SV39 @ SV291 )
!= SV291 )
| ( subset @ SV291 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1107,plain,
! [SV292: $i,SV40: $i] :
( ( ~ ( subset @ SV40 @ SV292 )
| ( ( setminus @ SV40 @ SV292 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1108,plain,
! [SV41: $i,SV293: $i] :
( ( ~ ( in @ SV293 @ ( powerset @ SV41 ) )
| ! [SY724: $i] :
( ~ ( in @ SY724 @ ( powerset @ SV41 ) )
| ~ ( subset @ SV293 @ ( setminus @ SV41 @ SY724 ) )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV41 )
| ~ ( in @ SY725 @ SY724 )
| ( in @ SY725 @ ( setminus @ SV41 @ SV293 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1109,plain,
! [SV294: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV294 )
!= SV42 )
| ( subset @ SV42 @ SV294 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1110,plain,
! [SV43: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ ( powerset @ SV43 ) )
| ! [SY726: $i] :
( ~ ( in @ SY726 @ ( powerset @ SV43 ) )
| ! [SY727: $i] :
( ~ ( in @ SY727 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SY726 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY727 ) @ ( binunion @ SY726 @ SY727 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1111,plain,
! [SV296: $i,SV44: $i] :
( ( ! [SY728: $i > $i] :
( ~ ! [SY729: $i] :
( ~ ( in @ SY729 @ SV44 )
| ( in @ ( SY728 @ SY729 ) @ SV296 ) )
| ! [SY730: $i] :
( ~ ( in @ SY730 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SX4: $i] : ( SY728 @ SX4 ) )
@ SY730 )
= ( SY728 @ SY730 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1112,plain,
! [SV297: $i,SV45: $i] :
( ( ! [SY732: $i] :
( ~ ( in @ SY732 @ SV45 )
| ~ ~ ( in @ SY732 @ SV297 )
| ( in @ SY732 @ ( symdiff @ SV45 @ SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1113,plain,
! [SV46: $i > $i > $o,SV298: $i] :
( ( ~ ! [SY733: $i] :
( ~ ( in @ SY733 @ SV298 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( SV46 @ SY733 @ SY131 )
| ~ ! [SY132: $i] :
( ~ ( SV46 @ SY733 @ SY132 )
| ( SY131 = SY132 ) ) ) )
| ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1114,plain,
! [SV48: $i] :
( ( ( ~ ( in @ SV48 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(1115,plain,
! [SV299: $i,SV49: $i] :
( ( ! [SY740: $i] :
( ~ ( in @ SY740 @ SV49 )
| ( in @ SY740 @ ( binunion @ SV49 @ SV299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1116,plain,
! [SV50: $i,SV300: $i] :
( ( ~ ( in @ SV300 @ ( powerset @ SV50 ) )
| ! [SY741: $i] :
( ~ ( in @ SY741 @ ( powerset @ SV50 ) )
| ! [SY742: $i] :
( ~ ( in @ SY742 @ SV50 )
| ~ ~ ( in @ SY742 @ SV300 )
| ~ ( in @ SY742 @ ( binintersect @ SV300 @ SY741 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1117,plain,
! [SV301: $i,SV51: $i] :
( ( ! [SY743: $i] :
( ~ ~ ( in @ SY743 @ SV51 )
| ~ ~ ( in @ SY743 @ SV301 )
| ~ ( in @ SY743 @ ( symdiff @ SV51 @ SV301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1118,plain,
! [SV52: $i] :
( ( ( ~ ~ ! [SY144: $i] :
~ ( in @ SY144 @ SV52 ) )
= $true )
| ( ( SV52 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(1119,plain,
! [SV302: $i,SV54: $i] :
( ( ! [SY744: $i] :
( ~ ( func @ SV54 @ SV302 @ SY744 )
| ! [SY745: $i] :
( ~ ( in @ SY745 @ SV54 )
| ( in @ ( ap @ SV54 @ SV302 @ SY744 @ SY745 ) @ SV302 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1120,plain,
! [SV303: $i > $o,SV55: $i] :
( ( ~ ~ ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV55 )
| ~ ( SV303 @ SY746 ) )
| ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1121,plain,
! [SV304: $i,SV56: $i] :
( ( ! [SY748: $i] :
( ~ ( in @ SY748 @ ( binunion @ SV56 @ SV304 ) )
| ( in @ SY748 @ SV56 )
| ( in @ SY748 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1122,plain,
! [SV305: $i,SV57: $i] :
( ( ! [SY749: $i] :
( ~ ( in @ SY749 @ ( binintersect @ SV57 @ SV305 ) )
| ( in @ SY749 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1123,plain,
! [SV306: $i,SV58: $i] :
( ( ~ ( ( SV58 != SV306 ) )
| ~ ( in @ SV306 @ ( setadjoin @ SV58 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1124,plain,
! [SV307: $i > $o,SV59: $i] :
( ( ! [SY750: $i] :
( ~ ( in @ SY750
@ ( dsetconstr @ SV59
@ ^ [SY751: $i] : ( SV307 @ SY751 ) ) )
| ( in @ SY750 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1125,plain,
! [SV308: $i,SV60: $i] :
( ( ! [SY752: $i] :
( ~ ( in @ SY752 @ ( setminus @ SV60 @ SV308 ) )
| ~ ( in @ SY752 @ SV308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1126,plain,
! [SV309: $i,SV61: $i] :
( ( ! [SY753: $i] :
( ~ ( in @ SY753 @ SV61 )
| ~ ( in @ SY753 @ SV309 )
| ( in @ SY753 @ ( binintersect @ SV61 @ SV309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1127,plain,
! [SV62: $i,SV310: $i] :
( ( ~ ( in @ SV310 @ ( powerset @ SV62 ) )
| ! [SY754: $i] :
( ~ ( in @ SY754 @ ( powerset @ SV62 ) )
| ! [SY755: $i] :
( ~ ( in @ SY755 @ ( powerset @ SV62 ) )
| ! [SY756: $i] :
( ~ ( in @ SY756 @ SV62 )
| ~ ( in @ SY756 @ ( binintersect @ SV310 @ SY754 ) )
| ( in @ SY756 @ ( binintersect @ ( binunion @ SV310 @ SY755 ) @ ( binunion @ SY754 @ SY755 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1128,plain,
! [SV311: $i > $o,SV63: $i] :
( ( ~ ~ ! [SY757: $i] :
~ ~ ( ~ ( in @ SY757 @ SV63 )
| ~ ~ ( SV311 @ SY757 ) )
| ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1129,plain,
! [SV64: $o] :
( ( ( ~ SV64 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(1130,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(1131,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[865]) ).
thf(1132,plain,
! [SV65: $i] :
( ( ( ~ ( ( SV65 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( in @ SY170 @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1133,plain,
! [SV66: $i] :
( ( in @ SV66 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(1134,plain,
! [SV312: $i,SV67: $i] :
( ( ! [SY759: $i] :
( ~ ( subset @ SV67 @ SV312 )
| ~ ~ ( in @ SY759 @ SV312 )
| ~ ( in @ SY759 @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1135,plain,
! [SV68: $i,SV313: $i] :
( ( ~ ( in @ SV313 @ ( powerset @ SV68 ) )
| ! [SY760: $i] :
( ~ ( in @ SY760 @ ( powerset @ SV68 ) )
| ~ ! [SY761: $i] :
( ~ ( in @ SY761 @ SV68 )
| ~ ( in @ SY761 @ SV313 )
| ( in @ SY761 @ SY760 ) )
| ( subset @ SV313 @ SY760 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1136,plain,
! [SV314: $i,SV69: $i] :
( ( ( SV69 != SV314 )
| ( ( powerset @ SV69 )
= ( powerset @ SV314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1137,plain,
! [SV315: $i,SV70: $i] :
( ( ! [SY762: $i] :
( ~ ( func @ SV70 @ SV315 @ SY762 )
| ( in @ SY762 @ ( funcSet @ SV70 @ SV315 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1138,plain,
! [SV316: $i,SV71: $i] :
( ( ! [SY763: $i,SY764: $i] :
( ( ( kpair @ SV71 @ SV316 )
!= ( kpair @ SY763 @ SY764 ) )
| ( SV316 = SY764 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1139,plain,
! [SV317: $i,SV72: $i] :
( ( ! [SY765: $i] :
( ~ ( subset @ SV72 @ SV317 )
| ~ ( subset @ SV317 @ SY765 )
| ( subset @ SV72 @ SY765 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1140,plain,
! [SV318: $i,SV73: $i] :
( ( ! [SY766: $i] :
( ~ ( in @ SY766 @ ( funcSet @ SV73 @ SV318 ) )
| ! [SY767: $i] :
( ~ ( in @ SY767 @ SV73 )
| ( ( ap @ SV73 @ SV318 @ SY766 @ SY767 )
= ( ap @ SV73 @ SV318 @ SY766 @ SY767 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1141,plain,
! [SV319: $i,SV74: $i] :
( ( ~ ! [SY768: $i] :
~ ( ~ ( ~ ( in @ SY768 @ SV74 )
| ( in @ SY768 @ SV319 ) )
| ~ ( ~ ( in @ SY768 @ SV319 )
| ( in @ SY768 @ SV74 ) ) )
| ( SV74 = SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1142,plain,
! [SV320: $i,SV75: $i] :
( ( ( SV75 != SV320 )
| ( ( setadjoin @ SV75 @ ( setadjoin @ SV320 @ emptyset ) )
= ( setadjoin @ SV75 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1143,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ~ ! [SY769: $i] :
( ~ ( in @ SY769 @ SV76 )
| ! [SY770: $i] :
( ~ ( in @ SY770 @ SV76 )
| ~ ( SV321 @ SY769 )
| ~ ( SV321 @ SY770 )
| ( SY769 = SY770 ) ) )
| ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1144,plain,
! [SV77: $i,SV322: $i] :
( ( ~ ( in @ SV322 @ ( powerset @ SV77 ) )
| ! [SY773: $i] :
( ~ ( in @ SY773 @ ( powerset @ SV77 ) )
| ! [SY774: $i] :
( ~ ( in @ SY774 @ SV77 )
| ~ ( subset @ SV322 @ SY773 )
| ~ ~ ( in @ SY774 @ SY773 )
| ~ ( in @ SY774 @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1145,plain,
! [SV323: $i,SV78: $i] :
( ( in @ SV78 @ ( setadjoin @ SV78 @ SV323 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1146,plain,
! [SV79: $i,SV324: $i] :
( ( ! [SY775: $i] :
( ~ ( in @ SV324 @ SY775 )
| ~ ( in @ SY775 @ SV79 )
| ( in @ SV324 @ ( setunion @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1147,plain,
! [SV80: $i] :
( ( ( ~ ( iskpair @ SV80 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV80 )
@ ^ [SY201: $i] : ( in @ ( setadjoin @ SY201 @ emptyset ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(1148,plain,
! [SV325: $i,SV81: $i] :
( ( ! [SY776: $i] :
( ~ ( in @ SY776 @ ( funcSet @ SV81 @ SV325 ) )
| ( func @ SV81 @ SV325 @ SY776 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1149,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ( ~ ( ~ ( in @ SV326 @ ( powerset @ SV82 ) )
| ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) )
| ~ ( ~ ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) )
| ( in @ SV326 @ ( powerset @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1150,plain,
! [SV327: $i > $o,SV83: $i] :
( ( ~ ~ ! [SY779: $i] :
~ ~ ( ~ ( in @ SY779 @ SV83 )
| ~ ( SV327 @ SY779 ) )
| ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1151,plain,
! [SV328: $o,SV84: $i] :
( ( ! [SY781: $i] :
( ~ ( in @ SY781 @ SV84 )
| ! [SY782: $i] :
( ~ ( in @ SY782 @ SV84 )
| ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY783: $i] :
( ~ ( ~ SV328
| ( SY783 != SY781 ) )
| ~ ( ~ ~ SV328
| ( SY783 != SY782 ) ) ) )
= ( setadjoin @ SY781 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[885]) ).
thf(1152,plain,
! [SV84: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV84 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV84 )
| ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[885]) ).
thf(1153,plain,
! [SV84: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV84 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV84 )
| ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[885]) ).
thf(1154,plain,
! [SV329: $i,SV85: $i] :
( ( ! [SY784: $i] :
( ~ ( in @ SY784 @ SV85 )
| ! [SY785: $i] :
( ~ ( in @ SY785 @ SV329 )
| ( in @ ( kpair @ SY784 @ SY785 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1155,plain,
! [SV330: $i,SV86: $i] :
( ( ! [SY786: $i] :
( ~ ( func @ SV86 @ SV330 @ SY786 )
| ! [SY787: $i] :
( ~ ( in @ SY787 @ SV86 )
| ! [SY788: $i] :
( ~ ( in @ SY788 @ SV330 )
| ~ ( in @ ( kpair @ SY787 @ SY788 ) @ SY786 )
| ( ( ap @ SV86 @ SV330 @ SY786 @ SY787 )
= SY788 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1156,plain,
! [SV331: $i,SV87: $i] :
( ( ( SV87 != SV331 )
| ( subset @ SV331 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1157,plain,
! [SV88: $o,SV332: $i] :
( ( ~ ( in @ SV332 @ ( prop2set @ SV88 ) )
| SV88 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1158,plain,
! [SV333: $i] :
( ( ~ ( in @ SV333 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1159,plain,
! [SV334: $i] :
( ( ~ ( in @ SV334 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1160,plain,
! [SV89: $i > $o] :
( ( ( ~ ~ ! [SY223: $i] :
~ ~ ( ~ ( SV89 @ SY223 )
| ~ ! [SY224: $i] :
( ~ ( SV89 @ SY224 )
| ( SY223 = SY224 ) ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[892]) ).
thf(1161,plain,
! [SV335: $i,SV90: $i] :
( ( ! [SY789: $i] :
( ~ ( func @ SV90 @ SV335 @ SY789 )
| ! [SY790: $i] :
( ~ ( in @ SY790 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SX4: $i] : ( in @ ( kpair @ SY790 @ SX4 ) @ SY789 ) ) )
@ SV335 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1162,plain,
! [SV336: $i,SV91: $i] :
( ( subset @ ( binintersect @ SV91 @ SV336 ) @ SV336 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1163,plain,
! [SV337: $i > $o,SV92: $i] :
( ( ! [SY792: $i] :
( ~ ( in @ SY792 @ SV92 )
| ~ ( SV337 @ SY792 )
| ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1164,plain,
! [SV338: $i,SV93: $i] :
( ( ! [SY794: $i] :
( ~ ( in @ SY794 @ ( setminus @ SV93 @ SV338 ) )
| ( in @ SY794 @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1165,plain,
! [SV339: $i,SV94: $i] :
( ( ( ( setminus @ SV94 @ SV339 )
!= emptyset )
| ( subset @ SV94 @ SV339 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1166,plain,
! [SV340: $i > $o,SV95: $i] :
( ( ! [SY795: $i] :
( ~ ( in @ SY795 @ SV95 )
| ~ ( ~ ( ~ ( in @ SY795
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SY795 ) )
| ~ ( ~ ( SV340 @ SY795 )
| ( in @ SY795
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1167,plain,
! [SV96: $i,SV341: $i] :
( ( ~ ( in @ SV341 @ ( powerset @ SV96 ) )
| ! [SY798: $i] :
( ~ ( in @ SY798 @ ( powerset @ SV96 ) )
| ! [SY799: $i] :
( ~ ( in @ SY799 @ SV96 )
| ~ ( in @ SY799 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SY798 ) ) )
| ~ ( in @ SY799 @ SV341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1168,plain,
! [SV342: $i,SV97: $i] :
( ( ! [SY800: $i] :
( ~ ( in @ SY800 @ SV97 )
| ! [SY801: $i] :
( ~ ( in @ SY801 @ SV342 )
| ( ( kpair @ SY800 @ SY801 )
= ( kpair @ SY800 @ SY801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1169,plain,
! [SV98: $i,SV343: $i] :
( ( ~ ( in @ SV343 @ ( powerset @ SV98 ) )
| ( in @ ( setminus @ SV98 @ SV343 ) @ ( powerset @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1170,plain,
! [SV99: $o] :
( ( ( ~ SV99 ) = $true )
| ( ( set2prop @ ( prop2set @ SV99 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[902]) ).
thf(1171,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(1172,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(1173,plain,
! [SV344: $i,SV100: $i] :
( ( ( SV100 != SV344 )
| ! [SY802: $i,SY803: $i] :
( ( SY802 != SY803 )
| ~ ( in @ SY802 @ SV100 )
| ( in @ SY803 @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1174,plain,
! [SV101: $i,SV345: $i] :
( ( ~ ( in @ SV345 @ ( powerset @ SV101 ) )
| ! [SY804: $i] :
( ~ ( in @ SY804 @ ( powerset @ SV101 ) )
| ~ ( subset @ ( setminus @ SV101 @ SY804 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SY804 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1175,plain,
! [SV102: $i,SV346: $i] :
( ( ~ ( in @ SV346 @ ( powerset @ SV102 ) )
| ! [SY805: $i] :
( ~ ( in @ SY805 @ ( powerset @ SV102 ) )
| ! [SY806: $i] :
( ~ ( in @ SY806 @ ( powerset @ SV102 ) )
| ! [SY807: $i] :
( ~ ( in @ SY807 @ SV102 )
| ~ ( in @ SY807 @ ( binintersect @ SV346 @ SY805 ) )
| ( in @ SY807 @ ( binunion @ SV346 @ SY806 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1176,plain,
! [SV103: $i,SV347: $i] :
( ( subset @ SV347 @ ( setadjoin @ SV103 @ SV347 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1177,plain,
! [SV348: $i,SV104: $i] :
( ( ! [SY808: $i] :
( ~ ( func @ SV104 @ SV348 @ SY808 )
| ! [SY809: $i] :
( ~ ( in @ SY809 @ SV104 )
| ( in @ ( kpair @ SY809 @ ( ap @ SV104 @ SV348 @ SY808 @ SY809 ) ) @ SY808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1178,plain,
! [SV105: $i] :
( ( ( ~ ( ( SV105 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV105 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1179,plain,
! [SV349: $i,SV106: $i] :
( ( ! [SY810: $i] :
( ~ ( in @ SY810 @ ( cartprod @ SV106 @ SV349 ) )
| ( in @ ( kfst @ SY810 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1180,plain,
! [SV350: $i,SV108: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV108 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV108 @ ( setadjoin @ SV350 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1181,plain,
! [SV351: $i,SV109: $i] :
( ( ! [SY811: $i] :
( ~ ( in @ SY811 @ SV109 )
| ! [SY812: $i] :
( ~ ( in @ SY812 @ SV351 )
| ( in @ ( kpair @ SY811 @ SY812 ) @ ( cartprod @ SV109 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1182,plain,
! [SV110: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ ( powerset @ SV110 ) )
| ! [SY813: $i] :
( ~ ( in @ SY813 @ ( powerset @ SV110 ) )
| ! [SY814: $i] :
( ~ ( in @ SY814 @ ( powerset @ SV110 ) )
| ! [SY815: $i] :
( ~ ( in @ SY815 @ SV110 )
| ~ ( in @ SY815 @ ( binintersect @ SV352 @ SY813 ) )
| ( in @ SY815 @ ( binunion @ SY813 @ SY814 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1183,plain,
! [SV111: $i,SV353: $i] :
( ( ~ ( in @ SV353 @ ( powerset @ SV111 ) )
| ! [SY816: $i] :
( ~ ( in @ SY816 @ ( powerset @ SV111 ) )
| ~ ( subset @ SV353 @ SY816 )
| ( subset @ ( setminus @ SV111 @ SY816 ) @ ( setminus @ SV111 @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1184,plain,
! [SV112: $i,SV354: $i] :
( ( ~ ( in @ SV354 @ ( powerset @ SV112 ) )
| ! [SY817: $i] :
( ~ ( in @ SY817 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV354 @ ( setminus @ SV112 @ SY817 ) )
| ( subset @ SY817 @ ( setminus @ SV112 @ SV354 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1185,plain,
! [SV355: $i,SV113: $i] :
( ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV113 )
| ( in @ SY818 @ SV355 ) )
| ( subset @ SV113 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1186,plain,
! [SV356: $i,SV114: $i] :
( ( ! [SY819: $i] :
( ~ ( in @ SY819 @ SV114 )
| ! [SY820: $i] :
( ~ ( in @ SY820 @ SV356 )
| ( ( kfst @ ( kpair @ SY819 @ SY820 ) )
= SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1187,plain,
! [SV115: $i,SV357: $i] :
( ( ~ ( in @ SV357 @ ( powerset @ SV115 ) )
| ( SV357
= ( setminus @ SV115 @ ( setminus @ SV115 @ SV357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1188,plain,
! [SV358: $o,SV116: $i] :
( ( ! [SY821: $i] :
( ~ ( in @ SY821 @ SV116 )
| ! [SY822: $i] :
( ~ ( in @ SY822 @ SV116 )
| ~ ~ SV358
| ( in @ SY822
@ ( dsetconstr @ SV116
@ ^ [SY823: $i] :
( ~ ( ~ SV358
| ( SY823 != SY821 ) )
| ~ ( ~ ~ SV358
| ( SY823 != SY822 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[921]) ).
thf(1189,plain,
! [SV116: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV116 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV116 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV116
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[921]) ).
thf(1190,plain,
! [SV116: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV116 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV116 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV116
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[921]) ).
thf(1191,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV117 )
| ~ ( SV359 @ SY824 ) )
| ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1192,plain,
! [SV360: $i,SV118: $i] :
( ( ! [SY826: $i] :
( ~ ( func @ SV118 @ SV360 @ SY826 )
| ! [SY827: $i] :
( ~ ( func @ SV118 @ SV360 @ SY827 )
| ~ ! [SY828: $i] :
( ~ ( in @ SY828 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SY826 @ SY828 )
= ( ap @ SV118 @ SV360 @ SY827 @ SY828 ) ) )
| ! [SY829: $i] :
( ~ ( in @ SY829 @ SV118 )
| ! [SY830: $i] :
( ~ ( in @ SY830 @ SV360 )
| ~ ( in @ ( kpair @ SY829 @ SY830 ) @ SY827 )
| ( in @ ( kpair @ SY829 @ SY830 ) @ SY826 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1193,plain,
! [SV361: $i,SV119: $i] :
( ( ~ ( in @ SV119 @ ( setadjoin @ SV361 @ emptyset ) )
| ( SV119 = SV361 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1194,plain,
! [SV120: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ ( powerset @ SV120 ) )
| ! [SY831: $i] :
( ~ ( in @ SY831 @ SV120 )
| ~ ( in @ SY831 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SY831 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1195,plain,
! [SV363: $i,SV121: $i] :
( ( ! [SY832: $i] :
( ~ ( in @ SY832 @ SV121 )
| ! [SY833: $i] :
( ~ ( in @ SY833 @ SV363 )
| ( in @ ( setadjoin @ ( setadjoin @ SY832 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY832 @ ( setadjoin @ SY833 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1196,plain,
! [SV122: $i] :
( ( ( ~ ! [SY302: $i] :
~ ( in @ SY302 @ SV122 ) )
= $true )
| ( ( SV122 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1197,plain,
! [SV124: $i,SV364: $i] :
( ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ SV364 )
| ( in @ SY834 @ SV124 ) )
| ( in @ SV364 @ ( powerset @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1198,plain,
! [SV365: $i,SV125: $i] :
( ( ! [SY835: $i] :
( ~ ( in @ SY835 @ ( cartprod @ SV125 @ SV365 ) )
| ( ( kpair @ ( kfst @ SY835 ) @ ( ksnd @ SY835 ) )
= SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1199,plain,
! [SV366: $i,SV126: $i] :
( ( ! [SY836: $i] :
( ~ ( subset @ SY836 @ ( cartprod @ SV126 @ SV366 ) )
| ! [SY837: $i] :
( ~ ( subset @ SY837 @ ( cartprod @ SV126 @ SV366 ) )
| ~ ! [SY838: $i] :
( ~ ( in @ SY838 @ SV126 )
| ! [SY839: $i] :
( ~ ( in @ SY839 @ SV366 )
| ~ ( in @ ( kpair @ SY838 @ SY839 ) @ SY836 )
| ( in @ ( kpair @ SY838 @ SY839 ) @ SY837 ) ) )
| ( subset @ SY836 @ SY837 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1200,plain,
! [SV127: $i,SV367: $i] :
( ( in @ SV367 @ ( setadjoin @ SV127 @ ( setadjoin @ SV367 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1201,plain,
! [SV368: $i,SV128: $i] :
( ( ! [SY840: $i > $i > $o,SY841: $i] :
( ~ ( in @ SY841 @ SV128 )
| ! [SY842: $i] :
( ~ ( in @ SY842 @ SV368 )
| ~ ( in @ ( kpair @ SY841 @ SY842 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SX5: $i,SX6: $i] : ( SY840 @ SX5 @ SX6 ) ) )
| ( SY840 @ SY841 @ SY842 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1202,plain,
! [SV129: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( powerset @ SV129 ) )
| ! [SY845: $i] :
( ~ ( in @ SY845 @ SV129 )
| ~ ~ ( in @ SY845 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SY845 @ SV369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1203,plain,
! [SV370: $i,SV130: $i] :
( ( ! [SY846: $i,SY847: $i] :
( ~ ( in @ ( kpair @ SY846 @ SY847 ) @ ( cartprod @ SV130 @ SV370 ) )
| ( in @ SY847 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1204,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV131 )
| ! [SY849: $i] :
( ~ ( in @ SY849 @ SV131 )
| ~ ( SV371 @ SY848 )
| ~ ( SV371 @ SY849 )
| ( SY848 = SY849 ) ) )
| ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1205,plain,
! [SV372: $i > $o,SV132: $i] :
( ( ! [SY852: $i] :
( ~ ( in @ SY852
@ ( dsetconstr @ SV132
@ ^ [SY853: $i] : ( SV372 @ SY853 ) ) )
| ( SV372 @ SY852 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1206,plain,
! [SV373: $i,SV133: $i] :
( ( ! [SY854: $i] :
( ~ ( in @ SY854 @ SV133 )
| ~ ~ ( in @ SY854 @ SV373 )
| ( SV133 != SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1207,plain,
! [SV374: $i > $o,SV134: $i] :
( ( in
@ ( dsetconstr @ SV134
@ ^ [SY855: $i] : ( SV374 @ SY855 ) )
@ ( powerset @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1208,plain,
! [SV135: $i,SV375: $i] :
( ( subset @ SV375 @ ( binunion @ SV135 @ SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1209,plain,
! [SV136: $i,SV376: $i] :
( ( ~ ( in @ SV376 @ ( powerset @ SV136 ) )
| ! [SY856: $i] :
( ~ ( in @ SY856 @ ( powerset @ SV136 ) )
| ! [SY857: $i] :
( ~ ( in @ SY857 @ SV136 )
| ~ ( in @ SY857 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SY856 ) ) )
| ( in @ SY857 @ ( setminus @ SV136 @ SV376 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1210,plain,
! [SV377: $i,SV137: $i] :
( ( ( SV137 != SV377 )
| ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV137 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV377 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV377
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1211,plain,
! [SV378: $i,SV138: $i] :
( ( ! [SY864: $i] :
( ~ ( in @ SY864 @ SV138 )
| ! [SY865: $i] :
( ~ ( in @ SY865 @ SV378 )
| ( ( ksnd @ ( kpair @ SY864 @ SY865 ) )
= SY865 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1212,plain,
! [SV379: $i,SV139: $i] :
( ( ! [SY866: $i] :
( ~ ( subset @ SY866 @ SV139 )
| ~ ( subset @ SY866 @ SV379 )
| ( subset @ SY866 @ ( binintersect @ SV139 @ SV379 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1213,plain,
! [SV380: $i,SV140: $i] :
( ( ! [SY867: $i] :
( ~ ( in @ SY867 @ SV140 )
| ~ ~ ( in @ SY867 @ SV380 )
| ~ ( subset @ SV140 @ SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1214,plain,
! [SV141: $i,SV381: $i] :
( ( ~ ( in @ SV381 @ ( powerset @ SV141 ) )
| ! [SY868: $i] :
( ~ ( in @ SY868 @ SV141 )
| ~ ( in @ SY868 @ SV381 )
| ( in @ SY868 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1215,plain,
! [SV142: $i] :
( ( ( ~ ( in @ SV142 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1216,plain,
! [SV382: $i,SV143: $i] :
( ( subset @ ( setminus @ SV143 @ SV382 ) @ SV143 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1217,plain,
! [SV144: $i,SV383: $i] :
( ( ~ ( in @ SV383 @ ( powerset @ SV144 ) )
| ! [SY869: $i] :
( ~ ( in @ SY869 @ ( powerset @ SV144 ) )
| ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SY869 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1218,plain,
! [SV145: $i] :
( ( ( ~ ( subset @ SV145 @ emptyset ) )
= $true )
| ( ( SV145 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1219,plain,
! [SV146: $i > $o] :
( ( ( ~ ~ ! [SY360: $i] :
~ ~ ( ~ ( SV146 @ SY360 )
| ~ ! [SY361: $i] :
( ~ ( SV146 @ SY361 )
| ( SY360 = SY361 ) ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1220,plain,
! [SV147: $i,SV384: $i] :
( ( ~ ( in @ SV384 @ ( powerset @ SV147 ) )
| ! [SY870: $i] :
( ~ ( in @ SY870 @ ( powerset @ SV147 ) )
| ! [SY871: $i] :
( ~ ( in @ SY871 @ SV147 )
| ~ ~ ( in @ SY871 @ ( binunion @ SV384 @ SY870 ) )
| ~ ( in @ SY871 @ SY870 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1221,plain,
! [SV148: $i,SV385: $i] :
( ( ~ ( in @ SV385 @ ( powerset @ SV148 ) )
| ! [SY872: $i] :
( ~ ( in @ SY872 @ ( powerset @ SV148 ) )
| ~ ! [SY873: $i] :
( ~ ( in @ SY873 @ SV148 )
| ~ ( in @ SY873 @ SV385 )
| ( in @ SY873 @ SY872 ) )
| ( in @ SV385 @ ( powerset @ SY872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1222,plain,
! [SV386: $i,SV149: $i] :
( ( ~ ( subset @ SV149 @ SV386 )
| ( subset @ ( powerset @ SV149 ) @ ( powerset @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1223,plain,
! [SV150: $i,SV387: $i] :
( ( in @ SV387 @ ( setadjoin @ SV150 @ ( setadjoin @ SV387 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1224,plain,
! [SV388: $i,SV151: $i] :
( ( ! [SY874: $i] :
( ~ ( subset @ SV151 @ SY874 )
| ( subset @ SV151 @ ( setadjoin @ SV388 @ SY874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1225,plain,
! [SV389: $i,SV152: $i] :
( ( ! [SY875: $i > $i] :
( ~ ! [SY876: $i] :
( ~ ( in @ SY876 @ SV152 )
| ( in @ ( SY875 @ SY876 ) @ SV389 ) )
| ! [SY877: $i] :
( ~ ( in @ SY877 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SX4: $i] : ( SY875 @ SX4 ) )
@ SY877 )
= ( SY875 @ SY877 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1226,plain,
! [SV153: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( powerset @ SV153 ) )
| ! [SY879: $i] :
( ~ ( in @ SY879 @ ( powerset @ SV153 ) )
| ( in @ ( setminus @ SV390 @ SY879 ) @ ( powerset @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1227,plain,
! [SV391: $o,SV154: $i] :
( ( ! [SY880: $i] :
( ~ ( in @ SY880 @ SV154 )
| ! [SY881: $i] :
( ~ ( in @ SY881 @ SV154 )
| ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY882: $i] :
( ~ ( ~ SV391
| ( SY882 != SY880 ) )
| ~ ( ~ ~ SV391
| ( SY882 != SY881 ) ) ) )
= ( setadjoin @ SY881 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[959]) ).
thf(1228,plain,
! [SV154: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV154 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV154 )
| ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[959]) ).
thf(1229,plain,
! [SV154: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV154 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV154 )
| ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[959]) ).
thf(1230,plain,
! [SV392: $i,SV156: $i] :
( ( ! [SY883: $i > $i > $o,SY884: $i,SY885: $i] :
( ~ ( in @ ( kpair @ SY884 @ SY885 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SX5: $i,SX6: $i] : ( SY883 @ SX5 @ SX6 ) ) )
| ( in @ SY885 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1231,plain,
! [SV393: $o,SV157: $i] :
( ( ! [SY888: $i] :
( ~ ( in @ SY888 @ SV157 )
| ! [SY889: $i] :
( ~ ( in @ SY889 @ SV157 )
| ( in @ ( if @ SV157 @ SV393 @ SY888 @ SY889 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[962]) ).
thf(1232,plain,
! [SV157: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV157 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV157 )
| ( in @ ( if @ SV157 @ $true @ SX0 @ SX1 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[962]) ).
thf(1233,plain,
! [SV157: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV157 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV157 )
| ( in @ ( if @ SV157 @ $false @ SX0 @ SX1 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[962]) ).
thf(1234,plain,
! [SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV158 )
| ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) ) )
= $true )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1235,plain,
! [SV159: $i] :
( ( ( ~ ( iskpair @ SV159 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV159 ) @ ( ksnd @ SV159 ) )
= SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1236,plain,
! [SV394: $i,SV160: $i] :
( ( ! [SY890: $i] :
( ~ ( in @ SY890 @ ( setadjoin @ SV160 @ ( setadjoin @ SV394 @ emptyset ) ) )
| ( SY890 = SV160 )
| ( SY890 = SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1237,plain,
! [SV395: $i,SV161: $i] :
( ( ! [SY891: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV161 @ SV395
@ ^ [SX3: $i,SX4: $i] : ( SY891 @ SX3 @ SX4 ) )
@ ( cartprod @ SV161 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1238,plain,
! [SV396: $i,SV162: $i] :
( ( ! [SY894: $i > $i] :
( ~ ! [SY895: $i] :
( ~ ( in @ SY895 @ SV162 )
| ( in @ ( SY894 @ SY895 ) @ SV396 ) )
| ( in
@ ( lam @ SV162 @ SV396
@ ^ [SX3: $i] : ( SY894 @ SX3 ) )
@ ( funcSet @ SV162 @ SV396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1239,plain,
! [SV163: $i,SV397: $i] :
( ( ~ ( in @ SV397 @ ( powerset @ SV163 ) )
| ( subset @ SV397 @ ( setminus @ SV163 @ ( setminus @ SV163 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1240,plain,
! [SV398: $i,SV164: $i] :
( ( ! [SY897: $i > $i > $o,SY898: $i,SY899: $i] :
( ~ ( in @ ( kpair @ SY898 @ SY899 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SX5: $i,SX6: $i] : ( SY897 @ SX5 @ SX6 ) ) )
| ( SY897 @ SY898 @ SY899 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1241,plain,
! [SV399: $i,SV165: $i] :
( ( ~ ( subset @ SV165 @ SV399 )
| ~ ( subset @ SV399 @ SV165 )
| ( SV165 = SV399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1242,plain,
! [SV400: $i,SV166: $i] :
( ( ! [SY902: $i] :
( ~ ( in @ SY902 @ ( binintersect @ SV166 @ SV400 ) )
| ( in @ SY902 @ SV400 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1243,plain,
! [SV167: $i,SV401: $i] :
( ( ~ ( in @ SV401 @ SV167 )
| ( in @ SV401 @ ( powerset @ ( setunion @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1244,plain,
! [SV168: $i,SV402: $i] :
( ( ~ ( in @ SV402 @ ( powerset @ SV168 ) )
| ! [SY903: $i] :
( ~ ( in @ SY903 @ ( powerset @ SV168 ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV168 )
| ~ ( in @ SY904 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY904 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SY903 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1245,plain,
! [SV403: $i > $o,SV169: $i] :
( ( ~ ~ ~ ! [SY905: $i] :
~ ~ ( ~ ( in @ SY905 @ SV169 )
| ~ ( SV403 @ SY905 ) )
| ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1246,plain,
! [SV404: $i,SV170: $i] :
( ( ( ( setadjoin @ SV170 @ emptyset )
!= ( setadjoin @ SV404 @ emptyset ) )
| ( SV170 = SV404 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1247,plain,
! [SV171: $i,SV405: $i] :
( ( ! [SY907: $i] :
( ~ ( in @ SY907 @ SV405 )
| ~ ( in @ SY907 @ ( setminus @ SV171 @ SV405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1248,plain,
! [SV406: $i,SV172: $i] :
( ( ( SV172 != SV406 )
| ( subset @ SV172 @ SV406 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1249,plain,
! [SV173: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ ( powerset @ SV173 ) )
| ( subset @ SV407 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1250,plain,
! [SV408: $i > $o,SV174: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
| ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SV174 )
| ~ ( SV408 @ SY909 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1251,plain,
! [SV409: $i,SV175: $i] :
( ( ! [SY910: $i] :
( ~ ( in @ SY910 @ ( funcSet @ SV175 @ SV409 ) )
| ! [SY911: $i] :
( ~ ( in @ SY911 @ ( funcSet @ SV175 @ SV409 ) )
| ~ ! [SY912: $i] :
( ~ ( in @ SY912 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SY910 @ SY912 )
= ( ap @ SV175 @ SV409 @ SY911 @ SY912 ) ) )
| ( SY910 = SY911 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1252,plain,
! [SV176: $i,SV410: $i] :
( ( ~ ( in @ SV410 @ ( powerset @ SV176 ) )
| ! [SY913: $i] :
( ~ ( in @ SY913 @ SV176 )
| ~ ( in @ SY913 @ SV410 )
| ~ ( in @ SY913 @ ( setminus @ SV176 @ SV410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1253,plain,
! [SV177: $i] :
( ( in @ SV177 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1254,plain,
! [SV178: $i,SV411: $i] :
( ( ! [SY914: $i] :
( ~ ( in @ SY914 @ SV411 )
| ( in @ SY914 @ ( setadjoin @ SV178 @ SV411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1255,plain,
! [SV412: $i,SV180: $i] :
( ( ! [SY915: $i > $i] :
( ~ ! [SY916: $i] :
( ~ ( in @ SY916 @ SV180 )
| ( in @ ( SY915 @ SY916 ) @ SV412 ) )
| ( ( lam @ SV180 @ SV412
@ ^ [SX3: $i] : ( SY915 @ SX3 ) )
= ( lam @ SV180 @ SV412
@ ^ [SX3: $i] : ( SY915 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1256,plain,
! [SV181: $i,SV413: $i] :
( ( ~ ( in @ SV413 @ ( powerset @ SV181 ) )
| ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV181 ) )
| ! [SY920: $o,SY921: $i] :
( ~ ( in @ SY921 @ SV181 )
| ~ ( in @ SY921 @ ( binunion @ SV413 @ SY919 ) )
| ~ ( ~ ( in @ SY921 @ SV413 )
| SY920 )
| ~ ( ~ ( in @ SY921 @ SY919 )
| SY920 )
| SY920 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1257,plain,
! [SV182: $i > $o] :
( ( ( ~ ~ ! [SY449: $i] :
~ ~ ( ~ ( SV182 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV182 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1258,plain,
! [SV414: $i,SV183: $i] :
( ( ( SV183 != SV414 )
| ( ( setunion @ SV183 )
= ( setunion @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1259,plain,
! [SV184: $i,SV415: $i] :
( ( ~ ( in @ SV415 @ ( powerset @ SV184 ) )
| ! [SY922: $i] :
( ~ ( in @ SY922 @ ( powerset @ SV184 ) )
| ( in @ ( binintersect @ SV415 @ SY922 ) @ ( powerset @ SV184 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1260,plain,
! [SV416: $i,SV185: $i] :
( ( ! [SY923: $i] :
( ~ ~ ( in @ SY923 @ ( setminus @ SV185 @ SV416 ) )
| ~ ( in @ SY923 @ SV185 )
| ( in @ SY923 @ SV416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1261,plain,
! [SV187: $i,SV417: $i] :
( ( ~ ( in @ SV417 @ ( powerset @ SV187 ) )
| ! [SY924: $i] :
( ~ ( in @ SY924 @ ( powerset @ SV187 ) )
| ( in @ ( binunion @ SV417 @ SY924 ) @ ( powerset @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1262,plain,
! [SV418: $i,SV188: $i] :
( ( ! [SY925: $i] :
( ~ ( func @ SV188 @ SV418 @ SY925 )
| ! [SY926: $i] :
( ~ ( in @ SY926 @ SV188 )
| ( ( ap @ SV188 @ SV418 @ SY925 @ SY926 )
= ( ap @ SV188 @ SV418 @ SY925 @ SY926 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1263,plain,
! [SV189: $i,SV419: $i] :
( ( ~ ( subset @ SV419 @ SV189 )
| ( ( binintersect @ SV189 @ SV419 )
= SV419 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1264,plain,
! [SV420: $i,SV190: $i] :
( ( ! [SY927: $i] :
( ~ ( in @ SY927 @ ( funcSet @ SV190 @ SV420 ) )
| ! [SY928: $i] :
( ~ ( in @ SY928 @ SV190 )
| ( in @ ( kpair @ SY928 @ ( ap @ SV190 @ SV420 @ SY927 @ SY928 ) ) @ SY927 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1265,plain,
! [SV421: $i > $o,SV191: $i] :
( ( ~ ~ ! [SY929: $i] :
( ~ ( in @ SY929 @ SV191 )
| ( SV421 @ SY929 ) )
| ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1266,plain,
! [SV422: $i,SV192: $i] :
( ( ! [SY931: $i,SY932: $i] :
( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY931 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY931 @ ( setadjoin @ SY932 @ emptyset ) ) @ emptyset ) ) )
| ( SV192 = SY931 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1267,plain,
! [SV423: $i,SV193: $i] :
( ( ! [SY933: $i] :
( ~ ( subset @ SY933 @ ( cartprod @ SV193 @ SV423 ) )
| ! [SY934: $i > $o] :
( ~ ! [SY935: $i] :
( ~ ( in @ SY935 @ SV193 )
| ! [SY936: $i] :
( ~ ( in @ SY936 @ SV423 )
| ~ ( in @ ( kpair @ SY935 @ SY936 ) @ SY933 )
| ( SY934 @ ( kpair @ SY935 @ SY936 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY933 )
| ( SY934 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1268,plain,
! [SV424: $i,SV194: $i] :
( ( ! [SY938: $i] :
( ~ ( in @ SY938 @ ( setadjoin @ SV194 @ SV424 ) )
| ! [SY939: $o] :
( ~ ( ( SY938 != SV194 )
| SY939 )
| ~ ( ~ ( in @ SY938 @ SV424 )
| SY939 )
| SY939 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1269,plain,
! [SV425: $i > $o,SV195: $i] :
( ( ~ ~ ! [SY940: $i] :
( ~ ( in @ SY940 @ SV195 )
| ( SV425 @ SY940 ) )
| ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1270,plain,
! [SV196: $i] :
( ( ! [SY484: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY485: $i] :
( ~ ( in @ SY485 @ SY484 )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY485 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY487: $i,SY488: $i] :
( ~ ~ ( ~ ( in @ SY487 @ SV196 )
| ~ ( in @ SY488 @ SV196 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY484 )
| ~ ( ~ ( ~ ( in @ SY487 @ SX4 )
| ( in @ SY488 @ SX4 ) )
| ~ ( ~ ( in @ SY488 @ SX4 )
| ( in @ SY487 @ SX4 ) ) ) )
| ( SY487 = SY488 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY484 )
| ~ ( in @ SX3 @ SY484 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY494: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY494 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY494 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY484 )
| ~ ( in @ SX4 @ SY494 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY494 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY484 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1271,plain,
! [SV426: $i,SV197: $i] :
( ( in @ SV197 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV197 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV197 @ ( setadjoin @ SV426 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1272,plain,
! [SV427: $i,SV198: $i] :
( ( ~ ( subset @ SV198 @ SV427 )
| ( in @ SV198 @ ( powerset @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1273,plain,
! [SV428: $i > $o,SV199: $i] :
( ( ! [SY942: $i] :
( ~ ( in @ SY942 @ SV199 )
| ~ ( SV428 @ SY942 )
| ~ ! [SY943: $i] :
( ~ ( in @ SY943 @ SV199 )
| ~ ( SV428 @ SY943 )
| ( SY943 = SY942 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1274,plain,
! [SV429: $i,SV200: $i] :
( ( ! [SY945: $i] :
( ~ ( subset @ SV200 @ SV429 )
| ~ ( in @ SY945 @ SV200 )
| ( in @ SY945 @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1275,plain,
! [SV430: $i,SV201: $i] :
( ( ~ ! [SY946: $i] :
( ~ ( in @ SY946 @ SV201 )
| ( in @ SY946 @ SV430 ) )
| ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1276,plain,
! [SV202: $i,SV431: $i] :
( ( ! [SY948: $i] :
( ~ ( in @ SV431 @ ( powerset @ SV202 ) )
| ~ ( in @ SY948 @ SV431 )
| ( in @ SY948 @ SV202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1277,plain,
! [SV432: $i,SV203: $i] :
( ( ! [SY949: $i] :
( ~ ( in @ SY949 @ ( funcSet @ SV203 @ SV432 ) )
| ( ( lam @ SV203 @ SV432
@ ^ [SY950: $i] : ( ap @ SV203 @ SV432 @ SY949 @ SY950 ) )
= SY949 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1278,plain,
! [SV204: $i,SV433: $i] :
( ( ~ ( in @ SV433 @ ( powerset @ SV204 ) )
| ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV204 ) )
| ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SY951 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1279,plain,
! [SV205: $i > $o] :
( ( ( ~ ~ ! [SY520: $i] :
~ ~ ( ~ ( SV205 @ SY520 )
| ~ ! [SY521: $i] :
( ~ ( SV205 @ SY521 )
| ( SY520 = SY521 ) ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1280,plain,
! [SV206: $i] :
( ( ( ~ ( singleton @ SV206 ) )
= $true )
| ( ( in @ ( setunion @ SV206 ) @ SV206 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1281,plain,
! [SV434: $i,SV207: $i] :
( ( ( kfst @ ( kpair @ SV207 @ SV434 ) )
= SV207 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1282,plain,
! [SV208: $i] :
( ( ( ~ ( iskpair @ SV208 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV208 )
@ ^ [SY525: $i] :
( SV208
= ( kpair @ ( kfst @ SV208 ) @ SY525 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1283,plain,
! [SV209: $i > $o] :
( ( ( ~ ~ ! [SY526: $i] :
~ ~ ( ~ ( SV209 @ SY526 )
| ~ ! [SY527: $i] :
( ~ ( SV209 @ SY527 )
| ( SY526 = SY527 ) ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1284,plain,
! [SV210: $i,SV435: $i] :
( ( ~ ( in @ SV435 @ ( setunion @ SV210 ) )
| ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SV210 )
| ~ ( in @ SV435 @ SY952 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1285,plain,
! [SV436: $i,SV211: $i] :
( ( ! [SY953: $i > $i > $o,SY954: $i,SY955: $i] :
( ~ ( in @ ( kpair @ SY954 @ SY955 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SX5: $i,SX6: $i] : ( SY953 @ SX5 @ SX6 ) ) )
| ( in @ SY954 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1286,plain,
! [SV437: $o,SV212: $i] :
( ( ! [SY958: $i] :
( ~ ( in @ SY958 @ SV212 )
| ! [SY959: $i] :
( ~ ( in @ SY959 @ SV212 )
| ( in @ ( if @ SV212 @ SV437 @ SY958 @ SY959 ) @ ( setadjoin @ SY958 @ ( setadjoin @ SY959 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1017]) ).
thf(1287,plain,
! [SV212: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV212 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV212 )
| ( in @ ( if @ SV212 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1017]) ).
thf(1288,plain,
! [SV212: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV212 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV212 )
| ( in @ ( if @ SV212 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1017]) ).
thf(1289,plain,
! [SV438: $i,SV213: $i] :
( ( ! [SY960: $i] :
( ~ ( func @ SV213 @ SV438 @ SY960 )
| ( ( lam @ SV213 @ SV438
@ ^ [SY961: $i] : ( ap @ SV213 @ SV438 @ SY960 @ SY961 ) )
= SY960 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1290,plain,
! [SV439: $i,SV214: $i] :
( ( ! [SY962: $i] :
( ~ ( func @ SV214 @ SV439 @ SY962 )
| ! [SY963: $i] :
( ~ ( in @ SY963 @ SV214 )
| ( singleton
@ ( dsetconstr @ SV439
@ ^ [SX4: $i] : ( in @ ( kpair @ SY963 @ SX4 ) @ SY962 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1291,plain,
! [SV440: $i,SV215: $i] :
( ( ! [SY965: $i > $i] :
( ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SV215 )
| ( in @ ( SY965 @ SY966 ) @ SV440 ) )
| ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SX3: $i,SX4: $i] :
( ( SY965 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1292,plain,
! [SV441: $i,SV216: $i] :
( ( ! [SY969: $i] :
( ~ ( in @ SY969 @ SV216 )
| ! [SY970: $i] :
( ~ ( in @ SY970 @ SV441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY969 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY969 @ ( setadjoin @ SY970 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1293,plain,
! [SV442: $i,SV217: $i] :
( ( ! [SY971: $i] :
( ~ ( in @ ( setadjoin @ SY971 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ ( setadjoin @ SV442 @ emptyset ) ) @ emptyset ) ) )
| ( SV217 = SY971 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1022]) ).
thf(1294,plain,
! [SV443: $i,SV218: $i] :
( ( in @ SV218 @ ( setadjoin @ SV218 @ ( setadjoin @ SV443 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1295,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ( ~ ( ~ ( in @ SV444 @ ( setunion @ SV219 ) )
| ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
| ~ ( ~ ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) )
| ( in @ SV444 @ ( setunion @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1296,plain,
! [SV445: $i,SV220: $i] :
( ( ~ ~ ~ ! [SY974: $i] :
~ ~ ( ~ ( in @ SY974 @ SV220 )
| ~ ( in @ SY974 @ SV445 ) )
| ( ( binintersect @ SV220 @ SV445 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1297,plain,
! [SV221: $i,SV446: $i] :
( ( in @ SV446 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV221 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV221 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1298,plain,
! [SV222: $i,SV447: $i] :
( ( ~ ( in @ SV447 @ ( powerset @ SV222 ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ ( powerset @ SV222 ) )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV222 )
| ~ ( in @ SY976 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY976 @ ( binintersect @ SV447 @ SY975 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1299,plain,
! [SV448: $i,SV223: $i] :
( ( ! [SY977: $i,SY978: $i] :
( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY977 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY977 @ ( setadjoin @ SY978 @ emptyset ) ) @ emptyset ) ) )
| ( SY977 != SY978 )
| ( SV448 = SY978 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1300,plain,
! [SV224: $i,SV449: $i] :
( ( ~ ( in @ SV449 @ ( powerset @ SV224 ) )
| ! [SY979: $i] :
( ~ ( in @ SY979 @ ( powerset @ SV224 ) )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV224 )
| ~ ~ ( in @ SY980 @ SV449 )
| ~ ~ ( in @ SY980 @ SY979 )
| ~ ( in @ SY980 @ ( binunion @ SV449 @ SY979 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1301,plain,
( ( ~ ( in @ sK2_SY0 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1302,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1030]) ).
thf(1303,plain,
! [SV450: $i,SV225: $i] :
( ( ~ ( in @ SV225 @ ( setadjoin @ SV450 @ emptyset ) )
| ( in @ SV450 @ ( setadjoin @ SV225 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1304,plain,
! [SV451: $o,SV226: $i] :
( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV226 )
| ! [SY982: $i] :
( ~ ( in @ SY982 @ SV226 )
| ~ SV451
| ( ( if @ SV226 @ SV451 @ SY981 @ SY982 )
= SY981 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1032]) ).
thf(1305,plain,
! [SV226: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV226 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV226 )
| ~ $true
| ( ( if @ SV226 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1032]) ).
thf(1306,plain,
! [SV226: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV226 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV226 )
| ~ $false
| ( ( if @ SV226 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1032]) ).
thf(1307,plain,
! [SV227: $i > $o] :
( ( ( ~ ~ ! [SY577: $i] :
~ ~ ( ~ ( SV227 @ SY577 )
| ~ ! [SY578: $i] :
( ~ ( SV227 @ SY578 )
| ( SY577 = SY578 ) ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1308,plain,
! [SV228: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ ( powerset @ SV228 ) )
| ! [SY983: $i] :
( ~ ( in @ SY983 @ ( powerset @ SV228 ) )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SY983 ) )
| ~ ( in @ SY984 @ SY983 )
| ~ ( in @ SY984 @ SV452 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1309,plain,
! [SV453: $o,SV229: $i] :
( ( ! [SY985: $i] :
( ~ ( in @ SY985 @ SV229 )
| ! [SY986: $i] :
( ~ ( in @ SY986 @ SV229 )
| ~ SV453
| ( in @ SY985
@ ( dsetconstr @ SV229
@ ^ [SY987: $i] :
( ~ ( ~ SV453
| ( SY987 != SY985 ) )
| ~ ( ~ ~ SV453
| ( SY987 != SY986 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1035]) ).
thf(1310,plain,
! [SV229: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV229 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV229 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV229
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1035]) ).
thf(1311,plain,
! [SV229: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV229 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV229 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV229
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1035]) ).
thf(1312,plain,
! [SV454: $i,SV230: $i] :
( ( ! [SY988: $i] :
( ( binintersect @ SV230 @ ( binunion @ SV454 @ SY988 ) )
= ( binunion @ ( binintersect @ SV230 @ SV454 ) @ ( binintersect @ SV230 @ SY988 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1313,plain,
! [SV455: $i,SV231: $i] :
( ( ! [SY989: $i] :
( ( ( setadjoin @ SV231 @ ( setadjoin @ SV455 @ emptyset ) )
!= ( setadjoin @ SY989 @ emptyset ) )
| ( SV231 = SV455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1314,plain,
! [SV232: $i > $o,SV456: $i] :
( ( ~ ( in @ SV456 @ emptyset )
| ( SV232 @ SV456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1315,plain,
! [SV233: $i,SV457: $i] :
( ( ~ ( subset @ SV457 @ SV233 )
| ( in @ SV457 @ ( powerset @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1316,plain,
! [SV458: $i,SV234: $i] :
( ( ! [SY990: $i] :
( ~ ( in @ SY990 @ ( cartprod @ SV234 @ SV458 ) )
| ( in @ ( ksnd @ SY990 ) @ SV458 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1317,plain,
! [SV459: $i,SV235: $i] :
( ( ! [SY991: $i,SY992: $o] :
( ~ ( in @ SY991 @ ( binunion @ SV235 @ SV459 ) )
| ~ ( ~ ( in @ SY991 @ SV235 )
| SY992 )
| ~ ( ~ ( in @ SY991 @ SV459 )
| SY992 )
| SY992 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1318,plain,
! [SV460: $i,SV236: $i] :
( ( ! [SY993: $i,SY994: $i] :
( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SV460 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY993 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY993 @ ( setadjoin @ SY994 @ emptyset ) ) @ emptyset ) ) )
| ( SV460 = SY994 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1319,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ~ ! [SY995: $i,SY996: $i] :
( ( SY995 != SY996 )
| ~ ( ~ ( ~ ( SV237 @ SY995 )
| ( SV461 @ SY996 ) )
| ~ ( ~ ( SV461 @ SY996 )
| ( SV237 @ SY995 ) ) ) )
| ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1320,plain,
! [SV238: $i,SV462: $i] :
( ( ~ ( in @ SV462 @ SV238 )
| ( in @ ( setadjoin @ SV462 @ emptyset ) @ ( powerset @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1321,plain,
! [SV463: $i > $o,SV239: $i] :
( ( ~ ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
| ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV239 )
| ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV239 )
| ~ ( SV463 @ SY1004 )
| ~ ( SV463 @ SY1005 )
| ( SY1004 = SY1005 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1322,plain,
! [SV464: $i,SV240: $i] :
( ( ! [SY1006: $i] :
( ~ ( in @ SY1006 @ SV240 )
| ~ ~ ( in @ SY1006 @ SV464 )
| ( in @ SY1006 @ ( setminus @ SV240 @ SV464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1323,plain,
! [SV465: $i,SV241: $i] :
( ( ! [SY1007: $i] :
( ~ ~ ( in @ SY1007 @ SV241 )
| ~ ( in @ SY1007 @ SV465 )
| ( in @ SY1007 @ ( symdiff @ SV241 @ SV465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1324,plain,
! [SV242: $i,SV466: $i] :
( ( ~ ( in @ SV466 @ ( powerset @ SV242 ) )
| ! [SY1008: $i] :
( ~ ( in @ SY1008 @ ( powerset @ SV242 ) )
| ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV242 )
| ~ ~ ( in @ SY1009 @ SY1008 )
| ~ ( in @ SY1009 @ ( binintersect @ SV466 @ SY1008 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1325,plain,
! [SV467: $o,SV243: $i] :
( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV243 )
| ! [SY1011: $i] :
( ~ ( in @ SY1011 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1012: $i] :
( ~ ( ~ SV467
| ( SY1012 != SY1010 ) )
| ~ ( ~ ~ SV467
| ( SY1012 != SY1011 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1049]) ).
thf(1326,plain,
! [SV243: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV243 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1049]) ).
thf(1327,plain,
! [SV243: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV243 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1049]) ).
thf(1328,plain,
! [SV468: $i,SV244: $i] :
( ( ! [SY1013: $i] :
( ~ ( in @ SY1013 @ SV244 )
| ! [SY1014: $i] :
( ~ ( in @ SY1014 @ SV468 )
| ( in @ ( setadjoin @ SY1013 @ ( setadjoin @ SY1014 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1329,plain,
! [SV469: $i,SV245: $i] :
( ( subset @ SV245 @ ( binunion @ SV245 @ SV469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1330,plain,
! [SV470: $i,SV246: $i] :
( ( ! [SY1015: $i] :
( ~ ( in @ SY1015 @ SV246 )
| ! [SY1016: $i] :
( ~ ( in @ SY1016 @ SV470 )
| ( subset @ ( setadjoin @ SY1015 @ ( setadjoin @ SY1016 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1331,plain,
! [SV471: $i,SV247: $i] :
( ( ! [SY1017: $i] :
( ~ ( func @ SV247 @ SV471 @ SY1017 )
| ! [SY1018: $i] :
( ~ ( func @ SV247 @ SV471 @ SY1018 )
| ~ ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SY1017 @ SY1019 )
= ( ap @ SV247 @ SV471 @ SY1018 @ SY1019 ) ) )
| ( SY1017 = SY1018 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1332,plain,
! [SV248: $i,SV472: $i] :
( ( ! [SY1020: $i] :
( ~ ( in @ SY1020 @ SV472 )
| ( in @ SY1020 @ ( binunion @ SV248 @ SV472 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1333,plain,
! [SV249: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ ( powerset @ SV249 ) )
| ! [SY1021: $i] :
( ~ ( in @ SY1021 @ ( powerset @ SV249 ) )
| ! [SY1022: $i] :
( ~ ( in @ SY1022 @ SV249 )
| ~ ~ ( in @ SY1022 @ ( binunion @ SV473 @ SY1021 ) )
| ~ ( in @ SY1022 @ SV473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1334,plain,
! [SV474: $i > $o,SV250: $i] :
( ( ! [SY1023: $i] :
( ~ ( in @ SY1023 @ SV250 )
| ~ ( SV474 @ SY1023 )
| ( in @ SY1023
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1335,plain,
! [SV251: $i,SV475: $i] :
( ( in @ SV475 @ ( setadjoin @ SV251 @ ( setadjoin @ SV475 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1336,plain,
! [SV476: $i,SV252: $i] :
( ( ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV252 )
| ~ ( in @ SY1025 @ SV476 )
| ~ ( in @ SY1025 @ ( symdiff @ SV252 @ SV476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1337,plain,
! [SV253: $i,SV477: $i] :
( ( ~ ( in @ SV477 @ ( powerset @ SV253 ) )
| ( in @ ( powerset @ SV477 ) @ ( powerset @ ( powerset @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1338,plain,
! [SV478: $i,SV254: $i] :
( ( ! [SY1026: $i] :
( ~ ( in @ SY1026 @ ( cartprod @ SV254 @ SV478 ) )
| ( iskpair @ SY1026 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1339,plain,
! [SV479: $i,SV255: $i] :
( ( subset @ ( binintersect @ SV255 @ SV479 ) @ SV255 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1340,plain,
! [SV480: $i,SV256: $i] :
( ( ( SV256 != SV480 )
| ! [SY1027: $i,SY1028: $i] :
( ( SY1027 != SY1028 )
| ( ( setadjoin @ SV256 @ SY1027 )
= ( setadjoin @ SV480 @ SY1028 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1341,plain,
! [SV481: $i,SV258: $i] :
( ( ( SV258 != SV481 )
| ( in @ SV258 @ ( setadjoin @ SV481 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1342,plain,
! [SV259: $i,SV482: $i] :
( ( ~ ( in @ SV482 @ ( powerset @ SV259 ) )
| ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV259 ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV259 )
| ~ ( in @ SY1030 @ SV482 )
| ( in @ SY1030 @ SY1029 ) )
| ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV259 )
| ~ ( in @ SY1031 @ SY1029 )
| ( in @ SY1031 @ SV482 ) )
| ( SV482 = SY1029 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1343,plain,
! [SV483: $i,SV260: $i] :
( ( ! [SY1032: $i] :
( ~ ( in @ SY1032 @ ( cartprod @ SV260 @ SV483 ) )
| ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV260 )
| ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV483 )
| ( SY1032
!= ( kpair @ SY1033 @ SY1034 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1344,plain,
! [SV261: $i,SV1: $i,SV484: $i] :
( ( ~ ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
| ! [SY1035: $i > $o] :
( ~ ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV1 )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV261 )
| ~ ( in @ ( kpair @ SY1036 @ SY1037 ) @ SV484 )
| ( SY1035 @ ( kpair @ SY1036 @ SY1037 ) ) ) )
| ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV484 )
| ( SY1035 @ SY1038 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1345,plain,
! [SV262: $i,SV2: $i] :
( ( ( SV2 != SV262 )
= $true )
| ( ( ! [SY670: $i,SY671: $i] :
( ( SY670 != SY671 )
| ~ ( ~ ( ~ ( in @ SY670 @ SV2 )
| ( in @ SY671 @ SV262 ) )
| ~ ( ~ ( in @ SY671 @ SV262 )
| ( in @ SY670 @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1346,plain,
! [SV3: $i,SV263: $i] :
( ( ( ~ ( in @ SV263 @ ( powerset @ SV3 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV263 ) ) @ SV263 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1347,plain,
! [SV264: $i,SV4: $i,SV485: $i] :
( ( ~ ( in @ SV485 @ ( setadjoin @ SV4 @ ( setadjoin @ SV264 @ emptyset ) ) )
| ( SV485 = SV4 )
| ( SV485 = SV264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1348,plain,
! [SV265: $i,SV5: $i,SV486: $i] :
( ( ~ ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
| ! [SY1039: $i] :
( ~ ( subset @ SY1039 @ ( cartprod @ SV5 @ SV265 ) )
| ~ ! [SY1040: $i] :
( ~ ( in @ SY1040 @ SV5 )
| ! [SY1041: $i] :
( ~ ( in @ SY1041 @ SV265 )
| ~ ( in @ ( kpair @ SY1040 @ SY1041 ) @ SV486 )
| ( in @ ( kpair @ SY1040 @ SY1041 ) @ SY1039 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ SV5 )
| ! [SY1043: $i] :
( ~ ( in @ SY1043 @ SV265 )
| ~ ( in @ ( kpair @ SY1042 @ SY1043 ) @ SY1039 )
| ( in @ ( kpair @ SY1042 @ SY1043 ) @ SV486 ) ) )
| ( SV486 = SY1039 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1349,plain,
! [SV6: $i] :
( ( ( ! [SY25: $i] :
~ ( in @ SY25 @ SV6 ) )
= $false )
| ( ( SV6 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1350,plain,
! [SV7: $i] :
( ( ( singleton @ SV7 )
= $false )
| ( ( ! [SY26: $i] :
( ~ ( in @ SY26 @ SV7 )
| ( ( setunion @ SV7 )
= SY26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1351,plain,
! [SV266: $i,SV8: $i] :
( ( ( ~ ! [SY679: $i] :
( ~ ( in @ SY679 @ SV8 )
| ( in @ SY679 @ SV266 ) ) )
= $true )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1352,plain,
! [SV9: $i] :
( ( ( ~ ! [SY29: $i] :
~ ( in @ SY29 @ SV9 ) )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1353,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( setunion @ SV10 ) ) )
= $true )
| ( ( ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV267 @ SY681 )
| ~ ( in @ SY681 @ SV10 )
| SY680 )
| SY680 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1354,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( ~ ( ~ ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
| ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ~ ( ~ ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1355,plain,
! [SV12: $i > $o] :
( ( ( ~ ! [SY37: $i] :
~ ! [SY38: $i] :
~ ( ~ ( ~ ( SV12 @ SY38 )
| ( SY38 = SY37 ) )
| ~ ( ( SY38 != SY37 )
| ( SV12 @ SY38 ) ) ) )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1078]) ).
thf(1356,plain,
! [SV13: $i > $o] :
( ( ( ~ ! [SY41: $i] :
~ ( SV13 @ SY41 ) )
= $false )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1357,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ~ ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
| ! [SY1044: $o] :
( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SY1044 )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SY1044 )
| SY1044 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1358,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY685: $i,SY686: $i] :
( ( SY685 != SY686 )
| ~ ( ~ ( ~ ( SV15 @ SY685 )
| ( SV270 @ SY686 ) )
| ~ ( ~ ( SV270 @ SY686 )
| ( SV15 @ SY685 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1359,plain,
! [SV271: $i,SV16: $i,SV489: $i] :
( ( ~ ~ ( in @ SV489 @ SV16 )
| ~ ( in @ SV489 @ ( setminus @ SV16 @ SV271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1360,plain,
! [SV18: $i] :
( ( ( in @ SV18 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV18 @ SV18 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1083]) ).
thf(1361,plain,
! [SV19: $i > $o] :
( ( ( ~ ! [SY62: $i] :
~ ~ ( ~ ( SV19 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( SV19 @ SY63 )
| ( SY62 = SY63 ) ) ) )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1362,plain,
! [SV272: $i,SV20: $i] :
( ( ( ~ ~ ( subset @ SV20 @ SV272 ) )
= $true )
| ( ( SV20 != SV272 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1363,plain,
! [SV21: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ! [SY696: $i] :
( ~ ( in @ SY696 @ ( powerset @ SV21 ) )
| ! [SY697: $i] :
( ~ ( in @ SY697 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SY696 ) )
| ~ ( in @ SY697 @ SV273 )
| ( in @ SY697 @ SY696 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1086]) ).
thf(1364,plain,
! [SV274: $i,SV22: $i,SV490: $i] :
( ( ~ ~ ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
| ~ ~ ( in @ SV490 @ SV274 )
| ~ ( in @ SV490 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1365,plain,
! [SV23: $i,SV275: $i] :
( ( ( ~ ( in @ SV275 @ SV23 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV275 @ emptyset ) @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1088]) ).
thf(1366,plain,
! [SV276: $i,SV24: $i,SV491: $i] :
( ( ~ ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) )
| ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV24 )
| ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SY1045 ) @ SV276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1367,plain,
! [SV492: $i,SV278: $i,SV26: $i] :
( ( ! [SY1046: $i] :
( ( ( kpair @ SV26 @ SV278 )
!= ( kpair @ SV492 @ SY1046 ) )
| ( SV26 = SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1368,plain,
! [SV279: $i,SV27: $i,SV493: $i] :
( ( ! [SY1047: $i] :
( ~ ( in @ ( kpair @ SV493 @ SY1047 ) @ ( cartprod @ SV27 @ SV279 ) )
| ( in @ SV493 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1369,plain,
! [SV494: $i > $i > $o,SV281: $i,SV29: $i] :
( ( ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV29 )
| ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV281 )
| ~ ( SV494 @ SY1048 @ SY1049 )
| ( in @ ( kpair @ SY1048 @ SY1049 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1370,plain,
! [SV495: $i > $i > $o,SV282: $i,SV30: $i] :
( ( subset
@ ( dpsetconstr @ SV30 @ SV282
@ ^ [SY1052: $i,SY1053: $i] : ( SV495 @ SY1052 @ SY1053 ) )
@ ( cartprod @ SV30 @ SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1371,plain,
! [SV283: $i,SV31: $i,SV496: $i] :
( ( ~ ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
| ! [SY1054: $i] :
( ~ ( in @ SY1054 @ SV31 )
| ! [SY1055: $i] :
( ~ ( in @ SY1055 @ SV283 )
| ~ ( in @ ( kpair @ SY1054 @ SY1055 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SY1054 )
= SY1055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1372,plain,
! [SV284: $i,SV32: $i] :
( ( ( SV32 != SV284 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV32 @ ( setadjoin @ SV284 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1097]) ).
thf(1373,plain,
! [SV285: $i,SV33: $i,SV497: $i] :
( ( ~ ( in @ SV497 @ ( setadjoin @ SV33 @ SV285 ) )
| ( SV497 = SV33 )
| ( in @ SV497 @ SV285 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1374,plain,
! [SV287: $o,SV35: $i,SV498: $i] :
( ( ~ ( in @ SV498 @ SV35 )
| ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV35 )
| ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SY1056 )
= SY1056 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1375,plain,
! [SV35: $i,SV499: $i] :
( ( ~ ( in @ SV499 @ SV35 )
| ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV35 )
| ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SY1057 )
= SY1057 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1376,plain,
! [SV35: $i,SV500: $i] :
( ( ~ ( in @ SV500 @ SV35 )
| ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV35 )
| ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SY1058 )
= SY1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1377,plain,
! [SV288: $i,SV501: $i > $i,SV36: $i] :
( ( ~ ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV36 )
| ( in @ ( SV501 @ SY1059 ) @ SV288 ) )
| ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1378,plain,
! [SV289: $i,SV37: $i,SV502: $i] :
( ( ~ ( in @ SV502 @ SV37 )
| ( in @ ( setadjoin @ SV502 @ emptyset ) @ ( powerset @ ( binunion @ SV37 @ SV289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1379,plain,
! [SV290: $i,SV38: $i] :
( ( ( ~ ( subset @ SV38 @ SV290 ) )
= $true )
| ( ( ( binintersect @ SV38 @ SV290 )
= SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1105]) ).
thf(1380,plain,
! [SV291: $i,SV39: $i] :
( ( ( ( binintersect @ SV39 @ SV291 )
!= SV291 )
= $true )
| ( ( subset @ SV291 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1381,plain,
! [SV292: $i,SV40: $i] :
( ( ( ~ ( subset @ SV40 @ SV292 ) )
= $true )
| ( ( ( setminus @ SV40 @ SV292 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1107]) ).
thf(1382,plain,
! [SV41: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( ! [SY724: $i] :
( ~ ( in @ SY724 @ ( powerset @ SV41 ) )
| ~ ( subset @ SV293 @ ( setminus @ SV41 @ SY724 ) )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV41 )
| ~ ( in @ SY725 @ SY724 )
| ( in @ SY725 @ ( setminus @ SV41 @ SV293 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1383,plain,
! [SV294: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV294 )
!= SV42 )
= $true )
| ( ( subset @ SV42 @ SV294 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1109]) ).
thf(1384,plain,
! [SV43: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ ( powerset @ SV43 ) )
| ! [SY727: $i] :
( ~ ( in @ SY727 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SY726 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY727 ) @ ( binunion @ SY726 @ SY727 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1385,plain,
! [SV296: $i,SV503: $i > $i,SV44: $i] :
( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV44 )
| ( in @ ( SV503 @ SY1061 ) @ SV296 ) )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1386,plain,
! [SV297: $i,SV45: $i,SV504: $i] :
( ( ~ ( in @ SV504 @ SV45 )
| ~ ~ ( in @ SV504 @ SV297 )
| ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1387,plain,
! [SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ! [SY733: $i] :
( ~ ( in @ SY733 @ SV298 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( SV46 @ SY733 @ SY131 )
| ~ ! [SY132: $i] :
( ~ ( SV46 @ SY733 @ SY132 )
| ( SY131 = SY132 ) ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1113]) ).
thf(1388,plain,
! [SV48: $i] :
( ( ( in @ SV48 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1389,plain,
! [SV299: $i,SV49: $i,SV505: $i] :
( ( ~ ( in @ SV505 @ SV49 )
| ( in @ SV505 @ ( binunion @ SV49 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1390,plain,
! [SV50: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( ! [SY741: $i] :
( ~ ( in @ SY741 @ ( powerset @ SV50 ) )
| ! [SY742: $i] :
( ~ ( in @ SY742 @ SV50 )
| ~ ~ ( in @ SY742 @ SV300 )
| ~ ( in @ SY742 @ ( binintersect @ SV300 @ SY741 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1116]) ).
thf(1391,plain,
! [SV301: $i,SV51: $i,SV506: $i] :
( ( ~ ~ ( in @ SV506 @ SV51 )
| ~ ~ ( in @ SV506 @ SV301 )
| ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1392,plain,
! [SV52: $i] :
( ( ( ~ ! [SY144: $i] :
~ ( in @ SY144 @ SV52 ) )
= $false )
| ( ( SV52 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1393,plain,
! [SV507: $i,SV302: $i,SV54: $i] :
( ( ~ ( func @ SV54 @ SV302 @ SV507 )
| ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV54 )
| ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SY1064 ) @ SV302 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1394,plain,
! [SV303: $i > $o,SV55: $i] :
( ( ( ~ ~ ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV55 )
| ~ ( SV303 @ SY746 ) ) )
= $true )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1120]) ).
thf(1395,plain,
! [SV304: $i,SV56: $i,SV508: $i] :
( ( ~ ( in @ SV508 @ ( binunion @ SV56 @ SV304 ) )
| ( in @ SV508 @ SV56 )
| ( in @ SV508 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1396,plain,
! [SV305: $i,SV57: $i,SV509: $i] :
( ( ~ ( in @ SV509 @ ( binintersect @ SV57 @ SV305 ) )
| ( in @ SV509 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1397,plain,
! [SV306: $i,SV58: $i] :
( ( ( ~ ( ( SV58 != SV306 ) ) )
= $true )
| ( ( ~ ( in @ SV306 @ ( setadjoin @ SV58 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1398,plain,
! [SV307: $i > $o,SV59: $i,SV510: $i] :
( ( ~ ( in @ SV510
@ ( dsetconstr @ SV59
@ ^ [SY751: $i] : ( SV307 @ SY751 ) ) )
| ( in @ SV510 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1399,plain,
! [SV308: $i,SV60: $i,SV511: $i] :
( ( ~ ( in @ SV511 @ ( setminus @ SV60 @ SV308 ) )
| ~ ( in @ SV511 @ SV308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1400,plain,
! [SV309: $i,SV61: $i,SV512: $i] :
( ( ~ ( in @ SV512 @ SV61 )
| ~ ( in @ SV512 @ SV309 )
| ( in @ SV512 @ ( binintersect @ SV61 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1401,plain,
! [SV62: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ! [SY754: $i] :
( ~ ( in @ SY754 @ ( powerset @ SV62 ) )
| ! [SY755: $i] :
( ~ ( in @ SY755 @ ( powerset @ SV62 ) )
| ! [SY756: $i] :
( ~ ( in @ SY756 @ SV62 )
| ~ ( in @ SY756 @ ( binintersect @ SV310 @ SY754 ) )
| ( in @ SY756 @ ( binintersect @ ( binunion @ SV310 @ SY755 ) @ ( binunion @ SY754 @ SY755 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1127]) ).
thf(1402,plain,
! [SV311: $i > $o,SV63: $i] :
( ( ( ~ ~ ! [SY757: $i] :
~ ~ ( ~ ( in @ SY757 @ SV63 )
| ~ ~ ( SV311 @ SY757 ) ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1403,plain,
! [SV64: $o] :
( ( SV64 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1129]) ).
thf(1404,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1405,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1131]) ).
thf(1406,plain,
! [SV65: $i] :
( ( ( SV65 != emptyset )
= $false )
| ( ( ~ ! [SY170: $i] :
~ ( in @ SY170 @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1407,plain,
! [SV513: $i,SV312: $i,SV67: $i] :
( ( ~ ( subset @ SV67 @ SV312 )
| ~ ~ ( in @ SV513 @ SV312 )
| ~ ( in @ SV513 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1408,plain,
! [SV68: $i,SV313: $i] :
( ( ( ~ ( in @ SV313 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ! [SY760: $i] :
( ~ ( in @ SY760 @ ( powerset @ SV68 ) )
| ~ ! [SY761: $i] :
( ~ ( in @ SY761 @ SV68 )
| ~ ( in @ SY761 @ SV313 )
| ( in @ SY761 @ SY760 ) )
| ( subset @ SV313 @ SY760 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1135]) ).
thf(1409,plain,
! [SV314: $i,SV69: $i] :
( ( ( SV69 != SV314 )
= $true )
| ( ( ( powerset @ SV69 )
= ( powerset @ SV314 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1410,plain,
! [SV514: $i,SV315: $i,SV70: $i] :
( ( ~ ( func @ SV70 @ SV315 @ SV514 )
| ( in @ SV514 @ ( funcSet @ SV70 @ SV315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1411,plain,
! [SV515: $i,SV316: $i,SV71: $i] :
( ( ! [SY1066: $i] :
( ( ( kpair @ SV71 @ SV316 )
!= ( kpair @ SV515 @ SY1066 ) )
| ( SV316 = SY1066 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1412,plain,
! [SV516: $i,SV317: $i,SV72: $i] :
( ( ~ ( subset @ SV72 @ SV317 )
| ~ ( subset @ SV317 @ SV516 )
| ( subset @ SV72 @ SV516 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1413,plain,
! [SV318: $i,SV73: $i,SV517: $i] :
( ( ~ ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) )
| ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV73 )
| ( ( ap @ SV73 @ SV318 @ SV517 @ SY1067 )
= ( ap @ SV73 @ SV318 @ SV517 @ SY1067 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1414,plain,
! [SV319: $i,SV74: $i] :
( ( ( ~ ! [SY768: $i] :
~ ( ~ ( ~ ( in @ SY768 @ SV74 )
| ( in @ SY768 @ SV319 ) )
| ~ ( ~ ( in @ SY768 @ SV319 )
| ( in @ SY768 @ SV74 ) ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1415,plain,
! [SV320: $i,SV75: $i] :
( ( ( SV75 != SV320 )
= $true )
| ( ( ( setadjoin @ SV75 @ ( setadjoin @ SV320 @ emptyset ) )
= ( setadjoin @ SV75 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1142]) ).
thf(1416,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY769: $i] :
( ~ ( in @ SY769 @ SV76 )
| ! [SY770: $i] :
( ~ ( in @ SY770 @ SV76 )
| ~ ( SV321 @ SY769 )
| ~ ( SV321 @ SY770 )
| ( SY769 = SY770 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1417,plain,
! [SV77: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ! [SY773: $i] :
( ~ ( in @ SY773 @ ( powerset @ SV77 ) )
| ! [SY774: $i] :
( ~ ( in @ SY774 @ SV77 )
| ~ ( subset @ SV322 @ SY773 )
| ~ ~ ( in @ SY774 @ SY773 )
| ~ ( in @ SY774 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1418,plain,
! [SV79: $i,SV518: $i,SV324: $i] :
( ( ~ ( in @ SV324 @ SV518 )
| ~ ( in @ SV518 @ SV79 )
| ( in @ SV324 @ ( setunion @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1419,plain,
! [SV80: $i] :
( ( ( iskpair @ SV80 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV80 )
@ ^ [SY201: $i] : ( in @ ( setadjoin @ SY201 @ emptyset ) @ SV80 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1420,plain,
! [SV325: $i,SV81: $i,SV519: $i] :
( ( ~ ( in @ SV519 @ ( funcSet @ SV81 @ SV325 ) )
| ( func @ SV81 @ SV325 @ SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1421,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ( ~ ( in @ SV326 @ ( powerset @ SV82 ) )
| ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) )
| ~ ( ~ ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) )
| ( in @ SV326 @ ( powerset @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1422,plain,
! [SV327: $i > $o,SV83: $i] :
( ( ( ~ ~ ! [SY779: $i] :
~ ~ ( ~ ( in @ SY779 @ SV83 )
| ~ ( SV327 @ SY779 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1423,plain,
! [SV328: $o,SV84: $i,SV520: $i] :
( ( ~ ( in @ SV520 @ SV84 )
| ! [SY1068: $i] :
( ~ ( in @ SY1068 @ SV84 )
| ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1069: $i] :
( ~ ( ~ SV328
| ( SY1069 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1069 != SY1068 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1424,plain,
! [SV84: $i,SV521: $i] :
( ( ~ ( in @ SV521 @ SV84 )
| ! [SY1070: $i] :
( ~ ( in @ SY1070 @ SV84 )
| ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1071: $i] :
( ~ ( ~ $true
| ( SY1071 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1071 != SY1070 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1425,plain,
! [SV84: $i,SV522: $i] :
( ( ~ ( in @ SV522 @ SV84 )
| ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV84 )
| ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1073: $i] :
( ~ ( ~ $false
| ( SY1073 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1073 != SY1072 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1426,plain,
! [SV329: $i,SV85: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ SV85 )
| ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV329 )
| ( in @ ( kpair @ SV523 @ SY1074 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1427,plain,
! [SV524: $i,SV330: $i,SV86: $i] :
( ( ~ ( func @ SV86 @ SV330 @ SV524 )
| ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV86 )
| ! [SY1076: $i] :
( ~ ( in @ SY1076 @ SV330 )
| ~ ( in @ ( kpair @ SY1075 @ SY1076 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SY1075 )
= SY1076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1428,plain,
! [SV331: $i,SV87: $i] :
( ( ( SV87 != SV331 )
= $true )
| ( ( subset @ SV331 @ SV87 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1156]) ).
thf(1429,plain,
! [SV88: $o,SV332: $i] :
( ( ( ~ ( in @ SV332 @ ( prop2set @ SV88 ) ) )
= $true )
| ( SV88 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1430,plain,
! [SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1431,plain,
! [SV334: $i] :
( ( ( ~ ( in @ SV334 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1432,plain,
! [SV89: $i > $o] :
( ( ( ~ ! [SY223: $i] :
~ ~ ( ~ ( SV89 @ SY223 )
| ~ ! [SY224: $i] :
( ~ ( SV89 @ SY224 )
| ( SY223 = SY224 ) ) ) )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1433,plain,
! [SV525: $i,SV335: $i,SV90: $i] :
( ( ~ ( func @ SV90 @ SV335 @ SV525 )
| ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1078: $i] : ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV525 ) ) )
@ SV335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1434,plain,
! [SV337: $i > $o,SV92: $i,SV526: $i] :
( ( ~ ( in @ SV526 @ SV92 )
| ~ ( SV337 @ SV526 )
| ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1435,plain,
! [SV338: $i,SV93: $i,SV527: $i] :
( ( ~ ( in @ SV527 @ ( setminus @ SV93 @ SV338 ) )
| ( in @ SV527 @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1436,plain,
! [SV339: $i,SV94: $i] :
( ( ( ( setminus @ SV94 @ SV339 )
!= emptyset )
= $true )
| ( ( subset @ SV94 @ SV339 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1437,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ~ ( in @ SV528 @ SV95 )
| ~ ( ~ ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) )
| ~ ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1438,plain,
! [SV96: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ ( powerset @ SV96 ) ) )
= $true )
| ( ( ! [SY798: $i] :
( ~ ( in @ SY798 @ ( powerset @ SV96 ) )
| ! [SY799: $i] :
( ~ ( in @ SY799 @ SV96 )
| ~ ( in @ SY799 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SY798 ) ) )
| ~ ( in @ SY799 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1439,plain,
! [SV342: $i,SV97: $i,SV529: $i] :
( ( ~ ( in @ SV529 @ SV97 )
| ! [SY1082: $i] :
( ~ ( in @ SY1082 @ SV342 )
| ( ( kpair @ SV529 @ SY1082 )
= ( kpair @ SV529 @ SY1082 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1440,plain,
! [SV98: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ ( powerset @ SV98 ) ) )
= $true )
| ( ( in @ ( setminus @ SV98 @ SV343 ) @ ( powerset @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1441,plain,
! [SV99: $o] :
( ( SV99 = $false )
| ( ( set2prop @ ( prop2set @ SV99 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1442,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1443,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1444,plain,
! [SV344: $i,SV100: $i] :
( ( ( SV100 != SV344 )
= $true )
| ( ( ! [SY802: $i,SY803: $i] :
( ( SY802 != SY803 )
| ~ ( in @ SY802 @ SV100 )
| ( in @ SY803 @ SV344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1173]) ).
thf(1445,plain,
! [SV101: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( powerset @ SV101 ) ) )
= $true )
| ( ( ! [SY804: $i] :
( ~ ( in @ SY804 @ ( powerset @ SV101 ) )
| ~ ( subset @ ( setminus @ SV101 @ SY804 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SY804 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1446,plain,
! [SV102: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ ( powerset @ SV102 ) )
| ! [SY806: $i] :
( ~ ( in @ SY806 @ ( powerset @ SV102 ) )
| ! [SY807: $i] :
( ~ ( in @ SY807 @ SV102 )
| ~ ( in @ SY807 @ ( binintersect @ SV346 @ SY805 ) )
| ( in @ SY807 @ ( binunion @ SV346 @ SY806 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1447,plain,
! [SV530: $i,SV348: $i,SV104: $i] :
( ( ~ ( func @ SV104 @ SV348 @ SV530 )
| ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV104 )
| ( in @ ( kpair @ SY1083 @ ( ap @ SV104 @ SV348 @ SV530 @ SY1083 ) ) @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1448,plain,
! [SV105: $i] :
( ( ( SV105 != emptyset )
= $false )
| ( ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV105 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1178]) ).
thf(1449,plain,
! [SV349: $i,SV106: $i,SV531: $i] :
( ( ~ ( in @ SV531 @ ( cartprod @ SV106 @ SV349 ) )
| ( in @ ( kfst @ SV531 ) @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1450,plain,
! [SV351: $i,SV109: $i,SV532: $i] :
( ( ~ ( in @ SV532 @ SV109 )
| ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV351 )
| ( in @ ( kpair @ SV532 @ SY1084 ) @ ( cartprod @ SV109 @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1181]) ).
thf(1451,plain,
! [SV110: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ! [SY813: $i] :
( ~ ( in @ SY813 @ ( powerset @ SV110 ) )
| ! [SY814: $i] :
( ~ ( in @ SY814 @ ( powerset @ SV110 ) )
| ! [SY815: $i] :
( ~ ( in @ SY815 @ SV110 )
| ~ ( in @ SY815 @ ( binintersect @ SV352 @ SY813 ) )
| ( in @ SY815 @ ( binunion @ SY813 @ SY814 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1452,plain,
! [SV111: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( powerset @ SV111 ) ) )
= $true )
| ( ( ! [SY816: $i] :
( ~ ( in @ SY816 @ ( powerset @ SV111 ) )
| ~ ( subset @ SV353 @ SY816 )
| ( subset @ ( setminus @ SV111 @ SY816 ) @ ( setminus @ SV111 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1183]) ).
thf(1453,plain,
! [SV112: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV354 @ ( setminus @ SV112 @ SY817 ) )
| ( subset @ SY817 @ ( setminus @ SV112 @ SV354 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1184]) ).
thf(1454,plain,
! [SV355: $i,SV113: $i] :
( ( ( ~ ! [SY818: $i] :
( ~ ( in @ SY818 @ SV113 )
| ( in @ SY818 @ SV355 ) ) )
= $true )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1185]) ).
thf(1455,plain,
! [SV356: $i,SV114: $i,SV533: $i] :
( ( ~ ( in @ SV533 @ SV114 )
| ! [SY1085: $i] :
( ~ ( in @ SY1085 @ SV356 )
| ( ( kfst @ ( kpair @ SV533 @ SY1085 ) )
= SV533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1456,plain,
! [SV115: $i,SV357: $i] :
( ( ( ~ ( in @ SV357 @ ( powerset @ SV115 ) ) )
= $true )
| ( ( SV357
= ( setminus @ SV115 @ ( setminus @ SV115 @ SV357 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1457,plain,
! [SV358: $o,SV116: $i,SV534: $i] :
( ( ~ ( in @ SV534 @ SV116 )
| ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV116 )
| ~ ~ SV358
| ( in @ SY1086
@ ( dsetconstr @ SV116
@ ^ [SY1087: $i] :
( ~ ( ~ SV358
| ( SY1087 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1087 != SY1086 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1188]) ).
thf(1458,plain,
! [SV116: $i,SV535: $i] :
( ( ~ ( in @ SV535 @ SV116 )
| ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV116 )
| ~ ~ $true
| ( in @ SY1088
@ ( dsetconstr @ SV116
@ ^ [SY1089: $i] :
( ~ ( ~ $true
| ( SY1089 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1089 != SY1088 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1189]) ).
thf(1459,plain,
! [SV116: $i,SV536: $i] :
( ( ~ ( in @ SV536 @ SV116 )
| ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV116 )
| ~ ~ $false
| ( in @ SY1090
@ ( dsetconstr @ SV116
@ ^ [SY1091: $i] :
( ~ ( ~ $false
| ( SY1091 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1091 != SY1090 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1460,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ~ ! [SY824: $i] :
( ~ ( in @ SY824 @ SV117 )
| ~ ( SV359 @ SY824 ) ) )
= $true )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1461,plain,
! [SV537: $i,SV360: $i,SV118: $i] :
( ( ~ ( func @ SV118 @ SV360 @ SV537 )
| ! [SY1092: $i] :
( ~ ( func @ SV118 @ SV360 @ SY1092 )
| ~ ! [SY1093: $i] :
( ~ ( in @ SY1093 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1093 )
= ( ap @ SV118 @ SV360 @ SY1092 @ SY1093 ) ) )
| ! [SY1094: $i] :
( ~ ( in @ SY1094 @ SV118 )
| ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV360 )
| ~ ( in @ ( kpair @ SY1094 @ SY1095 ) @ SY1092 )
| ( in @ ( kpair @ SY1094 @ SY1095 ) @ SV537 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1192]) ).
thf(1462,plain,
! [SV361: $i,SV119: $i] :
( ( ( ~ ( in @ SV119 @ ( setadjoin @ SV361 @ emptyset ) ) )
= $true )
| ( ( SV119 = SV361 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1463,plain,
! [SV120: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( powerset @ SV120 ) ) )
= $true )
| ( ( ! [SY831: $i] :
( ~ ( in @ SY831 @ SV120 )
| ~ ( in @ SY831 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SY831 @ SV362 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1464,plain,
! [SV363: $i,SV121: $i,SV538: $i] :
( ( ~ ( in @ SV538 @ SV121 )
| ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV363 )
| ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SY1096 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1465,plain,
! [SV122: $i] :
( ( ( ! [SY302: $i] :
~ ( in @ SY302 @ SV122 ) )
= $false )
| ( ( SV122 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1466,plain,
! [SV124: $i,SV364: $i] :
( ( ( ~ ! [SY834: $i] :
( ~ ( in @ SY834 @ SV364 )
| ( in @ SY834 @ SV124 ) ) )
= $true )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1467,plain,
! [SV365: $i,SV125: $i,SV539: $i] :
( ( ~ ( in @ SV539 @ ( cartprod @ SV125 @ SV365 ) )
| ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1468,plain,
! [SV366: $i,SV126: $i,SV540: $i] :
( ( ~ ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
| ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ ( cartprod @ SV126 @ SV366 ) )
| ~ ! [SY1098: $i] :
( ~ ( in @ SY1098 @ SV126 )
| ! [SY1099: $i] :
( ~ ( in @ SY1099 @ SV366 )
| ~ ( in @ ( kpair @ SY1098 @ SY1099 ) @ SV540 )
| ( in @ ( kpair @ SY1098 @ SY1099 ) @ SY1097 ) ) )
| ( subset @ SV540 @ SY1097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1469,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i] :
( ( ! [SY1100: $i] :
( ~ ( in @ SY1100 @ SV128 )
| ! [SY1101: $i] :
( ~ ( in @ SY1101 @ SV368 )
| ~ ( in @ ( kpair @ SY1100 @ SY1101 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SY1100 @ SY1101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1470,plain,
! [SV129: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( powerset @ SV129 ) ) )
= $true )
| ( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ SV129 )
| ~ ~ ( in @ SY845 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SY845 @ SV369 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1471,plain,
! [SV370: $i,SV130: $i,SV542: $i] :
( ( ! [SY1104: $i] :
( ~ ( in @ ( kpair @ SV542 @ SY1104 ) @ ( cartprod @ SV130 @ SV370 ) )
| ( in @ SY1104 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1472,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY848: $i] :
( ~ ( in @ SY848 @ SV131 )
| ! [SY849: $i] :
( ~ ( in @ SY849 @ SV131 )
| ~ ( SV371 @ SY848 )
| ~ ( SV371 @ SY849 )
| ( SY848 = SY849 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1204]) ).
thf(1473,plain,
! [SV372: $i > $o,SV132: $i,SV543: $i] :
( ( ~ ( in @ SV543
@ ( dsetconstr @ SV132
@ ^ [SY853: $i] : ( SV372 @ SY853 ) ) )
| ( SV372 @ SV543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1474,plain,
! [SV373: $i,SV133: $i,SV544: $i] :
( ( ~ ( in @ SV544 @ SV133 )
| ~ ~ ( in @ SV544 @ SV373 )
| ( SV133 != SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1475,plain,
! [SV136: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ ( powerset @ SV136 ) ) )
= $true )
| ( ( ! [SY856: $i] :
( ~ ( in @ SY856 @ ( powerset @ SV136 ) )
| ! [SY857: $i] :
( ~ ( in @ SY857 @ SV136 )
| ~ ( in @ SY857 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SY856 ) ) )
| ( in @ SY857 @ ( setminus @ SV136 @ SV376 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1476,plain,
! [SV377: $i,SV137: $i] :
( ( ( SV137 != SV377 )
= $true )
| ( ( ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV137 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV377 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV377
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1210]) ).
thf(1477,plain,
! [SV378: $i,SV138: $i,SV545: $i] :
( ( ~ ( in @ SV545 @ SV138 )
| ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV378 )
| ( ( ksnd @ ( kpair @ SV545 @ SY1106 ) )
= SY1106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1478,plain,
! [SV379: $i,SV139: $i,SV546: $i] :
( ( ~ ( subset @ SV546 @ SV139 )
| ~ ( subset @ SV546 @ SV379 )
| ( subset @ SV546 @ ( binintersect @ SV139 @ SV379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1479,plain,
! [SV380: $i,SV140: $i,SV547: $i] :
( ( ~ ( in @ SV547 @ SV140 )
| ~ ~ ( in @ SV547 @ SV380 )
| ~ ( subset @ SV140 @ SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1480,plain,
! [SV141: $i,SV381: $i] :
( ( ( ~ ( in @ SV381 @ ( powerset @ SV141 ) ) )
= $true )
| ( ( ! [SY868: $i] :
( ~ ( in @ SY868 @ SV141 )
| ~ ( in @ SY868 @ SV381 )
| ( in @ SY868 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1481,plain,
! [SV142: $i] :
( ( ( in @ SV142 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1482,plain,
! [SV144: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( ! [SY869: $i] :
( ~ ( in @ SY869 @ ( powerset @ SV144 ) )
| ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SY869 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1483,plain,
! [SV145: $i] :
( ( ( subset @ SV145 @ emptyset )
= $false )
| ( ( SV145 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1484,plain,
! [SV146: $i > $o] :
( ( ( ~ ! [SY360: $i] :
~ ~ ( ~ ( SV146 @ SY360 )
| ~ ! [SY361: $i] :
( ~ ( SV146 @ SY361 )
| ( SY360 = SY361 ) ) ) )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1485,plain,
! [SV147: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ ( powerset @ SV147 ) ) )
= $true )
| ( ( ! [SY870: $i] :
( ~ ( in @ SY870 @ ( powerset @ SV147 ) )
| ! [SY871: $i] :
( ~ ( in @ SY871 @ SV147 )
| ~ ~ ( in @ SY871 @ ( binunion @ SV384 @ SY870 ) )
| ~ ( in @ SY871 @ SY870 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1220]) ).
thf(1486,plain,
! [SV148: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( powerset @ SV148 ) ) )
= $true )
| ( ( ! [SY872: $i] :
( ~ ( in @ SY872 @ ( powerset @ SV148 ) )
| ~ ! [SY873: $i] :
( ~ ( in @ SY873 @ SV148 )
| ~ ( in @ SY873 @ SV385 )
| ( in @ SY873 @ SY872 ) )
| ( in @ SV385 @ ( powerset @ SY872 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1221]) ).
thf(1487,plain,
! [SV386: $i,SV149: $i] :
( ( ( ~ ( subset @ SV149 @ SV386 ) )
= $true )
| ( ( subset @ ( powerset @ SV149 ) @ ( powerset @ SV386 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1488,plain,
! [SV388: $i,SV548: $i,SV151: $i] :
( ( ~ ( subset @ SV151 @ SV548 )
| ( subset @ SV151 @ ( setadjoin @ SV388 @ SV548 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1489,plain,
! [SV389: $i,SV549: $i > $i,SV152: $i] :
( ( ~ ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV152 )
| ( in @ ( SV549 @ SY1107 ) @ SV389 ) )
| ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1490,plain,
! [SV153: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( powerset @ SV153 ) ) )
= $true )
| ( ( ! [SY879: $i] :
( ~ ( in @ SY879 @ ( powerset @ SV153 ) )
| ( in @ ( setminus @ SV390 @ SY879 ) @ ( powerset @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1491,plain,
! [SV391: $o,SV154: $i,SV550: $i] :
( ( ~ ( in @ SV550 @ SV154 )
| ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SV154 )
| ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1111: $i] :
( ~ ( ~ SV391
| ( SY1111 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1111 != SY1110 ) ) ) )
= ( setadjoin @ SY1110 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1492,plain,
! [SV154: $i,SV551: $i] :
( ( ~ ( in @ SV551 @ SV154 )
| ! [SY1112: $i] :
( ~ ( in @ SY1112 @ SV154 )
| ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1113: $i] :
( ~ ( ~ $true
| ( SY1113 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1113 != SY1112 ) ) ) )
= ( setadjoin @ SY1112 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1228]) ).
thf(1493,plain,
! [SV154: $i,SV552: $i] :
( ( ~ ( in @ SV552 @ SV154 )
| ! [SY1114: $i] :
( ~ ( in @ SY1114 @ SV154 )
| ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1115: $i] :
( ~ ( ~ $false
| ( SY1115 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1115 != SY1114 ) ) ) )
= ( setadjoin @ SY1114 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1494,plain,
! [SV553: $i > $i > $o,SV392: $i,SV156: $i] :
( ( ! [SY1116: $i,SY1117: $i] :
( ~ ( in @ ( kpair @ SY1116 @ SY1117 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SY1118: $i,SY1119: $i] : ( SV553 @ SY1118 @ SY1119 ) ) )
| ( in @ SY1117 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1230]) ).
thf(1495,plain,
! [SV393: $o,SV157: $i,SV554: $i] :
( ( ~ ( in @ SV554 @ SV157 )
| ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SV157 )
| ( in @ ( if @ SV157 @ SV393 @ SV554 @ SY1120 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1496,plain,
! [SV157: $i,SV555: $i] :
( ( ~ ( in @ SV555 @ SV157 )
| ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV157 )
| ( in @ ( if @ SV157 @ $true @ SV555 @ SY1121 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1497,plain,
! [SV157: $i,SV556: $i] :
( ( ~ ( in @ SV556 @ SV157 )
| ! [SY1122: $i] :
( ~ ( in @ SY1122 @ SV157 )
| ( in @ ( if @ SV157 @ $false @ SV556 @ SY1122 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1498,plain,
! [SV158: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV158 )
| ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) ) )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1234]) ).
thf(1499,plain,
! [SV159: $i] :
( ( ( iskpair @ SV159 )
= $false )
| ( ( ( kpair @ ( kfst @ SV159 ) @ ( ksnd @ SV159 ) )
= SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1500,plain,
! [SV394: $i,SV160: $i,SV557: $i] :
( ( ~ ( in @ SV557 @ ( setadjoin @ SV160 @ ( setadjoin @ SV394 @ emptyset ) ) )
| ( SV557 = SV160 )
| ( SV557 = SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1501,plain,
! [SV558: $i > $i > $o,SV395: $i,SV161: $i] :
( ( subset
@ ( dpsetconstr @ SV161 @ SV395
@ ^ [SY1123: $i,SY1124: $i] : ( SV558 @ SY1123 @ SY1124 ) )
@ ( cartprod @ SV161 @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1502,plain,
! [SV396: $i,SV559: $i > $i,SV162: $i] :
( ( ~ ! [SY1125: $i] :
( ~ ( in @ SY1125 @ SV162 )
| ( in @ ( SV559 @ SY1125 ) @ SV396 ) )
| ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1503,plain,
! [SV163: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ ( powerset @ SV163 ) ) )
= $true )
| ( ( subset @ SV397 @ ( setminus @ SV163 @ ( setminus @ SV163 @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1504,plain,
! [SV560: $i > $i > $o,SV398: $i,SV164: $i] :
( ( ! [SY1127: $i,SY1128: $i] :
( ~ ( in @ ( kpair @ SY1127 @ SY1128 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SY1129: $i,SY1130: $i] : ( SV560 @ SY1129 @ SY1130 ) ) )
| ( SV560 @ SY1127 @ SY1128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1505,plain,
! [SV399: $i,SV165: $i] :
( ( ( ~ ( subset @ SV165 @ SV399 ) )
= $true )
| ( ( ~ ( subset @ SV399 @ SV165 )
| ( SV165 = SV399 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1506,plain,
! [SV400: $i,SV166: $i,SV561: $i] :
( ( ~ ( in @ SV561 @ ( binintersect @ SV166 @ SV400 ) )
| ( in @ SV561 @ SV400 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1507,plain,
! [SV167: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV167 ) )
= $true )
| ( ( in @ SV401 @ ( powerset @ ( setunion @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1508,plain,
! [SV168: $i,SV402: $i] :
( ( ( ~ ( in @ SV402 @ ( powerset @ SV168 ) ) )
= $true )
| ( ( ! [SY903: $i] :
( ~ ( in @ SY903 @ ( powerset @ SV168 ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV168 )
| ~ ( in @ SY904 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY904 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SY903 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1509,plain,
! [SV403: $i > $o,SV169: $i] :
( ( ( ~ ~ ~ ! [SY905: $i] :
~ ~ ( ~ ( in @ SY905 @ SV169 )
| ~ ( SV403 @ SY905 ) ) )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1510,plain,
! [SV404: $i,SV170: $i] :
( ( ( ( setadjoin @ SV170 @ emptyset )
!= ( setadjoin @ SV404 @ emptyset ) )
= $true )
| ( ( SV170 = SV404 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1511,plain,
! [SV171: $i,SV405: $i,SV562: $i] :
( ( ~ ( in @ SV562 @ SV405 )
| ~ ( in @ SV562 @ ( setminus @ SV171 @ SV405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1512,plain,
! [SV406: $i,SV172: $i] :
( ( ( SV172 != SV406 )
= $true )
| ( ( subset @ SV172 @ SV406 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1248]) ).
thf(1513,plain,
! [SV173: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( powerset @ SV173 ) ) )
= $true )
| ( ( subset @ SV407 @ SV173 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1514,plain,
! [SV408: $i > $o,SV174: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) ) )
= $true )
| ( ( ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SV174 )
| ~ ( SV408 @ SY909 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1515,plain,
! [SV409: $i,SV175: $i,SV563: $i] :
( ( ~ ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
| ! [SY1131: $i] :
( ~ ( in @ SY1131 @ ( funcSet @ SV175 @ SV409 ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1132 )
= ( ap @ SV175 @ SV409 @ SY1131 @ SY1132 ) ) )
| ( SV563 = SY1131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1251]) ).
thf(1516,plain,
! [SV176: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ ( powerset @ SV176 ) ) )
= $true )
| ( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV176 )
| ~ ( in @ SY913 @ SV410 )
| ~ ( in @ SY913 @ ( setminus @ SV176 @ SV410 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1252]) ).
thf(1517,plain,
! [SV178: $i,SV411: $i,SV564: $i] :
( ( ~ ( in @ SV564 @ SV411 )
| ( in @ SV564 @ ( setadjoin @ SV178 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1518,plain,
! [SV412: $i,SV565: $i > $i,SV180: $i] :
( ( ~ ! [SY1133: $i] :
( ~ ( in @ SY1133 @ SV180 )
| ( in @ ( SV565 @ SY1133 ) @ SV412 ) )
| ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1519,plain,
! [SV181: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ ( powerset @ SV181 ) ) )
= $true )
| ( ( ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV181 ) )
| ! [SY920: $o,SY921: $i] :
( ~ ( in @ SY921 @ SV181 )
| ~ ( in @ SY921 @ ( binunion @ SV413 @ SY919 ) )
| ~ ( ~ ( in @ SY921 @ SV413 )
| SY920 )
| ~ ( ~ ( in @ SY921 @ SY919 )
| SY920 )
| SY920 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1520,plain,
! [SV182: $i > $o] :
( ( ( ~ ! [SY449: $i] :
~ ~ ( ~ ( SV182 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV182 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1257]) ).
thf(1521,plain,
! [SV414: $i,SV183: $i] :
( ( ( SV183 != SV414 )
= $true )
| ( ( ( setunion @ SV183 )
= ( setunion @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1258]) ).
thf(1522,plain,
! [SV184: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ ( powerset @ SV184 ) ) )
= $true )
| ( ( ! [SY922: $i] :
( ~ ( in @ SY922 @ ( powerset @ SV184 ) )
| ( in @ ( binintersect @ SV415 @ SY922 ) @ ( powerset @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1259]) ).
thf(1523,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ~ ~ ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) )
| ~ ( in @ SV566 @ SV185 )
| ( in @ SV566 @ SV416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1524,plain,
! [SV187: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ ( powerset @ SV187 ) ) )
= $true )
| ( ( ! [SY924: $i] :
( ~ ( in @ SY924 @ ( powerset @ SV187 ) )
| ( in @ ( binunion @ SV417 @ SY924 ) @ ( powerset @ SV187 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1261]) ).
thf(1525,plain,
! [SV567: $i,SV418: $i,SV188: $i] :
( ( ~ ( func @ SV188 @ SV418 @ SV567 )
| ! [SY1136: $i] :
( ~ ( in @ SY1136 @ SV188 )
| ( ( ap @ SV188 @ SV418 @ SV567 @ SY1136 )
= ( ap @ SV188 @ SV418 @ SV567 @ SY1136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1526,plain,
! [SV189: $i,SV419: $i] :
( ( ( ~ ( subset @ SV419 @ SV189 ) )
= $true )
| ( ( ( binintersect @ SV189 @ SV419 )
= SV419 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1527,plain,
! [SV420: $i,SV190: $i,SV568: $i] :
( ( ~ ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) )
| ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV190 )
| ( in @ ( kpair @ SY1137 @ ( ap @ SV190 @ SV420 @ SV568 @ SY1137 ) ) @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1528,plain,
! [SV421: $i > $o,SV191: $i] :
( ( ( ~ ~ ! [SY929: $i] :
( ~ ( in @ SY929 @ SV191 )
| ( SV421 @ SY929 ) ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1529,plain,
! [SV569: $i,SV422: $i,SV192: $i] :
( ( ! [SY1138: $i] :
( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV569 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV569 @ ( setadjoin @ SY1138 @ emptyset ) ) @ emptyset ) ) )
| ( SV192 = SV569 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1530,plain,
! [SV423: $i,SV193: $i,SV570: $i] :
( ( ~ ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
| ! [SY1139: $i > $o] :
( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV193 )
| ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV423 )
| ~ ( in @ ( kpair @ SY1140 @ SY1141 ) @ SV570 )
| ( SY1139 @ ( kpair @ SY1140 @ SY1141 ) ) ) )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV570 )
| ( SY1139 @ SY1142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1531,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ~ ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
| ! [SY1143: $o] :
( ~ ( ( SV571 != SV194 )
| SY1143 )
| ~ ( ~ ( in @ SV571 @ SV424 )
| SY1143 )
| SY1143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1532,plain,
! [SV425: $i > $o,SV195: $i] :
( ( ( ~ ~ ! [SY940: $i] :
( ~ ( in @ SY940 @ SV195 )
| ( SV425 @ SY940 ) ) )
= $true )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1533,plain,
! [SV196: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
| ~ ! [SY1153: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY1153 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1153 ) )
| ~ ! [SY1156: $i] :
~ ~ ! [SY1157: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1156 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1157 @ SY1153 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1156 )
| ~ ( in @ SX5 @ SY1153 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1156 ) )
| ( in @ SY1157 @ SY1159 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1270]) ).
thf(1534,plain,
! [SV427: $i,SV198: $i] :
( ( ( ~ ( subset @ SV198 @ SV427 ) )
= $true )
| ( ( in @ SV198 @ ( powerset @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1535,plain,
! [SV428: $i > $o,SV199: $i,SV572: $i] :
( ( ~ ( in @ SV572 @ SV199 )
| ~ ( SV428 @ SV572 )
| ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1536,plain,
! [SV573: $i,SV429: $i,SV200: $i] :
( ( ~ ( subset @ SV200 @ SV429 )
| ~ ( in @ SV573 @ SV200 )
| ( in @ SV573 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1537,plain,
! [SV430: $i,SV201: $i] :
( ( ( ~ ! [SY946: $i] :
( ~ ( in @ SY946 @ SV201 )
| ( in @ SY946 @ SV430 ) ) )
= $true )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1538,plain,
! [SV574: $i,SV202: $i,SV431: $i] :
( ( ~ ( in @ SV431 @ ( powerset @ SV202 ) )
| ~ ( in @ SV574 @ SV431 )
| ( in @ SV574 @ SV202 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1539,plain,
! [SV432: $i,SV203: $i,SV575: $i] :
( ( ~ ( in @ SV575 @ ( funcSet @ SV203 @ SV432 ) )
| ( ( lam @ SV203 @ SV432
@ ^ [SY1163: $i] : ( ap @ SV203 @ SV432 @ SV575 @ SY1163 ) )
= SV575 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1540,plain,
! [SV204: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV204 ) )
| ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SY951 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1278]) ).
thf(1541,plain,
! [SV205: $i > $o] :
( ( ( ~ ! [SY520: $i] :
~ ~ ( ~ ( SV205 @ SY520 )
| ~ ! [SY521: $i] :
( ~ ( SV205 @ SY521 )
| ( SY520 = SY521 ) ) ) )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1542,plain,
! [SV206: $i] :
( ( ( singleton @ SV206 )
= $false )
| ( ( in @ ( setunion @ SV206 ) @ SV206 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1543,plain,
! [SV208: $i] :
( ( ( iskpair @ SV208 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV208 )
@ ^ [SY525: $i] :
( SV208
= ( kpair @ ( kfst @ SV208 ) @ SY525 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1544,plain,
! [SV209: $i > $o] :
( ( ( ~ ! [SY526: $i] :
~ ~ ( ~ ( SV209 @ SY526 )
| ~ ! [SY527: $i] :
( ~ ( SV209 @ SY527 )
| ( SY526 = SY527 ) ) ) )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1545,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( setunion @ SV210 ) ) )
= $true )
| ( ( ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SV210 )
| ~ ( in @ SV435 @ SY952 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1284]) ).
thf(1546,plain,
! [SV576: $i > $i > $o,SV436: $i,SV211: $i] :
( ( ! [SY1164: $i,SY1165: $i] :
( ~ ( in @ ( kpair @ SY1164 @ SY1165 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SY1166: $i,SY1167: $i] : ( SV576 @ SY1166 @ SY1167 ) ) )
| ( in @ SY1164 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1285]) ).
thf(1547,plain,
! [SV437: $o,SV212: $i,SV577: $i] :
( ( ~ ( in @ SV577 @ SV212 )
| ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV212 )
| ( in @ ( if @ SV212 @ SV437 @ SV577 @ SY1168 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SY1168 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1286]) ).
thf(1548,plain,
! [SV212: $i,SV578: $i] :
( ( ~ ( in @ SV578 @ SV212 )
| ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV212 )
| ( in @ ( if @ SV212 @ $true @ SV578 @ SY1169 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SY1169 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1549,plain,
! [SV212: $i,SV579: $i] :
( ( ~ ( in @ SV579 @ SV212 )
| ! [SY1170: $i] :
( ~ ( in @ SY1170 @ SV212 )
| ( in @ ( if @ SV212 @ $false @ SV579 @ SY1170 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SY1170 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1550,plain,
! [SV580: $i,SV438: $i,SV213: $i] :
( ( ~ ( func @ SV213 @ SV438 @ SV580 )
| ( ( lam @ SV213 @ SV438
@ ^ [SY1171: $i] : ( ap @ SV213 @ SV438 @ SV580 @ SY1171 ) )
= SV580 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1551,plain,
! [SV581: $i,SV439: $i,SV214: $i] :
( ( ~ ( func @ SV214 @ SV439 @ SV581 )
| ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV214 )
| ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1173: $i] : ( in @ ( kpair @ SY1172 @ SY1173 ) @ SV581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1552,plain,
! [SV440: $i,SV582: $i > $i,SV215: $i] :
( ( ~ ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV215 )
| ( in @ ( SV582 @ SY1174 ) @ SV440 ) )
| ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1553,plain,
! [SV441: $i,SV216: $i,SV583: $i] :
( ( ~ ( in @ SV583 @ SV216 )
| ! [SY1177: $i] :
( ~ ( in @ SY1177 @ SV441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SY1177 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1554,plain,
! [SV442: $i,SV217: $i,SV584: $i] :
( ( ~ ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ ( setadjoin @ SV442 @ emptyset ) ) @ emptyset ) ) )
| ( SV217 = SV584 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1555,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ( ~ ( in @ SV444 @ ( setunion @ SV219 ) )
| ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
| ~ ( ~ ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) )
| ( in @ SV444 @ ( setunion @ SV219 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1295]) ).
thf(1556,plain,
! [SV445: $i,SV220: $i] :
( ( ( ~ ~ ~ ! [SY974: $i] :
~ ~ ( ~ ( in @ SY974 @ SV220 )
| ~ ( in @ SY974 @ SV445 ) ) )
= $true )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1296]) ).
thf(1557,plain,
! [SV222: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( powerset @ SV222 ) ) )
= $true )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ ( powerset @ SV222 ) )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV222 )
| ~ ( in @ SY976 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY976 @ ( binintersect @ SV447 @ SY975 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1558,plain,
! [SV585: $i,SV448: $i,SV223: $i] :
( ( ! [SY1178: $i] :
( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SY1178 @ emptyset ) ) @ emptyset ) ) )
| ( SV585 != SY1178 )
| ( SV448 = SY1178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1559,plain,
! [SV224: $i,SV449: $i] :
( ( ( ~ ( in @ SV449 @ ( powerset @ SV224 ) ) )
= $true )
| ( ( ! [SY979: $i] :
( ~ ( in @ SY979 @ ( powerset @ SV224 ) )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV224 )
| ~ ~ ( in @ SY980 @ SV449 )
| ~ ~ ( in @ SY980 @ SY979 )
| ~ ( in @ SY980 @ ( binunion @ SV449 @ SY979 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1300]) ).
thf(1560,plain,
( ( in @ sK2_SY0 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1301]) ).
thf(1561,plain,
( ( ~ ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1302]) ).
thf(1562,plain,
! [SV450: $i,SV225: $i] :
( ( ( ~ ( in @ SV225 @ ( setadjoin @ SV450 @ emptyset ) ) )
= $true )
| ( ( in @ SV450 @ ( setadjoin @ SV225 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1303]) ).
thf(1563,plain,
! [SV451: $o,SV226: $i,SV586: $i] :
( ( ~ ( in @ SV586 @ SV226 )
| ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SV226 )
| ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SY1179 )
= SV586 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1304]) ).
thf(1564,plain,
! [SV226: $i,SV587: $i] :
( ( ~ ( in @ SV587 @ SV226 )
| ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV226 )
| ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SY1180 )
= SV587 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1565,plain,
! [SV226: $i,SV588: $i] :
( ( ~ ( in @ SV588 @ SV226 )
| ! [SY1181: $i] :
( ~ ( in @ SY1181 @ SV226 )
| ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SY1181 )
= SV588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1566,plain,
! [SV227: $i > $o] :
( ( ( ~ ! [SY577: $i] :
~ ~ ( ~ ( SV227 @ SY577 )
| ~ ! [SY578: $i] :
( ~ ( SV227 @ SY578 )
| ( SY577 = SY578 ) ) ) )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1567,plain,
! [SV228: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ ( powerset @ SV228 ) ) )
= $true )
| ( ( ! [SY983: $i] :
( ~ ( in @ SY983 @ ( powerset @ SV228 ) )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SY983 ) )
| ~ ( in @ SY984 @ SY983 )
| ~ ( in @ SY984 @ SV452 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1568,plain,
! [SV453: $o,SV229: $i,SV589: $i] :
( ( ~ ( in @ SV589 @ SV229 )
| ! [SY1182: $i] :
( ~ ( in @ SY1182 @ SV229 )
| ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1183: $i] :
( ~ ( ~ SV453
| ( SY1183 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1183 != SY1182 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1569,plain,
! [SV229: $i,SV590: $i] :
( ( ~ ( in @ SV590 @ SV229 )
| ! [SY1184: $i] :
( ~ ( in @ SY1184 @ SV229 )
| ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1185: $i] :
( ~ ( ~ $true
| ( SY1185 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1185 != SY1184 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1570,plain,
! [SV229: $i,SV591: $i] :
( ( ~ ( in @ SV591 @ SV229 )
| ! [SY1186: $i] :
( ~ ( in @ SY1186 @ SV229 )
| ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1187: $i] :
( ~ ( ~ $false
| ( SY1187 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1187 != SY1186 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1571,plain,
! [SV592: $i,SV454: $i,SV230: $i] :
( ( ( binintersect @ SV230 @ ( binunion @ SV454 @ SV592 ) )
= ( binunion @ ( binintersect @ SV230 @ SV454 ) @ ( binintersect @ SV230 @ SV592 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1572,plain,
! [SV593: $i,SV455: $i,SV231: $i] :
( ( ( ( setadjoin @ SV231 @ ( setadjoin @ SV455 @ emptyset ) )
!= ( setadjoin @ SV593 @ emptyset ) )
| ( SV231 = SV455 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1573,plain,
! [SV232: $i > $o,SV456: $i] :
( ( ( ~ ( in @ SV456 @ emptyset ) )
= $true )
| ( ( SV232 @ SV456 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1574,plain,
! [SV233: $i,SV457: $i] :
( ( ( ~ ( subset @ SV457 @ SV233 ) )
= $true )
| ( ( in @ SV457 @ ( powerset @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1575,plain,
! [SV458: $i,SV234: $i,SV594: $i] :
( ( ~ ( in @ SV594 @ ( cartprod @ SV234 @ SV458 ) )
| ( in @ ( ksnd @ SV594 ) @ SV458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1576,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ! [SY1188: $o] :
( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
| ~ ( ~ ( in @ SV595 @ SV235 )
| SY1188 )
| ~ ( ~ ( in @ SV595 @ SV459 )
| SY1188 )
| SY1188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1577,plain,
! [SV596: $i,SV460: $i,SV236: $i] :
( ( ! [SY1189: $i] :
( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SV460 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV596 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV596 @ ( setadjoin @ SY1189 @ emptyset ) ) @ emptyset ) ) )
| ( SV460 = SY1189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1578,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY995: $i,SY996: $i] :
( ( SY995 != SY996 )
| ~ ( ~ ( ~ ( SV237 @ SY995 )
| ( SV461 @ SY996 ) )
| ~ ( ~ ( SV461 @ SY996 )
| ( SV237 @ SY995 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1579,plain,
! [SV238: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ SV238 ) )
= $true )
| ( ( in @ ( setadjoin @ SV462 @ emptyset ) @ ( powerset @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1580,plain,
! [SV463: $i > $o,SV239: $i] :
( ( ( ~ ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) ) )
= $true )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV239 )
| ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV239 )
| ~ ( SV463 @ SY1004 )
| ~ ( SV463 @ SY1005 )
| ( SY1004 = SY1005 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1321]) ).
thf(1581,plain,
! [SV464: $i,SV240: $i,SV597: $i] :
( ( ~ ( in @ SV597 @ SV240 )
| ~ ~ ( in @ SV597 @ SV464 )
| ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1582,plain,
! [SV465: $i,SV241: $i,SV598: $i] :
( ( ~ ~ ( in @ SV598 @ SV241 )
| ~ ( in @ SV598 @ SV465 )
| ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1583,plain,
! [SV242: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( powerset @ SV242 ) ) )
= $true )
| ( ( ! [SY1008: $i] :
( ~ ( in @ SY1008 @ ( powerset @ SV242 ) )
| ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV242 )
| ~ ~ ( in @ SY1009 @ SY1008 )
| ~ ( in @ SY1009 @ ( binintersect @ SV466 @ SY1008 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1584,plain,
! [SV467: $o,SV243: $i,SV599: $i] :
( ( ~ ( in @ SV599 @ SV243 )
| ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1191: $i] :
( ~ ( ~ SV467
| ( SY1191 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1191 != SY1190 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1585,plain,
! [SV243: $i,SV600: $i] :
( ( ~ ( in @ SV600 @ SV243 )
| ! [SY1192: $i] :
( ~ ( in @ SY1192 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1193: $i] :
( ~ ( ~ $true
| ( SY1193 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1193 != SY1192 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1586,plain,
! [SV243: $i,SV601: $i] :
( ( ~ ( in @ SV601 @ SV243 )
| ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1195: $i] :
( ~ ( ~ $false
| ( SY1195 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1195 != SY1194 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1587,plain,
! [SV468: $i,SV244: $i,SV602: $i] :
( ( ~ ( in @ SV602 @ SV244 )
| ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SV468 )
| ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SY1196 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1588,plain,
! [SV470: $i,SV246: $i,SV603: $i] :
( ( ~ ( in @ SV603 @ SV246 )
| ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV470 )
| ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY1197 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1589,plain,
! [SV604: $i,SV471: $i,SV247: $i] :
( ( ~ ( func @ SV247 @ SV471 @ SV604 )
| ! [SY1198: $i] :
( ~ ( func @ SV247 @ SV471 @ SY1198 )
| ~ ! [SY1199: $i] :
( ~ ( in @ SY1199 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1199 )
= ( ap @ SV247 @ SV471 @ SY1198 @ SY1199 ) ) )
| ( SV604 = SY1198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1331]) ).
thf(1590,plain,
! [SV248: $i,SV472: $i,SV605: $i] :
( ( ~ ( in @ SV605 @ SV472 )
| ( in @ SV605 @ ( binunion @ SV248 @ SV472 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1332]) ).
thf(1591,plain,
! [SV249: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ ( powerset @ SV249 ) ) )
= $true )
| ( ( ! [SY1021: $i] :
( ~ ( in @ SY1021 @ ( powerset @ SV249 ) )
| ! [SY1022: $i] :
( ~ ( in @ SY1022 @ SV249 )
| ~ ~ ( in @ SY1022 @ ( binunion @ SV473 @ SY1021 ) )
| ~ ( in @ SY1022 @ SV473 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1592,plain,
! [SV474: $i > $o,SV250: $i,SV606: $i] :
( ( ~ ( in @ SV606 @ SV250 )
| ~ ( SV474 @ SV606 )
| ( in @ SV606
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1593,plain,
! [SV476: $i,SV252: $i,SV607: $i] :
( ( ~ ( in @ SV607 @ SV252 )
| ~ ( in @ SV607 @ SV476 )
| ~ ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1594,plain,
! [SV253: $i,SV477: $i] :
( ( ( ~ ( in @ SV477 @ ( powerset @ SV253 ) ) )
= $true )
| ( ( in @ ( powerset @ SV477 ) @ ( powerset @ ( powerset @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1595,plain,
! [SV478: $i,SV254: $i,SV608: $i] :
( ( ~ ( in @ SV608 @ ( cartprod @ SV254 @ SV478 ) )
| ( iskpair @ SV608 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1596,plain,
! [SV480: $i,SV256: $i] :
( ( ( SV256 != SV480 )
= $true )
| ( ( ! [SY1027: $i,SY1028: $i] :
( ( SY1027 != SY1028 )
| ( ( setadjoin @ SV256 @ SY1027 )
= ( setadjoin @ SV480 @ SY1028 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1597,plain,
! [SV481: $i,SV258: $i] :
( ( ( SV258 != SV481 )
= $true )
| ( ( in @ SV258 @ ( setadjoin @ SV481 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1598,plain,
! [SV259: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ ( powerset @ SV259 ) ) )
= $true )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV259 ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV259 )
| ~ ( in @ SY1030 @ SV482 )
| ( in @ SY1030 @ SY1029 ) )
| ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV259 )
| ~ ( in @ SY1031 @ SY1029 )
| ( in @ SY1031 @ SV482 ) )
| ( SV482 = SY1029 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1342]) ).
thf(1599,plain,
! [SV483: $i,SV260: $i,SV609: $i] :
( ( ~ ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
| ~ ! [SY1201: $i] :
~ ~ ( ~ ( in @ SY1201 @ SV260 )
| ~ ~ ! [SY1202: $i] :
~ ~ ( ~ ( in @ SY1202 @ SV483 )
| ( SV609
!= ( kpair @ SY1201 @ SY1202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1343]) ).
thf(1600,plain,
! [SV261: $i,SV1: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) ) )
= $true )
| ( ( ! [SY1035: $i > $o] :
( ~ ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV1 )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV261 )
| ~ ( in @ ( kpair @ SY1036 @ SY1037 ) @ SV484 )
| ( SY1035 @ ( kpair @ SY1036 @ SY1037 ) ) ) )
| ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV484 )
| ( SY1035 @ SY1038 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1344]) ).
thf(1601,plain,
! [SV262: $i,SV2: $i] :
( ( ( SV2 = SV262 )
= $false )
| ( ( ! [SY670: $i,SY671: $i] :
( ( SY670 != SY671 )
| ~ ( ~ ( ~ ( in @ SY670 @ SV2 )
| ( in @ SY671 @ SV262 ) )
| ~ ( ~ ( in @ SY671 @ SV262 )
| ( in @ SY670 @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1602,plain,
! [SV3: $i,SV263: $i] :
( ( ( in @ SV263 @ ( powerset @ SV3 ) )
= $false )
| ( ( subset @ ( setminus @ SV3 @ ( setminus @ SV3 @ SV263 ) ) @ SV263 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1346]) ).
thf(1603,plain,
! [SV264: $i,SV4: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( setadjoin @ SV4 @ ( setadjoin @ SV264 @ emptyset ) ) ) )
= $true )
| ( ( ( SV485 = SV4 )
| ( SV485 = SV264 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1604,plain,
! [SV265: $i,SV5: $i,SV486: $i] :
( ( ( ~ ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) ) )
= $true )
| ( ( ! [SY1039: $i] :
( ~ ( subset @ SY1039 @ ( cartprod @ SV5 @ SV265 ) )
| ~ ! [SY1040: $i] :
( ~ ( in @ SY1040 @ SV5 )
| ! [SY1041: $i] :
( ~ ( in @ SY1041 @ SV265 )
| ~ ( in @ ( kpair @ SY1040 @ SY1041 ) @ SV486 )
| ( in @ ( kpair @ SY1040 @ SY1041 ) @ SY1039 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ SV5 )
| ! [SY1043: $i] :
( ~ ( in @ SY1043 @ SV265 )
| ~ ( in @ ( kpair @ SY1042 @ SY1043 ) @ SY1039 )
| ( in @ ( kpair @ SY1042 @ SY1043 ) @ SV486 ) ) )
| ( SV486 = SY1039 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1605,plain,
! [SV6: $i] :
( ( ( ~ ( in @ ( sK6_SY25 @ SV6 ) @ SV6 ) )
= $false )
| ( ( SV6 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1349]) ).
thf(1606,plain,
! [SV7: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV7 )
| ( ( setunion @ SV7 )
= SV610 ) )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1350]) ).
thf(1607,plain,
! [SV266: $i,SV8: $i] :
( ( ( ! [SY679: $i] :
( ~ ( in @ SY679 @ SV8 )
| ( in @ SY679 @ SV266 ) ) )
= $false )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1608,plain,
! [SV9: $i] :
( ( ( ! [SY29: $i] :
~ ( in @ SY29 @ SV9 ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1352]) ).
thf(1609,plain,
! [SV10: $i,SV267: $i] :
( ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false )
| ( ( ! [SY680: $o] :
( ~ ! [SY681: $i] :
( ~ ( in @ SV267 @ SY681 )
| ~ ( in @ SY681 @ SV10 )
| SY680 )
| SY680 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1353]) ).
thf(1610,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( ~ ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
| ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ~ ( ~ ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1611,plain,
! [SV12: $i > $o] :
( ( ( ! [SY37: $i] :
~ ! [SY38: $i] :
~ ( ~ ( ~ ( SV12 @ SY38 )
| ( SY38 = SY37 ) )
| ~ ( ( SY38 != SY37 )
| ( SV12 @ SY38 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1612,plain,
! [SV13: $i > $o] :
( ( ( ! [SY41: $i] :
~ ( SV13 @ SY41 ) )
= $true )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1613,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) ) )
= $true )
| ( ( ! [SY1044: $o] :
( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SY1044 )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SY1044 )
| SY1044 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1614,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY685: $i,SY686: $i] :
( ( SY685 != SY686 )
| ~ ( ~ ( ~ ( SV15 @ SY685 )
| ( SV270 @ SY686 ) )
| ~ ( ~ ( SV270 @ SY686 )
| ( SV15 @ SY685 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1358]) ).
thf(1615,plain,
! [SV271: $i,SV16: $i,SV489: $i] :
( ( ( ~ ~ ( in @ SV489 @ SV16 ) )
= $true )
| ( ( ~ ( in @ SV489 @ ( setminus @ SV16 @ SV271 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1359]) ).
thf(1616,plain,
! [SV19: $i > $o] :
( ( ( ! [SY62: $i] :
~ ~ ( ~ ( SV19 @ SY62 )
| ~ ! [SY63: $i] :
( ~ ( SV19 @ SY63 )
| ( SY62 = SY63 ) ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1617,plain,
! [SV272: $i,SV20: $i] :
( ( ( ~ ( subset @ SV20 @ SV272 ) )
= $false )
| ( ( SV20 != SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1618,plain,
! [SV21: $i,SV273: $i] :
( ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false )
| ( ( ! [SY696: $i] :
( ~ ( in @ SY696 @ ( powerset @ SV21 ) )
| ! [SY697: $i] :
( ~ ( in @ SY697 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SY696 ) )
| ~ ( in @ SY697 @ SV273 )
| ( in @ SY697 @ SY696 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1619,plain,
! [SV274: $i,SV22: $i,SV490: $i] :
( ( ( ~ ~ ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV490 @ SV274 )
| ~ ( in @ SV490 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1620,plain,
! [SV23: $i,SV275: $i] :
( ( ( in @ SV275 @ SV23 )
= $false )
| ( ( subset @ ( setadjoin @ SV275 @ emptyset ) @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1621,plain,
! [SV276: $i,SV24: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) ) )
= $true )
| ( ( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV24 )
| ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SY1045 ) @ SV276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1366]) ).
thf(1622,plain,
! [SV611: $i,SV492: $i,SV278: $i,SV26: $i] :
( ( ( ( kpair @ SV26 @ SV278 )
!= ( kpair @ SV492 @ SV611 ) )
| ( SV26 = SV492 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1367]) ).
thf(1623,plain,
! [SV279: $i,SV27: $i,SV612: $i,SV493: $i] :
( ( ~ ( in @ ( kpair @ SV493 @ SV612 ) @ ( cartprod @ SV27 @ SV279 ) )
| ( in @ SV493 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1368]) ).
thf(1624,plain,
! [SV494: $i > $i > $o,SV281: $i,SV29: $i,SV613: $i] :
( ( ~ ( in @ SV613 @ SV29 )
| ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV281 )
| ~ ( SV494 @ SV613 @ SY1203 )
| ( in @ ( kpair @ SV613 @ SY1203 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1369]) ).
thf(1625,plain,
! [SV283: $i,SV31: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) ) )
= $true )
| ( ( ! [SY1054: $i] :
( ~ ( in @ SY1054 @ SV31 )
| ! [SY1055: $i] :
( ~ ( in @ SY1055 @ SV283 )
| ~ ( in @ ( kpair @ SY1054 @ SY1055 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SY1054 )
= SY1055 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1371]) ).
thf(1626,plain,
! [SV284: $i,SV32: $i] :
( ( ( SV32 = SV284 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV32 @ ( setadjoin @ SV284 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV32 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1627,plain,
! [SV285: $i,SV33: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ ( setadjoin @ SV33 @ SV285 ) ) )
= $true )
| ( ( ( SV497 = SV33 )
| ( in @ SV497 @ SV285 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1628,plain,
! [SV287: $o,SV35: $i,SV498: $i] :
( ( ( ~ ( in @ SV498 @ SV35 ) )
= $true )
| ( ( ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV35 )
| ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SY1056 )
= SY1056 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1629,plain,
! [SV35: $i,SV499: $i] :
( ( ( ~ ( in @ SV499 @ SV35 ) )
= $true )
| ( ( ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV35 )
| ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SY1057 )
= SY1057 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1375]) ).
thf(1630,plain,
! [SV35: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ SV35 ) )
= $true )
| ( ( ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV35 )
| ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SY1058 )
= SY1058 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1376]) ).
thf(1631,plain,
! [SV288: $i,SV501: $i > $i,SV36: $i] :
( ( ( ~ ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV36 )
| ( in @ ( SV501 @ SY1059 ) @ SV288 ) ) )
= $true )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1632,plain,
! [SV289: $i,SV37: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV37 ) )
= $true )
| ( ( in @ ( setadjoin @ SV502 @ emptyset ) @ ( powerset @ ( binunion @ SV37 @ SV289 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1633,plain,
! [SV290: $i,SV38: $i] :
( ( ( subset @ SV38 @ SV290 )
= $false )
| ( ( ( binintersect @ SV38 @ SV290 )
= SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1379]) ).
thf(1634,plain,
! [SV291: $i,SV39: $i] :
( ( ( ( binintersect @ SV39 @ SV291 )
= SV291 )
= $false )
| ( ( subset @ SV291 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1635,plain,
! [SV292: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV292 )
= $false )
| ( ( ( setminus @ SV40 @ SV292 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1636,plain,
! [SV41: $i,SV293: $i] :
( ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false )
| ( ( ! [SY724: $i] :
( ~ ( in @ SY724 @ ( powerset @ SV41 ) )
| ~ ( subset @ SV293 @ ( setminus @ SV41 @ SY724 ) )
| ! [SY725: $i] :
( ~ ( in @ SY725 @ SV41 )
| ~ ( in @ SY725 @ SY724 )
| ( in @ SY725 @ ( setminus @ SV41 @ SV293 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1382]) ).
thf(1637,plain,
! [SV294: $i,SV42: $i] :
( ( ( ( binintersect @ SV42 @ SV294 )
= SV42 )
= $false )
| ( ( subset @ SV42 @ SV294 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1638,plain,
! [SV43: $i,SV295: $i] :
( ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false )
| ( ( ! [SY726: $i] :
( ~ ( in @ SY726 @ ( powerset @ SV43 ) )
| ! [SY727: $i] :
( ~ ( in @ SY727 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SY726 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY727 ) @ ( binunion @ SY726 @ SY727 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1639,plain,
! [SV296: $i,SV503: $i > $i,SV44: $i] :
( ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV44 )
| ( in @ ( SV503 @ SY1061 ) @ SV296 ) ) )
= $true )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1640,plain,
! [SV297: $i,SV45: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV45 ) )
= $true )
| ( ( ~ ~ ( in @ SV504 @ SV297 )
| ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1641,plain,
! [SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY733: $i] :
( ~ ( in @ SY733 @ SV298 )
| ~ ! [SY131: $i] :
~ ~ ( ~ ( SV46 @ SY733 @ SY131 )
| ~ ! [SY132: $i] :
( ~ ( SV46 @ SY733 @ SY132 )
| ( SY131 = SY132 ) ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1642,plain,
! [SV299: $i,SV49: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV49 ) )
= $true )
| ( ( in @ SV505 @ ( binunion @ SV49 @ SV299 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1643,plain,
! [SV50: $i,SV300: $i] :
( ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false )
| ( ( ! [SY741: $i] :
( ~ ( in @ SY741 @ ( powerset @ SV50 ) )
| ! [SY742: $i] :
( ~ ( in @ SY742 @ SV50 )
| ~ ~ ( in @ SY742 @ SV300 )
| ~ ( in @ SY742 @ ( binintersect @ SV300 @ SY741 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1644,plain,
! [SV301: $i,SV51: $i,SV506: $i] :
( ( ( ~ ~ ( in @ SV506 @ SV51 ) )
= $true )
| ( ( ~ ~ ( in @ SV506 @ SV301 )
| ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1645,plain,
! [SV52: $i] :
( ( ( ! [SY144: $i] :
~ ( in @ SY144 @ SV52 ) )
= $true )
| ( ( SV52 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1392]) ).
thf(1646,plain,
! [SV507: $i,SV302: $i,SV54: $i] :
( ( ( ~ ( func @ SV54 @ SV302 @ SV507 ) )
= $true )
| ( ( ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV54 )
| ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SY1064 ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1647,plain,
! [SV303: $i > $o,SV55: $i] :
( ( ( ~ ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV55 )
| ~ ( SV303 @ SY746 ) ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1648,plain,
! [SV304: $i,SV56: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ ( binunion @ SV56 @ SV304 ) ) )
= $true )
| ( ( ( in @ SV508 @ SV56 )
| ( in @ SV508 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1649,plain,
! [SV305: $i,SV57: $i,SV509: $i] :
( ( ( ~ ( in @ SV509 @ ( binintersect @ SV57 @ SV305 ) ) )
= $true )
| ( ( in @ SV509 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1396]) ).
thf(1650,plain,
! [SV306: $i,SV58: $i] :
( ( ( SV58 != SV306 )
= $false )
| ( ( ~ ( in @ SV306 @ ( setadjoin @ SV58 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1651,plain,
! [SV307: $i > $o,SV59: $i,SV510: $i] :
( ( ( ~ ( in @ SV510
@ ( dsetconstr @ SV59
@ ^ [SY751: $i] : ( SV307 @ SY751 ) ) ) )
= $true )
| ( ( in @ SV510 @ SV59 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1652,plain,
! [SV308: $i,SV60: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ ( setminus @ SV60 @ SV308 ) ) )
= $true )
| ( ( ~ ( in @ SV511 @ SV308 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1399]) ).
thf(1653,plain,
! [SV309: $i,SV61: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV61 ) )
= $true )
| ( ( ~ ( in @ SV512 @ SV309 )
| ( in @ SV512 @ ( binintersect @ SV61 @ SV309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1654,plain,
! [SV62: $i,SV310: $i] :
( ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false )
| ( ( ! [SY754: $i] :
( ~ ( in @ SY754 @ ( powerset @ SV62 ) )
| ! [SY755: $i] :
( ~ ( in @ SY755 @ ( powerset @ SV62 ) )
| ! [SY756: $i] :
( ~ ( in @ SY756 @ SV62 )
| ~ ( in @ SY756 @ ( binintersect @ SV310 @ SY754 ) )
| ( in @ SY756 @ ( binintersect @ ( binunion @ SV310 @ SY755 ) @ ( binunion @ SY754 @ SY755 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1655,plain,
! [SV311: $i > $o,SV63: $i] :
( ( ( ~ ! [SY757: $i] :
~ ~ ( ~ ( in @ SY757 @ SV63 )
| ~ ~ ( SV311 @ SY757 ) ) )
= $false )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1656,plain,
! [SV65: $i] :
( ( ( SV65 = emptyset )
= $true )
| ( ( ~ ! [SY170: $i] :
~ ( in @ SY170 @ SV65 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1406]) ).
thf(1657,plain,
! [SV513: $i,SV312: $i,SV67: $i] :
( ( ( ~ ( subset @ SV67 @ SV312 ) )
= $true )
| ( ( ~ ~ ( in @ SV513 @ SV312 )
| ~ ( in @ SV513 @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1658,plain,
! [SV68: $i,SV313: $i] :
( ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false )
| ( ( ! [SY760: $i] :
( ~ ( in @ SY760 @ ( powerset @ SV68 ) )
| ~ ! [SY761: $i] :
( ~ ( in @ SY761 @ SV68 )
| ~ ( in @ SY761 @ SV313 )
| ( in @ SY761 @ SY760 ) )
| ( subset @ SV313 @ SY760 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1659,plain,
! [SV314: $i,SV69: $i] :
( ( ( SV69 = SV314 )
= $false )
| ( ( ( powerset @ SV69 )
= ( powerset @ SV314 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1409]) ).
thf(1660,plain,
! [SV514: $i,SV315: $i,SV70: $i] :
( ( ( ~ ( func @ SV70 @ SV315 @ SV514 ) )
= $true )
| ( ( in @ SV514 @ ( funcSet @ SV70 @ SV315 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1661,plain,
! [SV614: $i,SV515: $i,SV316: $i,SV71: $i] :
( ( ( ( kpair @ SV71 @ SV316 )
!= ( kpair @ SV515 @ SV614 ) )
| ( SV316 = SV614 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1411]) ).
thf(1662,plain,
! [SV516: $i,SV317: $i,SV72: $i] :
( ( ( ~ ( subset @ SV72 @ SV317 ) )
= $true )
| ( ( ~ ( subset @ SV317 @ SV516 )
| ( subset @ SV72 @ SV516 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1663,plain,
! [SV318: $i,SV73: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) ) )
= $true )
| ( ( ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV73 )
| ( ( ap @ SV73 @ SV318 @ SV517 @ SY1067 )
= ( ap @ SV73 @ SV318 @ SV517 @ SY1067 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1664,plain,
! [SV319: $i,SV74: $i] :
( ( ( ! [SY768: $i] :
~ ( ~ ( ~ ( in @ SY768 @ SV74 )
| ( in @ SY768 @ SV319 ) )
| ~ ( ~ ( in @ SY768 @ SV319 )
| ( in @ SY768 @ SV74 ) ) ) )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1665,plain,
! [SV320: $i,SV75: $i] :
( ( ( SV75 = SV320 )
= $false )
| ( ( ( setadjoin @ SV75 @ ( setadjoin @ SV320 @ emptyset ) )
= ( setadjoin @ SV75 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1666,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY769: $i] :
( ~ ( in @ SY769 @ SV76 )
| ! [SY770: $i] :
( ~ ( in @ SY770 @ SV76 )
| ~ ( SV321 @ SY769 )
| ~ ( SV321 @ SY770 )
| ( SY769 = SY770 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1667,plain,
! [SV77: $i,SV322: $i] :
( ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false )
| ( ( ! [SY773: $i] :
( ~ ( in @ SY773 @ ( powerset @ SV77 ) )
| ! [SY774: $i] :
( ~ ( in @ SY774 @ SV77 )
| ~ ( subset @ SV322 @ SY773 )
| ~ ~ ( in @ SY774 @ SY773 )
| ~ ( in @ SY774 @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1668,plain,
! [SV79: $i,SV518: $i,SV324: $i] :
( ( ( ~ ( in @ SV324 @ SV518 ) )
= $true )
| ( ( ~ ( in @ SV518 @ SV79 )
| ( in @ SV324 @ ( setunion @ SV79 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1669,plain,
! [SV325: $i,SV81: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ ( funcSet @ SV81 @ SV325 ) ) )
= $true )
| ( ( func @ SV81 @ SV325 @ SV519 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1670,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ( ~ ( in @ SV326 @ ( powerset @ SV82 ) )
| ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1671,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ( ~ ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) )
| ( in @ SV326 @ ( powerset @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1421]) ).
thf(1672,plain,
! [SV327: $i > $o,SV83: $i] :
( ( ( ~ ! [SY779: $i] :
~ ~ ( ~ ( in @ SY779 @ SV83 )
| ~ ( SV327 @ SY779 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1673,plain,
! [SV328: $o,SV84: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV84 ) )
= $true )
| ( ( ! [SY1068: $i] :
( ~ ( in @ SY1068 @ SV84 )
| ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1069: $i] :
( ~ ( ~ SV328
| ( SY1069 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1069 != SY1068 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1674,plain,
! [SV84: $i,SV521: $i] :
( ( ( ~ ( in @ SV521 @ SV84 ) )
= $true )
| ( ( ! [SY1070: $i] :
( ~ ( in @ SY1070 @ SV84 )
| ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1071: $i] :
( ~ ( ~ $true
| ( SY1071 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1071 != SY1070 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1675,plain,
! [SV84: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV84 ) )
= $true )
| ( ( ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV84 )
| ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1073: $i] :
( ~ ( ~ $false
| ( SY1073 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1073 != SY1072 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1676,plain,
! [SV329: $i,SV85: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV85 ) )
= $true )
| ( ( ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV329 )
| ( in @ ( kpair @ SV523 @ SY1074 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1677,plain,
! [SV524: $i,SV330: $i,SV86: $i] :
( ( ( ~ ( func @ SV86 @ SV330 @ SV524 ) )
= $true )
| ( ( ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV86 )
| ! [SY1076: $i] :
( ~ ( in @ SY1076 @ SV330 )
| ~ ( in @ ( kpair @ SY1075 @ SY1076 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SY1075 )
= SY1076 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1678,plain,
! [SV331: $i,SV87: $i] :
( ( ( SV87 = SV331 )
= $false )
| ( ( subset @ SV331 @ SV87 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1679,plain,
! [SV88: $o,SV332: $i] :
( ( ( in @ SV332 @ ( prop2set @ SV88 ) )
= $false )
| ( SV88 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1680,plain,
! [SV333: $i] :
( ( ( in @ SV333 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1430]) ).
thf(1681,plain,
! [SV334: $i] :
( ( ( in @ SV334 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1682,plain,
! [SV89: $i > $o] :
( ( ( ! [SY223: $i] :
~ ~ ( ~ ( SV89 @ SY223 )
| ~ ! [SY224: $i] :
( ~ ( SV89 @ SY224 )
| ( SY223 = SY224 ) ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1683,plain,
! [SV525: $i,SV335: $i,SV90: $i] :
( ( ( ~ ( func @ SV90 @ SV335 @ SV525 ) )
= $true )
| ( ( ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1078: $i] : ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV525 ) ) )
@ SV335 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1684,plain,
! [SV337: $i > $o,SV92: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV92 ) )
= $true )
| ( ( ~ ( SV337 @ SV526 )
| ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1434]) ).
thf(1685,plain,
! [SV338: $i,SV93: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ ( setminus @ SV93 @ SV338 ) ) )
= $true )
| ( ( in @ SV527 @ SV93 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1686,plain,
! [SV339: $i,SV94: $i] :
( ( ( ( setminus @ SV94 @ SV339 )
= emptyset )
= $false )
| ( ( subset @ SV94 @ SV339 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1687,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( ~ ( in @ SV528 @ SV95 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) )
| ~ ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1688,plain,
! [SV96: $i,SV341: $i] :
( ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false )
| ( ( ! [SY798: $i] :
( ~ ( in @ SY798 @ ( powerset @ SV96 ) )
| ! [SY799: $i] :
( ~ ( in @ SY799 @ SV96 )
| ~ ( in @ SY799 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SY798 ) ) )
| ~ ( in @ SY799 @ SV341 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1689,plain,
! [SV342: $i,SV97: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ SV97 ) )
= $true )
| ( ( ! [SY1082: $i] :
( ~ ( in @ SY1082 @ SV342 )
| ( ( kpair @ SV529 @ SY1082 )
= ( kpair @ SV529 @ SY1082 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1690,plain,
! [SV98: $i,SV343: $i] :
( ( ( in @ SV343 @ ( powerset @ SV98 ) )
= $false )
| ( ( in @ ( setminus @ SV98 @ SV343 ) @ ( powerset @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1691,plain,
! [SV344: $i,SV100: $i] :
( ( ( SV100 = SV344 )
= $false )
| ( ( ! [SY802: $i,SY803: $i] :
( ( SY802 != SY803 )
| ~ ( in @ SY802 @ SV100 )
| ( in @ SY803 @ SV344 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1692,plain,
! [SV101: $i,SV345: $i] :
( ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false )
| ( ( ! [SY804: $i] :
( ~ ( in @ SY804 @ ( powerset @ SV101 ) )
| ~ ( subset @ ( setminus @ SV101 @ SY804 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SY804 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1693,plain,
! [SV102: $i,SV346: $i] :
( ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false )
| ( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ ( powerset @ SV102 ) )
| ! [SY806: $i] :
( ~ ( in @ SY806 @ ( powerset @ SV102 ) )
| ! [SY807: $i] :
( ~ ( in @ SY807 @ SV102 )
| ~ ( in @ SY807 @ ( binintersect @ SV346 @ SY805 ) )
| ( in @ SY807 @ ( binunion @ SV346 @ SY806 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1446]) ).
thf(1694,plain,
! [SV530: $i,SV348: $i,SV104: $i] :
( ( ( ~ ( func @ SV104 @ SV348 @ SV530 ) )
= $true )
| ( ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV104 )
| ( in @ ( kpair @ SY1083 @ ( ap @ SV104 @ SV348 @ SV530 @ SY1083 ) ) @ SV530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1447]) ).
thf(1695,plain,
! [SV105: $i] :
( ( ( SV105 = emptyset )
= $true )
| ( ( ~ ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV105 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1696,plain,
! [SV349: $i,SV106: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ ( cartprod @ SV106 @ SV349 ) ) )
= $true )
| ( ( in @ ( kfst @ SV531 ) @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1697,plain,
! [SV351: $i,SV109: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV109 ) )
= $true )
| ( ( ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV351 )
| ( in @ ( kpair @ SV532 @ SY1084 ) @ ( cartprod @ SV109 @ SV351 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1698,plain,
! [SV110: $i,SV352: $i] :
( ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false )
| ( ( ! [SY813: $i] :
( ~ ( in @ SY813 @ ( powerset @ SV110 ) )
| ! [SY814: $i] :
( ~ ( in @ SY814 @ ( powerset @ SV110 ) )
| ! [SY815: $i] :
( ~ ( in @ SY815 @ SV110 )
| ~ ( in @ SY815 @ ( binintersect @ SV352 @ SY813 ) )
| ( in @ SY815 @ ( binunion @ SY813 @ SY814 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1699,plain,
! [SV111: $i,SV353: $i] :
( ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false )
| ( ( ! [SY816: $i] :
( ~ ( in @ SY816 @ ( powerset @ SV111 ) )
| ~ ( subset @ SV353 @ SY816 )
| ( subset @ ( setminus @ SV111 @ SY816 ) @ ( setminus @ SV111 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1700,plain,
! [SV112: $i,SV354: $i] :
( ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false )
| ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV354 @ ( setminus @ SV112 @ SY817 ) )
| ( subset @ SY817 @ ( setminus @ SV112 @ SV354 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1453]) ).
thf(1701,plain,
! [SV355: $i,SV113: $i] :
( ( ( ! [SY818: $i] :
( ~ ( in @ SY818 @ SV113 )
| ( in @ SY818 @ SV355 ) ) )
= $false )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1454]) ).
thf(1702,plain,
! [SV356: $i,SV114: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ SV114 ) )
= $true )
| ( ( ! [SY1085: $i] :
( ~ ( in @ SY1085 @ SV356 )
| ( ( kfst @ ( kpair @ SV533 @ SY1085 ) )
= SV533 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1455]) ).
thf(1703,plain,
! [SV115: $i,SV357: $i] :
( ( ( in @ SV357 @ ( powerset @ SV115 ) )
= $false )
| ( ( SV357
= ( setminus @ SV115 @ ( setminus @ SV115 @ SV357 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1704,plain,
! [SV358: $o,SV116: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ SV116 ) )
= $true )
| ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV116 )
| ~ ~ SV358
| ( in @ SY1086
@ ( dsetconstr @ SV116
@ ^ [SY1087: $i] :
( ~ ( ~ SV358
| ( SY1087 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1087 != SY1086 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1705,plain,
! [SV116: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV116 ) )
= $true )
| ( ( ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV116 )
| ~ ~ $true
| ( in @ SY1088
@ ( dsetconstr @ SV116
@ ^ [SY1089: $i] :
( ~ ( ~ $true
| ( SY1089 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1089 != SY1088 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1458]) ).
thf(1706,plain,
! [SV116: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ SV116 ) )
= $true )
| ( ( ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV116 )
| ~ ~ $false
| ( in @ SY1090
@ ( dsetconstr @ SV116
@ ^ [SY1091: $i] :
( ~ ( ~ $false
| ( SY1091 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1091 != SY1090 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1707,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ! [SY824: $i] :
( ~ ( in @ SY824 @ SV117 )
| ~ ( SV359 @ SY824 ) ) )
= $false )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1708,plain,
! [SV537: $i,SV360: $i,SV118: $i] :
( ( ( ~ ( func @ SV118 @ SV360 @ SV537 ) )
= $true )
| ( ( ! [SY1092: $i] :
( ~ ( func @ SV118 @ SV360 @ SY1092 )
| ~ ! [SY1093: $i] :
( ~ ( in @ SY1093 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1093 )
= ( ap @ SV118 @ SV360 @ SY1092 @ SY1093 ) ) )
| ! [SY1094: $i] :
( ~ ( in @ SY1094 @ SV118 )
| ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV360 )
| ~ ( in @ ( kpair @ SY1094 @ SY1095 ) @ SY1092 )
| ( in @ ( kpair @ SY1094 @ SY1095 ) @ SV537 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1461]) ).
thf(1709,plain,
! [SV361: $i,SV119: $i] :
( ( ( in @ SV119 @ ( setadjoin @ SV361 @ emptyset ) )
= $false )
| ( ( SV119 = SV361 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1462]) ).
thf(1710,plain,
! [SV120: $i,SV362: $i] :
( ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false )
| ( ( ! [SY831: $i] :
( ~ ( in @ SY831 @ SV120 )
| ~ ( in @ SY831 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SY831 @ SV362 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1711,plain,
! [SV363: $i,SV121: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV121 ) )
= $true )
| ( ( ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV363 )
| ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SY1096 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1712,plain,
! [SV122: $i] :
( ( ( ~ ( in @ ( sK7_SY302 @ SV122 ) @ SV122 ) )
= $false )
| ( ( SV122 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1465]) ).
thf(1713,plain,
! [SV124: $i,SV364: $i] :
( ( ( ! [SY834: $i] :
( ~ ( in @ SY834 @ SV364 )
| ( in @ SY834 @ SV124 ) ) )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1714,plain,
! [SV365: $i,SV125: $i,SV539: $i] :
( ( ( ~ ( in @ SV539 @ ( cartprod @ SV125 @ SV365 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1715,plain,
! [SV366: $i,SV126: $i,SV540: $i] :
( ( ( ~ ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) ) )
= $true )
| ( ( ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ ( cartprod @ SV126 @ SV366 ) )
| ~ ! [SY1098: $i] :
( ~ ( in @ SY1098 @ SV126 )
| ! [SY1099: $i] :
( ~ ( in @ SY1099 @ SV366 )
| ~ ( in @ ( kpair @ SY1098 @ SY1099 ) @ SV540 )
| ( in @ ( kpair @ SY1098 @ SY1099 ) @ SY1097 ) ) )
| ( subset @ SV540 @ SY1097 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1468]) ).
thf(1716,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i,SV615: $i] :
( ( ~ ( in @ SV615 @ SV128 )
| ! [SY1206: $i] :
( ~ ( in @ SY1206 @ SV368 )
| ~ ( in @ ( kpair @ SV615 @ SY1206 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SY1206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1717,plain,
! [SV129: $i,SV369: $i] :
( ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false )
| ( ( ! [SY845: $i] :
( ~ ( in @ SY845 @ SV129 )
| ~ ~ ( in @ SY845 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SY845 @ SV369 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1470]) ).
thf(1718,plain,
! [SV370: $i,SV130: $i,SV616: $i,SV542: $i] :
( ( ~ ( in @ ( kpair @ SV542 @ SV616 ) @ ( cartprod @ SV130 @ SV370 ) )
| ( in @ SV616 @ SV370 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1719,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY848: $i] :
( ~ ( in @ SY848 @ SV131 )
| ! [SY849: $i] :
( ~ ( in @ SY849 @ SV131 )
| ~ ( SV371 @ SY848 )
| ~ ( SV371 @ SY849 )
| ( SY848 = SY849 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1720,plain,
! [SV372: $i > $o,SV132: $i,SV543: $i] :
( ( ( ~ ( in @ SV543
@ ( dsetconstr @ SV132
@ ^ [SY853: $i] : ( SV372 @ SY853 ) ) ) )
= $true )
| ( ( SV372 @ SV543 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1721,plain,
! [SV373: $i,SV133: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV133 ) )
= $true )
| ( ( ~ ~ ( in @ SV544 @ SV373 )
| ( SV133 != SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1722,plain,
! [SV136: $i,SV376: $i] :
( ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false )
| ( ( ! [SY856: $i] :
( ~ ( in @ SY856 @ ( powerset @ SV136 ) )
| ! [SY857: $i] :
( ~ ( in @ SY857 @ SV136 )
| ~ ( in @ SY857 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SY856 ) ) )
| ( in @ SY857 @ ( setminus @ SV136 @ SV376 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1475]) ).
thf(1723,plain,
! [SV377: $i,SV137: $i] :
( ( ( SV137 = SV377 )
= $false )
| ( ( ! [SY858: $i > $o,SY859: $i > $o] :
( ~ ! [SY860: $i] :
( ~ ( in @ SY860 @ SV137 )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ SV377 )
| ( SY860 != SY861 )
| ~ ( ~ ( ~ ( SY858 @ SY860 )
| ( SY859 @ SY861 ) )
| ~ ( ~ ( SY859 @ SY861 )
| ( SY858 @ SY860 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SX4: $i] : ( SY858 @ SX4 ) )
= ( dsetconstr @ SV377
@ ^ [SX4: $i] : ( SY859 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1724,plain,
! [SV378: $i,SV138: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV138 ) )
= $true )
| ( ( ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV378 )
| ( ( ksnd @ ( kpair @ SV545 @ SY1106 ) )
= SY1106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1477]) ).
thf(1725,plain,
! [SV379: $i,SV139: $i,SV546: $i] :
( ( ( ~ ( subset @ SV546 @ SV139 ) )
= $true )
| ( ( ~ ( subset @ SV546 @ SV379 )
| ( subset @ SV546 @ ( binintersect @ SV139 @ SV379 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1726,plain,
! [SV380: $i,SV140: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV140 ) )
= $true )
| ( ( ~ ~ ( in @ SV547 @ SV380 )
| ~ ( subset @ SV140 @ SV380 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1727,plain,
! [SV141: $i,SV381: $i] :
( ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false )
| ( ( ! [SY868: $i] :
( ~ ( in @ SY868 @ SV141 )
| ~ ( in @ SY868 @ SV381 )
| ( in @ SY868 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1480]) ).
thf(1728,plain,
! [SV142: $i,SV617: $o] :
( ( SV617 = $true )
| ( ( in @ SV142 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1481]) ).
thf(1729,plain,
! [SV142: $i] :
( ( $true = $true )
| ( ( in @ SV142 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1481]) ).
thf(1730,plain,
! [SV142: $i] :
( ( $false = $true )
| ( ( in @ SV142 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1481]) ).
thf(1731,plain,
! [SV144: $i,SV383: $i] :
( ( ( in @ SV383 @ ( powerset @ SV144 ) )
= $false )
| ( ( ! [SY869: $i] :
( ~ ( in @ SY869 @ ( powerset @ SV144 ) )
| ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SY869 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1482]) ).
thf(1732,plain,
! [SV146: $i > $o] :
( ( ( ! [SY360: $i] :
~ ~ ( ~ ( SV146 @ SY360 )
| ~ ! [SY361: $i] :
( ~ ( SV146 @ SY361 )
| ( SY360 = SY361 ) ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1484]) ).
thf(1733,plain,
! [SV147: $i,SV384: $i] :
( ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false )
| ( ( ! [SY870: $i] :
( ~ ( in @ SY870 @ ( powerset @ SV147 ) )
| ! [SY871: $i] :
( ~ ( in @ SY871 @ SV147 )
| ~ ~ ( in @ SY871 @ ( binunion @ SV384 @ SY870 ) )
| ~ ( in @ SY871 @ SY870 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1734,plain,
! [SV148: $i,SV385: $i] :
( ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false )
| ( ( ! [SY872: $i] :
( ~ ( in @ SY872 @ ( powerset @ SV148 ) )
| ~ ! [SY873: $i] :
( ~ ( in @ SY873 @ SV148 )
| ~ ( in @ SY873 @ SV385 )
| ( in @ SY873 @ SY872 ) )
| ( in @ SV385 @ ( powerset @ SY872 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1735,plain,
! [SV386: $i,SV149: $i] :
( ( ( subset @ SV149 @ SV386 )
= $false )
| ( ( subset @ ( powerset @ SV149 ) @ ( powerset @ SV386 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1736,plain,
! [SV388: $i,SV548: $i,SV151: $i] :
( ( ( ~ ( subset @ SV151 @ SV548 ) )
= $true )
| ( ( subset @ SV151 @ ( setadjoin @ SV388 @ SV548 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1737,plain,
! [SV389: $i,SV549: $i > $i,SV152: $i] :
( ( ( ~ ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV152 )
| ( in @ ( SV549 @ SY1107 ) @ SV389 ) ) )
= $true )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1738,plain,
! [SV153: $i,SV390: $i] :
( ( ( in @ SV390 @ ( powerset @ SV153 ) )
= $false )
| ( ( ! [SY879: $i] :
( ~ ( in @ SY879 @ ( powerset @ SV153 ) )
| ( in @ ( setminus @ SV390 @ SY879 ) @ ( powerset @ SV153 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1739,plain,
! [SV391: $o,SV154: $i,SV550: $i] :
( ( ( ~ ( in @ SV550 @ SV154 ) )
= $true )
| ( ( ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SV154 )
| ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1111: $i] :
( ~ ( ~ SV391
| ( SY1111 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1111 != SY1110 ) ) ) )
= ( setadjoin @ SY1110 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1491]) ).
thf(1740,plain,
! [SV154: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ SV154 ) )
= $true )
| ( ( ! [SY1112: $i] :
( ~ ( in @ SY1112 @ SV154 )
| ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1113: $i] :
( ~ ( ~ $true
| ( SY1113 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1113 != SY1112 ) ) ) )
= ( setadjoin @ SY1112 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1741,plain,
! [SV154: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV154 ) )
= $true )
| ( ( ! [SY1114: $i] :
( ~ ( in @ SY1114 @ SV154 )
| ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1115: $i] :
( ~ ( ~ $false
| ( SY1115 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1115 != SY1114 ) ) ) )
= ( setadjoin @ SY1114 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1742,plain,
! [SV553: $i > $i > $o,SV392: $i,SV156: $i,SV618: $i] :
( ( ! [SY1209: $i] :
( ~ ( in @ ( kpair @ SV618 @ SY1209 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SY1118: $i,SY1119: $i] : ( SV553 @ SY1118 @ SY1119 ) ) )
| ( in @ SY1209 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1743,plain,
! [SV393: $o,SV157: $i,SV554: $i] :
( ( ( ~ ( in @ SV554 @ SV157 ) )
= $true )
| ( ( ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SV157 )
| ( in @ ( if @ SV157 @ SV393 @ SV554 @ SY1120 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1744,plain,
! [SV157: $i,SV555: $i] :
( ( ( ~ ( in @ SV555 @ SV157 ) )
= $true )
| ( ( ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV157 )
| ( in @ ( if @ SV157 @ $true @ SV555 @ SY1121 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1745,plain,
! [SV157: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ SV157 ) )
= $true )
| ( ( ! [SY1122: $i] :
( ~ ( in @ SY1122 @ SV157 )
| ( in @ ( if @ SV157 @ $false @ SV556 @ SY1122 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1497]) ).
thf(1746,plain,
! [SV158: $i] :
( ( ( ~ ( in @ emptyset @ SV158 )
| ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) )
= $true )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1747,plain,
! [SV394: $i,SV160: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( setadjoin @ SV160 @ ( setadjoin @ SV394 @ emptyset ) ) ) )
= $true )
| ( ( ( SV557 = SV160 )
| ( SV557 = SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1748,plain,
! [SV396: $i,SV559: $i > $i,SV162: $i] :
( ( ( ~ ! [SY1125: $i] :
( ~ ( in @ SY1125 @ SV162 )
| ( in @ ( SV559 @ SY1125 ) @ SV396 ) ) )
= $true )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1749,plain,
! [SV163: $i,SV397: $i] :
( ( ( in @ SV397 @ ( powerset @ SV163 ) )
= $false )
| ( ( subset @ SV397 @ ( setminus @ SV163 @ ( setminus @ SV163 @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1750,plain,
! [SV560: $i > $i > $o,SV398: $i,SV164: $i,SV619: $i] :
( ( ! [SY1212: $i] :
( ~ ( in @ ( kpair @ SV619 @ SY1212 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SY1129: $i,SY1130: $i] : ( SV560 @ SY1129 @ SY1130 ) ) )
| ( SV560 @ SV619 @ SY1212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1504]) ).
thf(1751,plain,
! [SV399: $i,SV165: $i] :
( ( ( subset @ SV165 @ SV399 )
= $false )
| ( ( ~ ( subset @ SV399 @ SV165 )
| ( SV165 = SV399 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1752,plain,
! [SV400: $i,SV166: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ ( binintersect @ SV166 @ SV400 ) ) )
= $true )
| ( ( in @ SV561 @ SV400 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1506]) ).
thf(1753,plain,
! [SV167: $i,SV401: $i] :
( ( ( in @ SV401 @ SV167 )
= $false )
| ( ( in @ SV401 @ ( powerset @ ( setunion @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1507]) ).
thf(1754,plain,
! [SV168: $i,SV402: $i] :
( ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false )
| ( ( ! [SY903: $i] :
( ~ ( in @ SY903 @ ( powerset @ SV168 ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV168 )
| ~ ( in @ SY904 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY904 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SY903 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1755,plain,
! [SV403: $i > $o,SV169: $i] :
( ( ( ~ ~ ! [SY905: $i] :
~ ~ ( ~ ( in @ SY905 @ SV169 )
| ~ ( SV403 @ SY905 ) ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1756,plain,
! [SV404: $i,SV170: $i] :
( ( ( ( setadjoin @ SV170 @ emptyset )
= ( setadjoin @ SV404 @ emptyset ) )
= $false )
| ( ( SV170 = SV404 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1757,plain,
! [SV171: $i,SV405: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ SV405 ) )
= $true )
| ( ( ~ ( in @ SV562 @ ( setminus @ SV171 @ SV405 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1758,plain,
! [SV406: $i,SV172: $i] :
( ( ( SV172 = SV406 )
= $false )
| ( ( subset @ SV172 @ SV406 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1759,plain,
! [SV173: $i,SV407: $i] :
( ( ( in @ SV407 @ ( powerset @ SV173 ) )
= $false )
| ( ( subset @ SV407 @ SV173 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1513]) ).
thf(1760,plain,
! [SV408: $i > $o,SV174: $i] :
( ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false )
| ( ( ~ ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SV174 )
| ~ ( SV408 @ SY909 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1761,plain,
! [SV409: $i,SV175: $i,SV563: $i] :
( ( ( ~ ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) ) )
= $true )
| ( ( ! [SY1131: $i] :
( ~ ( in @ SY1131 @ ( funcSet @ SV175 @ SV409 ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1132 )
= ( ap @ SV175 @ SV409 @ SY1131 @ SY1132 ) ) )
| ( SV563 = SY1131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1515]) ).
thf(1762,plain,
! [SV176: $i,SV410: $i] :
( ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false )
| ( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV176 )
| ~ ( in @ SY913 @ SV410 )
| ~ ( in @ SY913 @ ( setminus @ SV176 @ SV410 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1516]) ).
thf(1763,plain,
! [SV178: $i,SV411: $i,SV564: $i] :
( ( ( ~ ( in @ SV564 @ SV411 ) )
= $true )
| ( ( in @ SV564 @ ( setadjoin @ SV178 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1764,plain,
! [SV412: $i,SV565: $i > $i,SV180: $i] :
( ( ( ~ ! [SY1133: $i] :
( ~ ( in @ SY1133 @ SV180 )
| ( in @ ( SV565 @ SY1133 ) @ SV412 ) ) )
= $true )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1765,plain,
! [SV181: $i,SV413: $i] :
( ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false )
| ( ( ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV181 ) )
| ! [SY920: $o,SY921: $i] :
( ~ ( in @ SY921 @ SV181 )
| ~ ( in @ SY921 @ ( binunion @ SV413 @ SY919 ) )
| ~ ( ~ ( in @ SY921 @ SV413 )
| SY920 )
| ~ ( ~ ( in @ SY921 @ SY919 )
| SY920 )
| SY920 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1766,plain,
! [SV182: $i > $o] :
( ( ( ! [SY449: $i] :
~ ~ ( ~ ( SV182 @ SY449 )
| ~ ! [SY450: $i] :
( ~ ( SV182 @ SY450 )
| ( SY449 = SY450 ) ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1520]) ).
thf(1767,plain,
! [SV414: $i,SV183: $i] :
( ( ( SV183 = SV414 )
= $false )
| ( ( ( setunion @ SV183 )
= ( setunion @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1768,plain,
! [SV184: $i,SV415: $i] :
( ( ( in @ SV415 @ ( powerset @ SV184 ) )
= $false )
| ( ( ! [SY922: $i] :
( ~ ( in @ SY922 @ ( powerset @ SV184 ) )
| ( in @ ( binintersect @ SV415 @ SY922 ) @ ( powerset @ SV184 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1769,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ( ~ ~ ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) ) )
= $true )
| ( ( ~ ( in @ SV566 @ SV185 )
| ( in @ SV566 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1523]) ).
thf(1770,plain,
! [SV187: $i,SV417: $i] :
( ( ( in @ SV417 @ ( powerset @ SV187 ) )
= $false )
| ( ( ! [SY924: $i] :
( ~ ( in @ SY924 @ ( powerset @ SV187 ) )
| ( in @ ( binunion @ SV417 @ SY924 ) @ ( powerset @ SV187 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1771,plain,
! [SV567: $i,SV418: $i,SV188: $i] :
( ( ( ~ ( func @ SV188 @ SV418 @ SV567 ) )
= $true )
| ( ( ! [SY1136: $i] :
( ~ ( in @ SY1136 @ SV188 )
| ( ( ap @ SV188 @ SV418 @ SV567 @ SY1136 )
= ( ap @ SV188 @ SV418 @ SV567 @ SY1136 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1772,plain,
! [SV189: $i,SV419: $i] :
( ( ( subset @ SV419 @ SV189 )
= $false )
| ( ( ( binintersect @ SV189 @ SV419 )
= SV419 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1773,plain,
! [SV420: $i,SV190: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) ) )
= $true )
| ( ( ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV190 )
| ( in @ ( kpair @ SY1137 @ ( ap @ SV190 @ SV420 @ SV568 @ SY1137 ) ) @ SV568 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1774,plain,
! [SV421: $i > $o,SV191: $i] :
( ( ( ~ ! [SY929: $i] :
( ~ ( in @ SY929 @ SV191 )
| ( SV421 @ SY929 ) ) )
= $false )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1775,plain,
! [SV620: $i,SV569: $i,SV422: $i,SV192: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV569 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV569 @ ( setadjoin @ SV620 @ emptyset ) ) @ emptyset ) ) )
| ( SV192 = SV569 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1776,plain,
! [SV423: $i,SV193: $i,SV570: $i] :
( ( ( ~ ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) ) )
= $true )
| ( ( ! [SY1139: $i > $o] :
( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV193 )
| ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV423 )
| ~ ( in @ ( kpair @ SY1140 @ SY1141 ) @ SV570 )
| ( SY1139 @ ( kpair @ SY1140 @ SY1141 ) ) ) )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV570 )
| ( SY1139 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1777,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) ) )
= $true )
| ( ( ! [SY1143: $o] :
( ~ ( ( SV571 != SV194 )
| SY1143 )
| ~ ( ~ ( in @ SV571 @ SV424 )
| SY1143 )
| SY1143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1778,plain,
! [SV425: $i > $o,SV195: $i] :
( ( ( ~ ! [SY940: $i] :
( ~ ( in @ SY940 @ SV195 )
| ( SV425 @ SY940 ) ) )
= $false )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1532]) ).
thf(1779,plain,
! [SV196: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
| ~ ! [SY1153: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY1153 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1153 ) )
| ~ ! [SY1156: $i] :
~ ~ ! [SY1157: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1156 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1157 @ SY1153 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1156 )
| ~ ( in @ SX5 @ SY1153 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1156 ) )
| ( in @ SY1157 @ SY1159 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1533]) ).
thf(1780,plain,
! [SV427: $i,SV198: $i] :
( ( ( subset @ SV198 @ SV427 )
= $false )
| ( ( in @ SV198 @ ( powerset @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1781,plain,
! [SV428: $i > $o,SV199: $i,SV572: $i] :
( ( ( ~ ( in @ SV572 @ SV199 ) )
= $true )
| ( ( ~ ( SV428 @ SV572 )
| ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1782,plain,
! [SV573: $i,SV429: $i,SV200: $i] :
( ( ( ~ ( subset @ SV200 @ SV429 ) )
= $true )
| ( ( ~ ( in @ SV573 @ SV200 )
| ( in @ SV573 @ SV429 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1783,plain,
! [SV430: $i,SV201: $i] :
( ( ( ! [SY946: $i] :
( ~ ( in @ SY946 @ SV201 )
| ( in @ SY946 @ SV430 ) ) )
= $false )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1537]) ).
thf(1784,plain,
! [SV574: $i,SV202: $i,SV431: $i] :
( ( ( ~ ( in @ SV431 @ ( powerset @ SV202 ) ) )
= $true )
| ( ( ~ ( in @ SV574 @ SV431 )
| ( in @ SV574 @ SV202 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1538]) ).
thf(1785,plain,
! [SV432: $i,SV203: $i,SV575: $i] :
( ( ( ~ ( in @ SV575 @ ( funcSet @ SV203 @ SV432 ) ) )
= $true )
| ( ( ( lam @ SV203 @ SV432
@ ^ [SY1163: $i] : ( ap @ SV203 @ SV432 @ SV575 @ SY1163 ) )
= SV575 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1539]) ).
thf(1786,plain,
! [SV204: $i,SV433: $i] :
( ( ( in @ SV433 @ ( powerset @ SV204 ) )
= $false )
| ( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV204 ) )
| ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SY951 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1787,plain,
! [SV205: $i > $o] :
( ( ( ! [SY520: $i] :
~ ~ ( ~ ( SV205 @ SY520 )
| ~ ! [SY521: $i] :
( ~ ( SV205 @ SY521 )
| ( SY520 = SY521 ) ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1541]) ).
thf(1788,plain,
! [SV209: $i > $o] :
( ( ( ! [SY526: $i] :
~ ~ ( ~ ( SV209 @ SY526 )
| ~ ! [SY527: $i] :
( ~ ( SV209 @ SY527 )
| ( SY526 = SY527 ) ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1789,plain,
! [SV210: $i,SV435: $i] :
( ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false )
| ( ( ~ ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SV210 )
| ~ ( in @ SV435 @ SY952 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1790,plain,
! [SV576: $i > $i > $o,SV436: $i,SV211: $i,SV621: $i] :
( ( ! [SY1215: $i] :
( ~ ( in @ ( kpair @ SV621 @ SY1215 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SY1166: $i,SY1167: $i] : ( SV576 @ SY1166 @ SY1167 ) ) )
| ( in @ SV621 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1546]) ).
thf(1791,plain,
! [SV437: $o,SV212: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV212 ) )
= $true )
| ( ( ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV212 )
| ( in @ ( if @ SV212 @ SV437 @ SV577 @ SY1168 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SY1168 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1547]) ).
thf(1792,plain,
! [SV212: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV212 ) )
= $true )
| ( ( ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV212 )
| ( in @ ( if @ SV212 @ $true @ SV578 @ SY1169 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SY1169 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1793,plain,
! [SV212: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV212 ) )
= $true )
| ( ( ! [SY1170: $i] :
( ~ ( in @ SY1170 @ SV212 )
| ( in @ ( if @ SV212 @ $false @ SV579 @ SY1170 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SY1170 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1794,plain,
! [SV580: $i,SV438: $i,SV213: $i] :
( ( ( ~ ( func @ SV213 @ SV438 @ SV580 ) )
= $true )
| ( ( ( lam @ SV213 @ SV438
@ ^ [SY1171: $i] : ( ap @ SV213 @ SV438 @ SV580 @ SY1171 ) )
= SV580 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1795,plain,
! [SV581: $i,SV439: $i,SV214: $i] :
( ( ( ~ ( func @ SV214 @ SV439 @ SV581 ) )
= $true )
| ( ( ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV214 )
| ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1173: $i] : ( in @ ( kpair @ SY1172 @ SY1173 ) @ SV581 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1551]) ).
thf(1796,plain,
! [SV440: $i,SV582: $i > $i,SV215: $i] :
( ( ( ~ ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV215 )
| ( in @ ( SV582 @ SY1174 ) @ SV440 ) ) )
= $true )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1797,plain,
! [SV441: $i,SV216: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV216 ) )
= $true )
| ( ( ! [SY1177: $i] :
( ~ ( in @ SY1177 @ SV441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SY1177 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1798,plain,
! [SV442: $i,SV217: $i,SV584: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ ( setadjoin @ SV442 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV217 = SV584 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1799,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ( ~ ( in @ SV444 @ ( setunion @ SV219 ) )
| ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1800,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ( ~ ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) )
| ( in @ SV444 @ ( setunion @ SV219 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1555]) ).
thf(1801,plain,
! [SV445: $i,SV220: $i] :
( ( ( ~ ~ ! [SY974: $i] :
~ ~ ( ~ ( in @ SY974 @ SV220 )
| ~ ( in @ SY974 @ SV445 ) ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1802,plain,
! [SV222: $i,SV447: $i] :
( ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ ( powerset @ SV222 ) )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV222 )
| ~ ( in @ SY976 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY976 @ ( binintersect @ SV447 @ SY975 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1803,plain,
! [SV622: $i,SV585: $i,SV448: $i,SV223: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SV622 @ emptyset ) ) @ emptyset ) ) )
| ( SV585 != SV622 )
| ( SV448 = SV622 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1804,plain,
! [SV224: $i,SV449: $i] :
( ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false )
| ( ( ! [SY979: $i] :
( ~ ( in @ SY979 @ ( powerset @ SV224 ) )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV224 )
| ~ ~ ( in @ SY980 @ SV449 )
| ~ ~ ( in @ SY980 @ SY979 )
| ~ ( in @ SY980 @ ( binunion @ SV449 @ SY979 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1805,plain,
( ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1806,plain,
! [SV450: $i,SV225: $i] :
( ( ( in @ SV225 @ ( setadjoin @ SV450 @ emptyset ) )
= $false )
| ( ( in @ SV450 @ ( setadjoin @ SV225 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1807,plain,
! [SV451: $o,SV226: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV226 ) )
= $true )
| ( ( ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SV226 )
| ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SY1179 )
= SV586 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1563]) ).
thf(1808,plain,
! [SV226: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV226 ) )
= $true )
| ( ( ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV226 )
| ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SY1180 )
= SV587 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1809,plain,
! [SV226: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV226 ) )
= $true )
| ( ( ! [SY1181: $i] :
( ~ ( in @ SY1181 @ SV226 )
| ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SY1181 )
= SV588 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1565]) ).
thf(1810,plain,
! [SV227: $i > $o] :
( ( ( ! [SY577: $i] :
~ ~ ( ~ ( SV227 @ SY577 )
| ~ ! [SY578: $i] :
( ~ ( SV227 @ SY578 )
| ( SY577 = SY578 ) ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1566]) ).
thf(1811,plain,
! [SV228: $i,SV452: $i] :
( ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false )
| ( ( ! [SY983: $i] :
( ~ ( in @ SY983 @ ( powerset @ SV228 ) )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SY983 ) )
| ~ ( in @ SY984 @ SY983 )
| ~ ( in @ SY984 @ SV452 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1567]) ).
thf(1812,plain,
! [SV453: $o,SV229: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV229 ) )
= $true )
| ( ( ! [SY1182: $i] :
( ~ ( in @ SY1182 @ SV229 )
| ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1183: $i] :
( ~ ( ~ SV453
| ( SY1183 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1183 != SY1182 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1813,plain,
! [SV229: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV229 ) )
= $true )
| ( ( ! [SY1184: $i] :
( ~ ( in @ SY1184 @ SV229 )
| ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1185: $i] :
( ~ ( ~ $true
| ( SY1185 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1185 != SY1184 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1814,plain,
! [SV229: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV229 ) )
= $true )
| ( ( ! [SY1186: $i] :
( ~ ( in @ SY1186 @ SV229 )
| ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1187: $i] :
( ~ ( ~ $false
| ( SY1187 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1187 != SY1186 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1570]) ).
thf(1815,plain,
! [SV593: $i,SV455: $i,SV231: $i] :
( ( ( ( setadjoin @ SV231 @ ( setadjoin @ SV455 @ emptyset ) )
!= ( setadjoin @ SV593 @ emptyset ) )
= $true )
| ( ( SV231 = SV455 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1816,plain,
! [SV232: $i > $o,SV456: $i] :
( ( ( in @ SV456 @ emptyset )
= $false )
| ( ( SV232 @ SV456 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1817,plain,
! [SV233: $i,SV457: $i] :
( ( ( subset @ SV457 @ SV233 )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1574]) ).
thf(1818,plain,
! [SV458: $i,SV234: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ ( cartprod @ SV234 @ SV458 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV594 ) @ SV458 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1819,plain,
! [SV623: $o,SV459: $i,SV235: $i,SV595: $i] :
( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
| ~ ( ~ ( in @ SV595 @ SV235 )
| SV623 )
| ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1576]) ).
thf(1820,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
| ~ ( ~ ( in @ SV595 @ SV235 )
| $true )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1576]) ).
thf(1821,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
| ~ ( ~ ( in @ SV595 @ SV235 )
| $false )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1576]) ).
thf(1822,plain,
! [SV624: $i,SV596: $i,SV460: $i,SV236: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SV460 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV596 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV596 @ ( setadjoin @ SV624 @ emptyset ) ) @ emptyset ) ) )
| ( SV460 = SV624 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1577]) ).
thf(1823,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY995: $i,SY996: $i] :
( ( SY995 != SY996 )
| ~ ( ~ ( ~ ( SV237 @ SY995 )
| ( SV461 @ SY996 ) )
| ~ ( ~ ( SV461 @ SY996 )
| ( SV237 @ SY995 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1578]) ).
thf(1824,plain,
! [SV238: $i,SV462: $i] :
( ( ( in @ SV462 @ SV238 )
= $false )
| ( ( in @ ( setadjoin @ SV462 @ emptyset ) @ ( powerset @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1825,plain,
! [SV463: $i > $o,SV239: $i] :
( ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV239 )
| ! [SY1005: $i] :
( ~ ( in @ SY1005 @ SV239 )
| ~ ( SV463 @ SY1004 )
| ~ ( SV463 @ SY1005 )
| ( SY1004 = SY1005 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1826,plain,
! [SV464: $i,SV240: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV240 ) )
= $true )
| ( ( ~ ~ ( in @ SV597 @ SV464 )
| ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1827,plain,
! [SV465: $i,SV241: $i,SV598: $i] :
( ( ( ~ ~ ( in @ SV598 @ SV241 ) )
= $true )
| ( ( ~ ( in @ SV598 @ SV465 )
| ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1828,plain,
! [SV242: $i,SV466: $i] :
( ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false )
| ( ( ! [SY1008: $i] :
( ~ ( in @ SY1008 @ ( powerset @ SV242 ) )
| ! [SY1009: $i] :
( ~ ( in @ SY1009 @ SV242 )
| ~ ~ ( in @ SY1009 @ SY1008 )
| ~ ( in @ SY1009 @ ( binintersect @ SV466 @ SY1008 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1829,plain,
! [SV467: $o,SV243: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV243 ) )
= $true )
| ( ( ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1191: $i] :
( ~ ( ~ SV467
| ( SY1191 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1191 != SY1190 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1584]) ).
thf(1830,plain,
! [SV243: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ SV243 ) )
= $true )
| ( ( ! [SY1192: $i] :
( ~ ( in @ SY1192 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1193: $i] :
( ~ ( ~ $true
| ( SY1193 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1193 != SY1192 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1585]) ).
thf(1831,plain,
! [SV243: $i,SV601: $i] :
( ( ( ~ ( in @ SV601 @ SV243 ) )
= $true )
| ( ( ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1195: $i] :
( ~ ( ~ $false
| ( SY1195 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1195 != SY1194 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1832,plain,
! [SV468: $i,SV244: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV244 ) )
= $true )
| ( ( ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SV468 )
| ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SY1196 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1833,plain,
! [SV470: $i,SV246: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV246 ) )
= $true )
| ( ( ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV470 )
| ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY1197 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1834,plain,
! [SV604: $i,SV471: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV471 @ SV604 ) )
= $true )
| ( ( ! [SY1198: $i] :
( ~ ( func @ SV247 @ SV471 @ SY1198 )
| ~ ! [SY1199: $i] :
( ~ ( in @ SY1199 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1199 )
= ( ap @ SV247 @ SV471 @ SY1198 @ SY1199 ) ) )
| ( SV604 = SY1198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1835,plain,
! [SV248: $i,SV472: $i,SV605: $i] :
( ( ( ~ ( in @ SV605 @ SV472 ) )
= $true )
| ( ( in @ SV605 @ ( binunion @ SV248 @ SV472 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1836,plain,
! [SV249: $i,SV473: $i] :
( ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false )
| ( ( ! [SY1021: $i] :
( ~ ( in @ SY1021 @ ( powerset @ SV249 ) )
| ! [SY1022: $i] :
( ~ ( in @ SY1022 @ SV249 )
| ~ ~ ( in @ SY1022 @ ( binunion @ SV473 @ SY1021 ) )
| ~ ( in @ SY1022 @ SV473 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1591]) ).
thf(1837,plain,
! [SV474: $i > $o,SV250: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV250 ) )
= $true )
| ( ( ~ ( SV474 @ SV606 )
| ( in @ SV606
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1838,plain,
! [SV476: $i,SV252: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV252 ) )
= $true )
| ( ( ~ ( in @ SV607 @ SV476 )
| ~ ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1593]) ).
thf(1839,plain,
! [SV253: $i,SV477: $i] :
( ( ( in @ SV477 @ ( powerset @ SV253 ) )
= $false )
| ( ( in @ ( powerset @ SV477 ) @ ( powerset @ ( powerset @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1840,plain,
! [SV478: $i,SV254: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ ( cartprod @ SV254 @ SV478 ) ) )
= $true )
| ( ( iskpair @ SV608 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1841,plain,
! [SV480: $i,SV256: $i] :
( ( ( SV256 = SV480 )
= $false )
| ( ( ! [SY1027: $i,SY1028: $i] :
( ( SY1027 != SY1028 )
| ( ( setadjoin @ SV256 @ SY1027 )
= ( setadjoin @ SV480 @ SY1028 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1842,plain,
! [SV481: $i,SV258: $i] :
( ( ( SV258 = SV481 )
= $false )
| ( ( in @ SV258 @ ( setadjoin @ SV481 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1843,plain,
! [SV259: $i,SV482: $i] :
( ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV259 ) )
| ~ ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SV259 )
| ~ ( in @ SY1030 @ SV482 )
| ( in @ SY1030 @ SY1029 ) )
| ~ ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV259 )
| ~ ( in @ SY1031 @ SY1029 )
| ( in @ SY1031 @ SV482 ) )
| ( SV482 = SY1029 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1844,plain,
! [SV483: $i,SV260: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) ) )
= $true )
| ( ( ~ ! [SY1201: $i] :
~ ~ ( ~ ( in @ SY1201 @ SV260 )
| ~ ~ ! [SY1202: $i] :
~ ~ ( ~ ( in @ SY1202 @ SV483 )
| ( SV609
!= ( kpair @ SY1201 @ SY1202 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1845,plain,
! [SV261: $i,SV1: $i,SV484: $i] :
( ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false )
| ( ( ! [SY1035: $i > $o] :
( ~ ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV1 )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV261 )
| ~ ( in @ ( kpair @ SY1036 @ SY1037 ) @ SV484 )
| ( SY1035 @ ( kpair @ SY1036 @ SY1037 ) ) ) )
| ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV484 )
| ( SY1035 @ SY1038 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1846,plain,
! [SV262: $i,SV2: $i,SV625: $i] :
( ( ( ! [SY1218: $i] :
( ( SV625 != SY1218 )
| ~ ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SY1218 @ SV262 ) )
| ~ ( ~ ( in @ SY1218 @ SV262 )
| ( in @ SV625 @ SV2 ) ) ) ) )
= $true )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1601]) ).
thf(1847,plain,
! [SV264: $i,SV4: $i,SV485: $i] :
( ( ( in @ SV485 @ ( setadjoin @ SV4 @ ( setadjoin @ SV264 @ emptyset ) ) )
= $false )
| ( ( ( SV485 = SV4 )
| ( SV485 = SV264 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1603]) ).
thf(1848,plain,
! [SV265: $i,SV5: $i,SV486: $i] :
( ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( ! [SY1039: $i] :
( ~ ( subset @ SY1039 @ ( cartprod @ SV5 @ SV265 ) )
| ~ ! [SY1040: $i] :
( ~ ( in @ SY1040 @ SV5 )
| ! [SY1041: $i] :
( ~ ( in @ SY1041 @ SV265 )
| ~ ( in @ ( kpair @ SY1040 @ SY1041 ) @ SV486 )
| ( in @ ( kpair @ SY1040 @ SY1041 ) @ SY1039 ) ) )
| ~ ! [SY1042: $i] :
( ~ ( in @ SY1042 @ SV5 )
| ! [SY1043: $i] :
( ~ ( in @ SY1043 @ SV265 )
| ~ ( in @ ( kpair @ SY1042 @ SY1043 ) @ SY1039 )
| ( in @ ( kpair @ SY1042 @ SY1043 ) @ SV486 ) ) )
| ( SV486 = SY1039 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1604]) ).
thf(1849,plain,
! [SV6: $i] :
( ( ( in @ ( sK6_SY25 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1605]) ).
thf(1850,plain,
! [SV7: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ SV7 ) )
= $true )
| ( ( ( setunion @ SV7 )
= SV610 )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1851,plain,
! [SV8: $i,SV266: $i] :
( ( ( ~ ( in @ ( sK8_SY679 @ SV266 @ SV8 ) @ SV8 )
| ( in @ ( sK8_SY679 @ SV266 @ SV8 ) @ SV266 ) )
= $false )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1607]) ).
thf(1852,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV9 ) )
= $true )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1608]) ).
thf(1853,plain,
! [SV627: $o,SV10: $i,SV267: $i] :
( ( ( ~ ! [SY1219: $i] :
( ~ ( in @ SV267 @ SY1219 )
| ~ ( in @ SY1219 @ SV10 )
| SV627 )
| SV627 )
= $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1609]) ).
thf(1854,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $true )
| $true )
= $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1609]) ).
thf(1855,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $false )
| $false )
= $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1609]) ).
thf(1856,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( ~ ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
| ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1857,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( ~ ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1610]) ).
thf(1858,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ! [SY1220: $i] :
~ ( ~ ( ~ ( SV12 @ SY1220 )
| ( SY1220 = SV628 ) )
| ~ ( ( SY1220 != SV628 )
| ( SV12 @ SY1220 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1859,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV629 ) )
= $true )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1860,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false )
| ( ( ! [SY1044: $o] :
( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SY1044 )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SY1044 )
| SY1044 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1861,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY1221: $i] :
( ( ( sK9_SY685 @ SV270 @ SV15 )
!= SY1221 )
| ~ ( ~ ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ SY1221 ) )
| ~ ( ~ ( SV270 @ SY1221 )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1614]) ).
thf(1862,plain,
! [SV271: $i,SV16: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ SV16 ) )
= $false )
| ( ( ~ ( in @ SV489 @ ( setminus @ SV16 @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1863,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ~ ( ~ ( SV19 @ SV630 )
| ~ ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1864,plain,
! [SV272: $i,SV20: $i] :
( ( ( subset @ SV20 @ SV272 )
= $true )
| ( ( SV20 != SV272 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1865,plain,
! [SV273: $i,SV21: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( powerset @ SV21 ) )
| ! [SY1223: $i] :
( ~ ( in @ SY1223 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SY1223 @ SV273 )
| ( in @ SY1223 @ SV631 ) ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1618]) ).
thf(1866,plain,
! [SV274: $i,SV22: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV490 @ SV274 )
| ~ ( in @ SV490 @ SV22 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1867,plain,
! [SV276: $i,SV24: $i,SV491: $i] :
( ( ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) )
= $false )
| ( ( ! [SY1045: $i] :
( ~ ( in @ SY1045 @ SV24 )
| ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SY1045 ) @ SV276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1868,plain,
! [SV611: $i,SV492: $i,SV278: $i,SV26: $i] :
( ( ( ( kpair @ SV26 @ SV278 )
!= ( kpair @ SV492 @ SV611 ) )
= $true )
| ( ( SV26 = SV492 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1622]) ).
thf(1869,plain,
! [SV279: $i,SV27: $i,SV612: $i,SV493: $i] :
( ( ( ~ ( in @ ( kpair @ SV493 @ SV612 ) @ ( cartprod @ SV27 @ SV279 ) ) )
= $true )
| ( ( in @ SV493 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1623]) ).
thf(1870,plain,
! [SV494: $i > $i > $o,SV281: $i,SV29: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV29 ) )
= $true )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV281 )
| ~ ( SV494 @ SV613 @ SY1203 )
| ( in @ ( kpair @ SV613 @ SY1203 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1871,plain,
! [SV283: $i,SV31: $i,SV496: $i] :
( ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false )
| ( ( ! [SY1054: $i] :
( ~ ( in @ SY1054 @ SV31 )
| ! [SY1055: $i] :
( ~ ( in @ SY1055 @ SV283 )
| ~ ( in @ ( kpair @ SY1054 @ SY1055 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SY1054 )
= SY1055 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1872,plain,
! [SV285: $i,SV33: $i,SV497: $i] :
( ( ( in @ SV497 @ ( setadjoin @ SV33 @ SV285 ) )
= $false )
| ( ( ( SV497 = SV33 )
| ( in @ SV497 @ SV285 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1873,plain,
! [SV287: $o,SV35: $i,SV498: $i] :
( ( ( in @ SV498 @ SV35 )
= $false )
| ( ( ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV35 )
| ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SY1056 )
= SY1056 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1874,plain,
! [SV35: $i,SV499: $i] :
( ( ( in @ SV499 @ SV35 )
= $false )
| ( ( ! [SY1057: $i] :
( ~ ( in @ SY1057 @ SV35 )
| ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SY1057 )
= SY1057 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1875,plain,
! [SV35: $i,SV500: $i] :
( ( ( in @ SV500 @ SV35 )
= $false )
| ( ( ! [SY1058: $i] :
( ~ ( in @ SY1058 @ SV35 )
| ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SY1058 )
= SY1058 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1876,plain,
! [SV288: $i,SV501: $i > $i,SV36: $i] :
( ( ( ! [SY1059: $i] :
( ~ ( in @ SY1059 @ SV36 )
| ( in @ ( SV501 @ SY1059 ) @ SV288 ) ) )
= $false )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1877,plain,
! [SV289: $i,SV37: $i,SV502: $i] :
( ( ( in @ SV502 @ SV37 )
= $false )
| ( ( in @ ( setadjoin @ SV502 @ emptyset ) @ ( powerset @ ( binunion @ SV37 @ SV289 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1632]) ).
thf(1878,plain,
! [SV293: $i,SV41: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ ( powerset @ SV41 ) )
| ~ ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV41 )
| ~ ( in @ SY1224 @ SV632 )
| ( in @ SY1224 @ ( setminus @ SV41 @ SV293 ) ) ) )
= $true )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1879,plain,
! [SV295: $i,SV43: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ ( powerset @ SV43 ) )
| ! [SY1225: $i] :
( ~ ( in @ SY1225 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY1225 ) @ ( binunion @ SV633 @ SY1225 ) ) ) ) ) )
= $true )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1880,plain,
! [SV296: $i,SV503: $i > $i,SV44: $i] :
( ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ SV44 )
| ( in @ ( SV503 @ SY1061 ) @ SV296 ) ) )
= $false )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1881,plain,
! [SV297: $i,SV45: $i,SV504: $i] :
( ( ( in @ SV504 @ SV45 )
= $false )
| ( ( ~ ~ ( in @ SV504 @ SV297 )
| ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1882,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
| ~ ! [SY1226: $i] :
~ ~ ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1226 )
| ~ ! [SY1227: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1227 )
| ( SY1226 = SY1227 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1641]) ).
thf(1883,plain,
! [SV299: $i,SV49: $i,SV505: $i] :
( ( ( in @ SV505 @ SV49 )
= $false )
| ( ( in @ SV505 @ ( binunion @ SV49 @ SV299 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1884,plain,
! [SV300: $i,SV50: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ ( powerset @ SV50 ) )
| ! [SY1228: $i] :
( ~ ( in @ SY1228 @ SV50 )
| ~ ~ ( in @ SY1228 @ SV300 )
| ~ ( in @ SY1228 @ ( binintersect @ SV300 @ SV634 ) ) ) )
= $true )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1643]) ).
thf(1885,plain,
! [SV301: $i,SV51: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV51 ) )
= $false )
| ( ( ~ ~ ( in @ SV506 @ SV301 )
| ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1886,plain,
! [SV52: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV52 ) )
= $true )
| ( ( SV52 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1887,plain,
! [SV507: $i,SV302: $i,SV54: $i] :
( ( ( func @ SV54 @ SV302 @ SV507 )
= $false )
| ( ( ! [SY1064: $i] :
( ~ ( in @ SY1064 @ SV54 )
| ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SY1064 ) @ SV302 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1888,plain,
! [SV303: $i > $o,SV55: $i] :
( ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV55 )
| ~ ( SV303 @ SY746 ) ) )
= $true )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1647]) ).
thf(1889,plain,
! [SV304: $i,SV56: $i,SV508: $i] :
( ( ( in @ SV508 @ ( binunion @ SV56 @ SV304 ) )
= $false )
| ( ( ( in @ SV508 @ SV56 )
| ( in @ SV508 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1890,plain,
! [SV305: $i,SV57: $i,SV509: $i] :
( ( ( in @ SV509 @ ( binintersect @ SV57 @ SV305 ) )
= $false )
| ( ( in @ SV509 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1649]) ).
thf(1891,plain,
! [SV306: $i,SV58: $i] :
( ( ( SV58 = SV306 )
= $true )
| ( ( ~ ( in @ SV306 @ ( setadjoin @ SV58 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1650]) ).
thf(1892,plain,
! [SV307: $i > $o,SV59: $i,SV510: $i] :
( ( ( in @ SV510
@ ( dsetconstr @ SV59
@ ^ [SY751: $i] : ( SV307 @ SY751 ) ) )
= $false )
| ( ( in @ SV510 @ SV59 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1893,plain,
! [SV308: $i,SV60: $i,SV511: $i] :
( ( ( in @ SV511 @ ( setminus @ SV60 @ SV308 ) )
= $false )
| ( ( ~ ( in @ SV511 @ SV308 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1652]) ).
thf(1894,plain,
! [SV309: $i,SV61: $i,SV512: $i] :
( ( ( in @ SV512 @ SV61 )
= $false )
| ( ( ~ ( in @ SV512 @ SV309 )
| ( in @ SV512 @ ( binintersect @ SV61 @ SV309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1895,plain,
! [SV310: $i,SV62: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ ( powerset @ SV62 ) )
| ! [SY1229: $i] :
( ~ ( in @ SY1229 @ ( powerset @ SV62 ) )
| ! [SY1230: $i] :
( ~ ( in @ SY1230 @ SV62 )
| ~ ( in @ SY1230 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1230 @ ( binintersect @ ( binunion @ SV310 @ SY1229 ) @ ( binunion @ SV636 @ SY1229 ) ) ) ) ) )
= $true )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1654]) ).
thf(1896,plain,
! [SV311: $i > $o,SV63: $i] :
( ( ( ! [SY757: $i] :
~ ~ ( ~ ( in @ SY757 @ SV63 )
| ~ ~ ( SV311 @ SY757 ) ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1897,plain,
! [SV65: $i] :
( ( ( ! [SY170: $i] :
~ ( in @ SY170 @ SV65 ) )
= $false )
| ( ( SV65 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1656]) ).
thf(1898,plain,
! [SV513: $i,SV312: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV312 )
= $false )
| ( ( ~ ~ ( in @ SV513 @ SV312 )
| ~ ( in @ SV513 @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1899,plain,
! [SV313: $i,SV68: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ ( powerset @ SV68 ) )
| ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV68 )
| ~ ( in @ SY1231 @ SV313 )
| ( in @ SY1231 @ SV637 ) )
| ( subset @ SV313 @ SV637 ) )
= $true )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1658]) ).
thf(1900,plain,
! [SV514: $i,SV315: $i,SV70: $i] :
( ( ( func @ SV70 @ SV315 @ SV514 )
= $false )
| ( ( in @ SV514 @ ( funcSet @ SV70 @ SV315 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1901,plain,
! [SV614: $i,SV515: $i,SV316: $i,SV71: $i] :
( ( ( ( kpair @ SV71 @ SV316 )
!= ( kpair @ SV515 @ SV614 ) )
= $true )
| ( ( SV316 = SV614 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1902,plain,
! [SV516: $i,SV317: $i,SV72: $i] :
( ( ( subset @ SV72 @ SV317 )
= $false )
| ( ( ~ ( subset @ SV317 @ SV516 )
| ( subset @ SV72 @ SV516 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1903,plain,
! [SV318: $i,SV73: $i,SV517: $i] :
( ( ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) )
= $false )
| ( ( ! [SY1067: $i] :
( ~ ( in @ SY1067 @ SV73 )
| ( ( ap @ SV73 @ SV318 @ SV517 @ SY1067 )
= ( ap @ SV73 @ SV318 @ SV517 @ SY1067 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1904,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) )
| ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) ) )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1664]) ).
thf(1905,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
| ! [SY1232: $i] :
( ~ ( in @ SY1232 @ SV76 )
| ~ ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
| ~ ( SV321 @ SY1232 )
| ( ( sK12_SY769 @ SV321 @ SV76 )
= SY1232 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1666]) ).
thf(1906,plain,
! [SV322: $i,SV77: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ ( powerset @ SV77 ) )
| ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SV77 )
| ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SY1233 @ SV638 )
| ~ ( in @ SY1233 @ SV322 ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1907,plain,
! [SV79: $i,SV518: $i,SV324: $i] :
( ( ( in @ SV324 @ SV518 )
= $false )
| ( ( ~ ( in @ SV518 @ SV79 )
| ( in @ SV324 @ ( setunion @ SV79 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1908,plain,
! [SV325: $i,SV81: $i,SV519: $i] :
( ( ( in @ SV519 @ ( funcSet @ SV81 @ SV325 ) )
= $false )
| ( ( func @ SV81 @ SV325 @ SV519 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1909,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ( in @ SV326 @ ( powerset @ SV82 ) )
| ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1670]) ).
thf(1910,plain,
! [SV82: $i,SV326: $i] :
( ( ~ ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) )
| ( in @ SV326 @ ( powerset @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1671]) ).
thf(1911,plain,
! [SV327: $i > $o,SV83: $i] :
( ( ( ! [SY779: $i] :
~ ~ ( ~ ( in @ SY779 @ SV83 )
| ~ ( SV327 @ SY779 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1672]) ).
thf(1912,plain,
! [SV328: $o,SV84: $i,SV520: $i] :
( ( ( in @ SV520 @ SV84 )
= $false )
| ( ( ! [SY1068: $i] :
( ~ ( in @ SY1068 @ SV84 )
| ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1069: $i] :
( ~ ( ~ SV328
| ( SY1069 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1069 != SY1068 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1913,plain,
! [SV84: $i,SV521: $i] :
( ( ( in @ SV521 @ SV84 )
= $false )
| ( ( ! [SY1070: $i] :
( ~ ( in @ SY1070 @ SV84 )
| ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1071: $i] :
( ~ ( ~ $true
| ( SY1071 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1071 != SY1070 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1914,plain,
! [SV84: $i,SV522: $i] :
( ( ( in @ SV522 @ SV84 )
= $false )
| ( ( ! [SY1072: $i] :
( ~ ( in @ SY1072 @ SV84 )
| ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1073: $i] :
( ~ ( ~ $false
| ( SY1073 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1073 != SY1072 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1915,plain,
! [SV329: $i,SV85: $i,SV523: $i] :
( ( ( in @ SV523 @ SV85 )
= $false )
| ( ( ! [SY1074: $i] :
( ~ ( in @ SY1074 @ SV329 )
| ( in @ ( kpair @ SV523 @ SY1074 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1916,plain,
! [SV524: $i,SV330: $i,SV86: $i] :
( ( ( func @ SV86 @ SV330 @ SV524 )
= $false )
| ( ( ! [SY1075: $i] :
( ~ ( in @ SY1075 @ SV86 )
| ! [SY1076: $i] :
( ~ ( in @ SY1076 @ SV330 )
| ~ ( in @ ( kpair @ SY1075 @ SY1076 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SY1075 )
= SY1076 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1677]) ).
thf(1917,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ SV639 )
| ~ ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1682]) ).
thf(1918,plain,
! [SV525: $i,SV335: $i,SV90: $i] :
( ( ( func @ SV90 @ SV335 @ SV525 )
= $false )
| ( ( ! [SY1077: $i] :
( ~ ( in @ SY1077 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1078: $i] : ( in @ ( kpair @ SY1077 @ SY1078 ) @ SV525 ) ) )
@ SV335 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1683]) ).
thf(1919,plain,
! [SV337: $i > $o,SV92: $i,SV526: $i] :
( ( ( in @ SV526 @ SV92 )
= $false )
| ( ( ~ ( SV337 @ SV526 )
| ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1684]) ).
thf(1920,plain,
! [SV338: $i,SV93: $i,SV527: $i] :
( ( ( in @ SV527 @ ( setminus @ SV93 @ SV338 ) )
= $false )
| ( ( in @ SV527 @ SV93 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1685]) ).
thf(1921,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( in @ SV528 @ SV95 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) )
| ~ ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1922,plain,
! [SV341: $i,SV96: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ ( powerset @ SV96 ) )
| ! [SY1235: $i] :
( ~ ( in @ SY1235 @ SV96 )
| ~ ( in @ SY1235 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SY1235 @ SV341 ) ) )
= $true )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1688]) ).
thf(1923,plain,
! [SV342: $i,SV97: $i,SV529: $i] :
( ( ( in @ SV529 @ SV97 )
= $false )
| ( ( ! [SY1082: $i] :
( ~ ( in @ SY1082 @ SV342 )
| ( ( kpair @ SV529 @ SY1082 )
= ( kpair @ SV529 @ SY1082 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1924,plain,
! [SV344: $i,SV100: $i,SV641: $i] :
( ( ( ! [SY1236: $i] :
( ( SV641 != SY1236 )
| ~ ( in @ SV641 @ SV100 )
| ( in @ SY1236 @ SV344 ) ) )
= $true )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1925,plain,
! [SV345: $i,SV101: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ ( powerset @ SV101 ) )
| ~ ( subset @ ( setminus @ SV101 @ SV642 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SV642 ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1926,plain,
! [SV346: $i,SV102: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( powerset @ SV102 ) )
| ! [SY1237: $i] :
( ~ ( in @ SY1237 @ ( powerset @ SV102 ) )
| ! [SY1238: $i] :
( ~ ( in @ SY1238 @ SV102 )
| ~ ( in @ SY1238 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1238 @ ( binunion @ SV346 @ SY1237 ) ) ) ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1693]) ).
thf(1927,plain,
! [SV530: $i,SV348: $i,SV104: $i] :
( ( ( func @ SV104 @ SV348 @ SV530 )
= $false )
| ( ( ! [SY1083: $i] :
( ~ ( in @ SY1083 @ SV104 )
| ( in @ ( kpair @ SY1083 @ ( ap @ SV104 @ SV348 @ SV530 @ SY1083 ) ) @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1928,plain,
! [SV105: $i] :
( ( ( ! [SY262: $i] :
~ ~ ( ~ ( in @ SY262 @ SV105 )
| ~ $true ) )
= $false )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1929,plain,
! [SV349: $i,SV106: $i,SV531: $i] :
( ( ( in @ SV531 @ ( cartprod @ SV106 @ SV349 ) )
= $false )
| ( ( in @ ( kfst @ SV531 ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(1930,plain,
! [SV351: $i,SV109: $i,SV532: $i] :
( ( ( in @ SV532 @ SV109 )
= $false )
| ( ( ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV351 )
| ( in @ ( kpair @ SV532 @ SY1084 ) @ ( cartprod @ SV109 @ SV351 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1697]) ).
thf(1931,plain,
! [SV352: $i,SV110: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ ( powerset @ SV110 ) )
| ! [SY1239: $i] :
( ~ ( in @ SY1239 @ ( powerset @ SV110 ) )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV110 )
| ~ ( in @ SY1240 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1240 @ ( binunion @ SV644 @ SY1239 ) ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1698]) ).
thf(1932,plain,
! [SV353: $i,SV111: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ ( powerset @ SV111 ) )
| ~ ( subset @ SV353 @ SV645 )
| ( subset @ ( setminus @ SV111 @ SV645 ) @ ( setminus @ SV111 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1699]) ).
thf(1933,plain,
! [SV354: $i,SV112: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ ( powerset @ SV112 ) )
| ~ ( subset @ SV354 @ ( setminus @ SV112 @ SV646 ) )
| ( subset @ SV646 @ ( setminus @ SV112 @ SV354 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1700]) ).
thf(1934,plain,
! [SV113: $i,SV355: $i] :
( ( ( ~ ( in @ ( sK13_SY818 @ SV355 @ SV113 ) @ SV113 )
| ( in @ ( sK13_SY818 @ SV355 @ SV113 ) @ SV355 ) )
= $false )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1701]) ).
thf(1935,plain,
! [SV356: $i,SV114: $i,SV533: $i] :
( ( ( in @ SV533 @ SV114 )
= $false )
| ( ( ! [SY1085: $i] :
( ~ ( in @ SY1085 @ SV356 )
| ( ( kfst @ ( kpair @ SV533 @ SY1085 ) )
= SV533 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1936,plain,
! [SV358: $o,SV116: $i,SV534: $i] :
( ( ( in @ SV534 @ SV116 )
= $false )
| ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV116 )
| ~ ~ SV358
| ( in @ SY1086
@ ( dsetconstr @ SV116
@ ^ [SY1087: $i] :
( ~ ( ~ SV358
| ( SY1087 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1087 != SY1086 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1937,plain,
! [SV116: $i,SV535: $i] :
( ( ( in @ SV535 @ SV116 )
= $false )
| ( ( ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV116 )
| ~ ~ $true
| ( in @ SY1088
@ ( dsetconstr @ SV116
@ ^ [SY1089: $i] :
( ~ ( ~ $true
| ( SY1089 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1089 != SY1088 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1938,plain,
! [SV116: $i,SV536: $i] :
( ( ( in @ SV536 @ SV116 )
= $false )
| ( ( ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV116 )
| ~ ~ $false
| ( in @ SY1090
@ ( dsetconstr @ SV116
@ ^ [SY1091: $i] :
( ~ ( ~ $false
| ( SY1091 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1091 != SY1090 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1939,plain,
! [SV117: $i,SV359: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
| ~ ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) ) )
= $false )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1707]) ).
thf(1940,plain,
! [SV537: $i,SV360: $i,SV118: $i] :
( ( ( func @ SV118 @ SV360 @ SV537 )
= $false )
| ( ( ! [SY1092: $i] :
( ~ ( func @ SV118 @ SV360 @ SY1092 )
| ~ ! [SY1093: $i] :
( ~ ( in @ SY1093 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1093 )
= ( ap @ SV118 @ SV360 @ SY1092 @ SY1093 ) ) )
| ! [SY1094: $i] :
( ~ ( in @ SY1094 @ SV118 )
| ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV360 )
| ~ ( in @ ( kpair @ SY1094 @ SY1095 ) @ SY1092 )
| ( in @ ( kpair @ SY1094 @ SY1095 ) @ SV537 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1941,plain,
! [SV362: $i,SV120: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV120 )
| ~ ( in @ SV647 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SV647 @ SV362 ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1710]) ).
thf(1942,plain,
! [SV363: $i,SV121: $i,SV538: $i] :
( ( ( in @ SV538 @ SV121 )
= $false )
| ( ( ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV363 )
| ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SY1096 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1943,plain,
! [SV122: $i] :
( ( ( in @ ( sK7_SY302 @ SV122 ) @ SV122 )
= $true )
| ( ( SV122 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1712]) ).
thf(1944,plain,
! [SV364: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK15_SY834 @ SV124 @ SV364 ) @ SV364 )
| ( in @ ( sK15_SY834 @ SV124 @ SV364 ) @ SV124 ) )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1713]) ).
thf(1945,plain,
! [SV365: $i,SV125: $i,SV539: $i] :
( ( ( in @ SV539 @ ( cartprod @ SV125 @ SV365 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV539 ) @ ( ksnd @ SV539 ) )
= SV539 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1946,plain,
! [SV366: $i,SV126: $i,SV540: $i] :
( ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( ! [SY1097: $i] :
( ~ ( subset @ SY1097 @ ( cartprod @ SV126 @ SV366 ) )
| ~ ! [SY1098: $i] :
( ~ ( in @ SY1098 @ SV126 )
| ! [SY1099: $i] :
( ~ ( in @ SY1099 @ SV366 )
| ~ ( in @ ( kpair @ SY1098 @ SY1099 ) @ SV540 )
| ( in @ ( kpair @ SY1098 @ SY1099 ) @ SY1097 ) ) )
| ( subset @ SV540 @ SY1097 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1947,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ SV128 ) )
= $true )
| ( ( ! [SY1206: $i] :
( ~ ( in @ SY1206 @ SV368 )
| ~ ( in @ ( kpair @ SV615 @ SY1206 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SY1206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1948,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV129 )
| ~ ~ ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SV648 @ SV369 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1717]) ).
thf(1949,plain,
! [SV370: $i,SV130: $i,SV616: $i,SV542: $i] :
( ( ( ~ ( in @ ( kpair @ SV542 @ SV616 ) @ ( cartprod @ SV130 @ SV370 ) ) )
= $true )
| ( ( in @ SV616 @ SV370 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1950,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
| ! [SY1241: $i] :
( ~ ( in @ SY1241 @ SV131 )
| ~ ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
| ~ ( SV371 @ SY1241 )
| ( ( sK16_SY848 @ SV371 @ SV131 )
= SY1241 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1719]) ).
thf(1951,plain,
! [SV372: $i > $o,SV132: $i,SV543: $i] :
( ( ( in @ SV543
@ ( dsetconstr @ SV132
@ ^ [SY853: $i] : ( SV372 @ SY853 ) ) )
= $false )
| ( ( SV372 @ SV543 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(1952,plain,
! [SV373: $i,SV133: $i,SV544: $i] :
( ( ( in @ SV544 @ SV133 )
= $false )
| ( ( ~ ~ ( in @ SV544 @ SV373 )
| ( SV133 != SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(1953,plain,
! [SV376: $i,SV136: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( powerset @ SV136 ) )
| ! [SY1242: $i] :
( ~ ( in @ SY1242 @ SV136 )
| ~ ( in @ SY1242 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SY1242 @ ( setminus @ SV136 @ SV376 ) ) ) )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1722]) ).
thf(1954,plain,
! [SV650: $i > $o,SV377: $i,SV137: $i] :
( ( ( ! [SY1243: $i > $o] :
( ~ ! [SY1244: $i] :
( ~ ( in @ SY1244 @ SV137 )
| ! [SY1245: $i] :
( ~ ( in @ SY1245 @ SV377 )
| ( SY1244 != SY1245 )
| ~ ( ~ ( ~ ( SV650 @ SY1244 )
| ( SY1243 @ SY1245 ) )
| ~ ( ~ ( SY1243 @ SY1245 )
| ( SV650 @ SY1244 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SX4: $i] : ( SY1243 @ SX4 ) ) ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(1955,plain,
! [SV378: $i,SV138: $i,SV545: $i] :
( ( ( in @ SV545 @ SV138 )
= $false )
| ( ( ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV378 )
| ( ( ksnd @ ( kpair @ SV545 @ SY1106 ) )
= SY1106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1956,plain,
! [SV379: $i,SV139: $i,SV546: $i] :
( ( ( subset @ SV546 @ SV139 )
= $false )
| ( ( ~ ( subset @ SV546 @ SV379 )
| ( subset @ SV546 @ ( binintersect @ SV139 @ SV379 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(1957,plain,
! [SV380: $i,SV140: $i,SV547: $i] :
( ( ( in @ SV547 @ SV140 )
= $false )
| ( ( ~ ~ ( in @ SV547 @ SV380 )
| ~ ( subset @ SV140 @ SV380 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(1958,plain,
! [SV381: $i,SV141: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV141 )
| ~ ( in @ SV651 @ SV381 )
| ( in @ SV651 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1727]) ).
thf(1959,plain,
! [SV383: $i,SV144: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( powerset @ SV144 ) )
| ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SV652 ) ) ) ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1731]) ).
thf(1960,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ~ ( ~ ( SV146 @ SV653 )
| ~ ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1961,plain,
! [SV384: $i,SV147: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ ( powerset @ SV147 ) )
| ! [SY1249: $i] :
( ~ ( in @ SY1249 @ SV147 )
| ~ ~ ( in @ SY1249 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SY1249 @ SV654 ) ) )
= $true )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1733]) ).
thf(1962,plain,
! [SV385: $i,SV148: $i,SV655: $i] :
( ( ( ~ ( in @ SV655 @ ( powerset @ SV148 ) )
| ~ ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV148 )
| ~ ( in @ SY1250 @ SV385 )
| ( in @ SY1250 @ SV655 ) )
| ( in @ SV385 @ ( powerset @ SV655 ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1734]) ).
thf(1963,plain,
! [SV388: $i,SV548: $i,SV151: $i] :
( ( ( subset @ SV151 @ SV548 )
= $false )
| ( ( subset @ SV151 @ ( setadjoin @ SV388 @ SV548 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1736]) ).
thf(1964,plain,
! [SV389: $i,SV549: $i > $i,SV152: $i] :
( ( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV152 )
| ( in @ ( SV549 @ SY1107 ) @ SV389 ) ) )
= $false )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1737]) ).
thf(1965,plain,
! [SV390: $i,SV153: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( powerset @ SV153 ) )
| ( in @ ( setminus @ SV390 @ SV656 ) @ ( powerset @ SV153 ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1966,plain,
! [SV391: $o,SV154: $i,SV550: $i] :
( ( ( in @ SV550 @ SV154 )
= $false )
| ( ( ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SV154 )
| ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1111: $i] :
( ~ ( ~ SV391
| ( SY1111 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1111 != SY1110 ) ) ) )
= ( setadjoin @ SY1110 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1739]) ).
thf(1967,plain,
! [SV154: $i,SV551: $i] :
( ( ( in @ SV551 @ SV154 )
= $false )
| ( ( ! [SY1112: $i] :
( ~ ( in @ SY1112 @ SV154 )
| ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1113: $i] :
( ~ ( ~ $true
| ( SY1113 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1113 != SY1112 ) ) ) )
= ( setadjoin @ SY1112 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1968,plain,
! [SV154: $i,SV552: $i] :
( ( ( in @ SV552 @ SV154 )
= $false )
| ( ( ! [SY1114: $i] :
( ~ ( in @ SY1114 @ SV154 )
| ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1115: $i] :
( ~ ( ~ $false
| ( SY1115 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1115 != SY1114 ) ) ) )
= ( setadjoin @ SY1114 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1969,plain,
! [SV553: $i > $i > $o,SV392: $i,SV156: $i,SV657: $i,SV618: $i] :
( ( ~ ( in @ ( kpair @ SV618 @ SV657 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SY1118: $i,SY1119: $i] : ( SV553 @ SY1118 @ SY1119 ) ) )
| ( in @ SV657 @ SV392 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1742]) ).
thf(1970,plain,
! [SV393: $o,SV157: $i,SV554: $i] :
( ( ( in @ SV554 @ SV157 )
= $false )
| ( ( ! [SY1120: $i] :
( ~ ( in @ SY1120 @ SV157 )
| ( in @ ( if @ SV157 @ SV393 @ SV554 @ SY1120 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1971,plain,
! [SV157: $i,SV555: $i] :
( ( ( in @ SV555 @ SV157 )
= $false )
| ( ( ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV157 )
| ( in @ ( if @ SV157 @ $true @ SV555 @ SY1121 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1972,plain,
! [SV157: $i,SV556: $i] :
( ( ( in @ SV556 @ SV157 )
= $false )
| ( ( ! [SY1122: $i] :
( ~ ( in @ SY1122 @ SV157 )
| ( in @ ( if @ SV157 @ $false @ SV556 @ SY1122 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1973,plain,
! [SV158: $i] :
( ( ( ~ ( in @ emptyset @ SV158 ) )
= $true )
| ( ( ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) )
= $true )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(1974,plain,
! [SV394: $i,SV160: $i,SV557: $i] :
( ( ( in @ SV557 @ ( setadjoin @ SV160 @ ( setadjoin @ SV394 @ emptyset ) ) )
= $false )
| ( ( ( SV557 = SV160 )
| ( SV557 = SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1975,plain,
! [SV396: $i,SV559: $i > $i,SV162: $i] :
( ( ( ! [SY1125: $i] :
( ~ ( in @ SY1125 @ SV162 )
| ( in @ ( SV559 @ SY1125 ) @ SV396 ) ) )
= $false )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1748]) ).
thf(1976,plain,
! [SV560: $i > $i > $o,SV398: $i,SV164: $i,SV658: $i,SV619: $i] :
( ( ~ ( in @ ( kpair @ SV619 @ SV658 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SY1129: $i,SY1130: $i] : ( SV560 @ SY1129 @ SY1130 ) ) )
| ( SV560 @ SV619 @ SV658 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1750]) ).
thf(1977,plain,
! [SV165: $i,SV399: $i] :
( ( ( ~ ( subset @ SV399 @ SV165 ) )
= $true )
| ( ( SV165 = SV399 )
= $true )
| ( ( subset @ SV165 @ SV399 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(1978,plain,
! [SV400: $i,SV166: $i,SV561: $i] :
( ( ( in @ SV561 @ ( binintersect @ SV166 @ SV400 ) )
= $false )
| ( ( in @ SV561 @ SV400 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(1979,plain,
! [SV402: $i,SV168: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ ( powerset @ SV168 ) )
| ! [SY1255: $i] :
( ~ ( in @ SY1255 @ SV168 )
| ~ ( in @ SY1255 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY1255 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) ) )
= $true )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1754]) ).
thf(1980,plain,
! [SV403: $i > $o,SV169: $i] :
( ( ( ~ ! [SY905: $i] :
~ ~ ( ~ ( in @ SY905 @ SV169 )
| ~ ( SV403 @ SY905 ) ) )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1755]) ).
thf(1981,plain,
! [SV171: $i,SV405: $i,SV562: $i] :
( ( ( in @ SV562 @ SV405 )
= $false )
| ( ( ~ ( in @ SV562 @ ( setminus @ SV171 @ SV405 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1982,plain,
! [SV408: $i > $o,SV174: $i] :
( ( ( ! [SY909: $i] :
~ ~ ( ~ ( in @ SY909 @ SV174 )
| ~ ( SV408 @ SY909 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1760]) ).
thf(1983,plain,
! [SV409: $i,SV175: $i,SV563: $i] :
( ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( ! [SY1131: $i] :
( ~ ( in @ SY1131 @ ( funcSet @ SV175 @ SV409 ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1132 )
= ( ap @ SV175 @ SV409 @ SY1131 @ SY1132 ) ) )
| ( SV563 = SY1131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(1984,plain,
! [SV410: $i,SV176: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV176 )
| ~ ( in @ SV660 @ SV410 )
| ~ ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) ) )
= $true )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1762]) ).
thf(1985,plain,
! [SV178: $i,SV411: $i,SV564: $i] :
( ( ( in @ SV564 @ SV411 )
= $false )
| ( ( in @ SV564 @ ( setadjoin @ SV178 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1986,plain,
! [SV412: $i,SV565: $i > $i,SV180: $i] :
( ( ( ! [SY1133: $i] :
( ~ ( in @ SY1133 @ SV180 )
| ( in @ ( SV565 @ SY1133 ) @ SV412 ) ) )
= $false )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1764]) ).
thf(1987,plain,
! [SV413: $i,SV181: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ ( powerset @ SV181 ) )
| ! [SY1256: $o,SY1257: $i] :
( ~ ( in @ SY1257 @ SV181 )
| ~ ( in @ SY1257 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SY1257 @ SV413 )
| SY1256 )
| ~ ( ~ ( in @ SY1257 @ SV661 )
| SY1256 )
| SY1256 ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1765]) ).
thf(1988,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ~ ( ~ ( SV182 @ SV662 )
| ~ ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1766]) ).
thf(1989,plain,
! [SV415: $i,SV184: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ ( powerset @ SV184 ) )
| ( in @ ( binintersect @ SV415 @ SV663 ) @ ( powerset @ SV184 ) ) )
= $true )
| ( ( in @ SV415 @ ( powerset @ SV184 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(1990,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) ) )
= $false )
| ( ( ~ ( in @ SV566 @ SV185 )
| ( in @ SV566 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1991,plain,
! [SV417: $i,SV187: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ ( powerset @ SV187 ) )
| ( in @ ( binunion @ SV417 @ SV664 ) @ ( powerset @ SV187 ) ) )
= $true )
| ( ( in @ SV417 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1770]) ).
thf(1992,plain,
! [SV567: $i,SV418: $i,SV188: $i] :
( ( ( func @ SV188 @ SV418 @ SV567 )
= $false )
| ( ( ! [SY1136: $i] :
( ~ ( in @ SY1136 @ SV188 )
| ( ( ap @ SV188 @ SV418 @ SV567 @ SY1136 )
= ( ap @ SV188 @ SV418 @ SV567 @ SY1136 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1771]) ).
thf(1993,plain,
! [SV420: $i,SV190: $i,SV568: $i] :
( ( ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) )
= $false )
| ( ( ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SV190 )
| ( in @ ( kpair @ SY1137 @ ( ap @ SV190 @ SV420 @ SV568 @ SY1137 ) ) @ SV568 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(1994,plain,
! [SV421: $i > $o,SV191: $i] :
( ( ( ! [SY929: $i] :
( ~ ( in @ SY929 @ SV191 )
| ( SV421 @ SY929 ) ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1774]) ).
thf(1995,plain,
! [SV620: $i,SV569: $i,SV422: $i,SV192: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV569 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV569 @ ( setadjoin @ SV620 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV192 = SV569 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1775]) ).
thf(1996,plain,
! [SV423: $i,SV193: $i,SV570: $i] :
( ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false )
| ( ( ! [SY1139: $i > $o] :
( ~ ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV193 )
| ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV423 )
| ~ ( in @ ( kpair @ SY1140 @ SY1141 ) @ SV570 )
| ( SY1139 @ ( kpair @ SY1140 @ SY1141 ) ) ) )
| ! [SY1142: $i] :
( ~ ( in @ SY1142 @ SV570 )
| ( SY1139 @ SY1142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(1997,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false )
| ( ( ! [SY1143: $o] :
( ~ ( ( SV571 != SV194 )
| SY1143 )
| ~ ( ~ ( in @ SV571 @ SV424 )
| SY1143 )
| SY1143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1777]) ).
thf(1998,plain,
! [SV425: $i > $o,SV195: $i] :
( ( ( ! [SY940: $i] :
( ~ ( in @ SY940 @ SV195 )
| ( SV425 @ SY940 ) ) )
= $true )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1778]) ).
thf(1999,plain,
! [SV196: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
| ~ ! [SY1153: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY1153 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1153 ) )
| ~ ! [SY1156: $i] :
~ ~ ! [SY1157: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1156 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1157 @ SY1153 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1156 )
| ~ ( in @ SX5 @ SY1153 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1156 ) )
| ( in @ SY1157 @ SY1159 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(2000,plain,
! [SV428: $i > $o,SV199: $i,SV572: $i] :
( ( ( in @ SV572 @ SV199 )
= $false )
| ( ( ~ ( SV428 @ SV572 )
| ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(2001,plain,
! [SV573: $i,SV429: $i,SV200: $i] :
( ( ( subset @ SV200 @ SV429 )
= $false )
| ( ( ~ ( in @ SV573 @ SV200 )
| ( in @ SV573 @ SV429 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2002,plain,
! [SV201: $i,SV430: $i] :
( ( ( ~ ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
| ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 ) )
= $false )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1783]) ).
thf(2003,plain,
! [SV574: $i,SV202: $i,SV431: $i] :
( ( ( in @ SV431 @ ( powerset @ SV202 ) )
= $false )
| ( ( ~ ( in @ SV574 @ SV431 )
| ( in @ SV574 @ SV202 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(2004,plain,
! [SV432: $i,SV203: $i,SV575: $i] :
( ( ( in @ SV575 @ ( funcSet @ SV203 @ SV432 ) )
= $false )
| ( ( ( lam @ SV203 @ SV432
@ ^ [SY1163: $i] : ( ap @ SV203 @ SV432 @ SV575 @ SY1163 ) )
= SV575 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(2005,plain,
! [SV433: $i,SV204: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ ( powerset @ SV204 ) )
| ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SV665 ) ) ) )
= $true )
| ( ( in @ SV433 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2006,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ~ ( ~ ( SV205 @ SV666 )
| ~ ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1787]) ).
thf(2007,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ~ ( ~ ( SV209 @ SV667 )
| ~ ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1788]) ).
thf(2008,plain,
! [SV435: $i,SV210: $i] :
( ( ( ! [SY952: $i] :
~ ~ ( ~ ( in @ SY952 @ SV210 )
| ~ ( in @ SV435 @ SY952 ) ) )
= $false )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2009,plain,
! [SV576: $i > $i > $o,SV436: $i,SV211: $i,SV668: $i,SV621: $i] :
( ( ~ ( in @ ( kpair @ SV621 @ SV668 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SY1166: $i,SY1167: $i] : ( SV576 @ SY1166 @ SY1167 ) ) )
| ( in @ SV621 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2010,plain,
! [SV437: $o,SV212: $i,SV577: $i] :
( ( ( in @ SV577 @ SV212 )
= $false )
| ( ( ! [SY1168: $i] :
( ~ ( in @ SY1168 @ SV212 )
| ( in @ ( if @ SV212 @ SV437 @ SV577 @ SY1168 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SY1168 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2011,plain,
! [SV212: $i,SV578: $i] :
( ( ( in @ SV578 @ SV212 )
= $false )
| ( ( ! [SY1169: $i] :
( ~ ( in @ SY1169 @ SV212 )
| ( in @ ( if @ SV212 @ $true @ SV578 @ SY1169 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SY1169 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(2012,plain,
! [SV212: $i,SV579: $i] :
( ( ( in @ SV579 @ SV212 )
= $false )
| ( ( ! [SY1170: $i] :
( ~ ( in @ SY1170 @ SV212 )
| ( in @ ( if @ SV212 @ $false @ SV579 @ SY1170 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SY1170 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1793]) ).
thf(2013,plain,
! [SV580: $i,SV438: $i,SV213: $i] :
( ( ( func @ SV213 @ SV438 @ SV580 )
= $false )
| ( ( ( lam @ SV213 @ SV438
@ ^ [SY1171: $i] : ( ap @ SV213 @ SV438 @ SV580 @ SY1171 ) )
= SV580 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(2014,plain,
! [SV581: $i,SV439: $i,SV214: $i] :
( ( ( func @ SV214 @ SV439 @ SV581 )
= $false )
| ( ( ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV214 )
| ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1173: $i] : ( in @ ( kpair @ SY1172 @ SY1173 ) @ SV581 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(2015,plain,
! [SV440: $i,SV582: $i > $i,SV215: $i] :
( ( ( ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV215 )
| ( in @ ( SV582 @ SY1174 ) @ SV440 ) ) )
= $false )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(2016,plain,
! [SV441: $i,SV216: $i,SV583: $i] :
( ( ( in @ SV583 @ SV216 )
= $false )
| ( ( ! [SY1177: $i] :
( ~ ( in @ SY1177 @ SV441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SY1177 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(2017,plain,
! [SV442: $i,SV217: $i,SV584: $i] :
( ( ( in @ ( setadjoin @ SV584 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV217 @ ( setadjoin @ SV442 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV217 = SV584 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(2018,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ( in @ SV444 @ ( setunion @ SV219 ) )
| ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(2019,plain,
! [SV219: $i,SV444: $i] :
( ( ~ ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) )
| ( in @ SV444 @ ( setunion @ SV219 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(2020,plain,
! [SV445: $i,SV220: $i] :
( ( ( ~ ! [SY974: $i] :
~ ~ ( ~ ( in @ SY974 @ SV220 )
| ~ ( in @ SY974 @ SV445 ) ) )
= $true )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(2021,plain,
! [SV447: $i,SV222: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ ( powerset @ SV222 ) )
| ! [SY1263: $i] :
( ~ ( in @ SY1263 @ SV222 )
| ~ ( in @ SY1263 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY1263 @ ( binintersect @ SV447 @ SV669 ) ) ) )
= $true )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2022,plain,
! [SV622: $i,SV585: $i,SV448: $i,SV223: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SV622 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV585 != SV622 )
| ( SV448 = SV622 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1803]) ).
thf(2023,plain,
! [SV449: $i,SV224: $i,SV670: $i] :
( ( ( ~ ( in @ SV670 @ ( powerset @ SV224 ) )
| ! [SY1264: $i] :
( ~ ( in @ SY1264 @ SV224 )
| ~ ~ ( in @ SY1264 @ SV449 )
| ~ ~ ( in @ SY1264 @ SV670 )
| ~ ( in @ SY1264 @ ( binunion @ SV449 @ SV670 ) ) ) )
= $true )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2024,plain,
( ( ~ ( in @ sK3_SY3 @ ( powerset @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(2025,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1805]) ).
thf(2026,plain,
! [SV451: $o,SV226: $i,SV586: $i] :
( ( ( in @ SV586 @ SV226 )
= $false )
| ( ( ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SV226 )
| ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SY1179 )
= SV586 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(2027,plain,
! [SV226: $i,SV587: $i] :
( ( ( in @ SV587 @ SV226 )
= $false )
| ( ( ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV226 )
| ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SY1180 )
= SV587 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(2028,plain,
! [SV226: $i,SV588: $i] :
( ( ( in @ SV588 @ SV226 )
= $false )
| ( ( ! [SY1181: $i] :
( ~ ( in @ SY1181 @ SV226 )
| ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SY1181 )
= SV588 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1809]) ).
thf(2029,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ~ ( ~ ( SV227 @ SV671 )
| ~ ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2030,plain,
! [SV452: $i,SV228: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ ( powerset @ SV228 ) )
| ! [SY1266: $i] :
( ~ ( in @ SY1266 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SY1266 @ SV672 )
| ~ ( in @ SY1266 @ SV452 ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2031,plain,
! [SV453: $o,SV229: $i,SV589: $i] :
( ( ( in @ SV589 @ SV229 )
= $false )
| ( ( ! [SY1182: $i] :
( ~ ( in @ SY1182 @ SV229 )
| ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1183: $i] :
( ~ ( ~ SV453
| ( SY1183 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1183 != SY1182 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(2032,plain,
! [SV229: $i,SV590: $i] :
( ( ( in @ SV590 @ SV229 )
= $false )
| ( ( ! [SY1184: $i] :
( ~ ( in @ SY1184 @ SV229 )
| ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1185: $i] :
( ~ ( ~ $true
| ( SY1185 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1185 != SY1184 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(2033,plain,
! [SV229: $i,SV591: $i] :
( ( ( in @ SV591 @ SV229 )
= $false )
| ( ( ! [SY1186: $i] :
( ~ ( in @ SY1186 @ SV229 )
| ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1187: $i] :
( ~ ( ~ $false
| ( SY1187 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1187 != SY1186 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2034,plain,
! [SV593: $i,SV455: $i,SV231: $i] :
( ( ( ( setadjoin @ SV231 @ ( setadjoin @ SV455 @ emptyset ) )
= ( setadjoin @ SV593 @ emptyset ) )
= $false )
| ( ( SV231 = SV455 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(2035,plain,
! [SV458: $i,SV234: $i,SV594: $i] :
( ( ( in @ SV594 @ ( cartprod @ SV234 @ SV458 ) )
= $false )
| ( ( in @ ( ksnd @ SV594 ) @ SV458 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2036,plain,
! [SV623: $o,SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| SV623 )
| ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2037,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $true )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(2038,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $false )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2039,plain,
! [SV624: $i,SV596: $i,SV460: $i,SV236: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SV460 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV596 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV596 @ ( setadjoin @ SV624 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV460 = SV624 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2040,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY1267: $i] :
( ( ( sK18_SY995 @ SV461 @ SV237 )
!= SY1267 )
| ~ ( ~ ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ SY1267 ) )
| ~ ( ~ ( SV461 @ SY1267 )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1823]) ).
thf(2041,plain,
! [SV463: $i > $o,SV239: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV239 )
| ! [SY1268: $i] :
( ~ ( in @ SY1268 @ SV239 )
| ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SY1268 )
| ( SV673 = SY1268 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1825]) ).
thf(2042,plain,
! [SV464: $i,SV240: $i,SV597: $i] :
( ( ( in @ SV597 @ SV240 )
= $false )
| ( ( ~ ~ ( in @ SV597 @ SV464 )
| ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(2043,plain,
! [SV465: $i,SV241: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV241 ) )
= $false )
| ( ( ~ ( in @ SV598 @ SV465 )
| ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(2044,plain,
! [SV466: $i,SV242: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ ( powerset @ SV242 ) )
| ! [SY1269: $i] :
( ~ ( in @ SY1269 @ SV242 )
| ~ ~ ( in @ SY1269 @ SV674 )
| ~ ( in @ SY1269 @ ( binintersect @ SV466 @ SV674 ) ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2045,plain,
! [SV467: $o,SV243: $i,SV599: $i] :
( ( ( in @ SV599 @ SV243 )
= $false )
| ( ( ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1191: $i] :
( ~ ( ~ SV467
| ( SY1191 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1191 != SY1190 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(2046,plain,
! [SV243: $i,SV600: $i] :
( ( ( in @ SV600 @ SV243 )
= $false )
| ( ( ! [SY1192: $i] :
( ~ ( in @ SY1192 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1193: $i] :
( ~ ( ~ $true
| ( SY1193 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1193 != SY1192 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(2047,plain,
! [SV243: $i,SV601: $i] :
( ( ( in @ SV601 @ SV243 )
= $false )
| ( ( ! [SY1194: $i] :
( ~ ( in @ SY1194 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1195: $i] :
( ~ ( ~ $false
| ( SY1195 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1195 != SY1194 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1831]) ).
thf(2048,plain,
! [SV468: $i,SV244: $i,SV602: $i] :
( ( ( in @ SV602 @ SV244 )
= $false )
| ( ( ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SV468 )
| ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SY1196 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2049,plain,
! [SV470: $i,SV246: $i,SV603: $i] :
( ( ( in @ SV603 @ SV246 )
= $false )
| ( ( ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV470 )
| ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SY1197 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2050,plain,
! [SV604: $i,SV471: $i,SV247: $i] :
( ( ( func @ SV247 @ SV471 @ SV604 )
= $false )
| ( ( ! [SY1198: $i] :
( ~ ( func @ SV247 @ SV471 @ SY1198 )
| ~ ! [SY1199: $i] :
( ~ ( in @ SY1199 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1199 )
= ( ap @ SV247 @ SV471 @ SY1198 @ SY1199 ) ) )
| ( SV604 = SY1198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2051,plain,
! [SV248: $i,SV472: $i,SV605: $i] :
( ( ( in @ SV605 @ SV472 )
= $false )
| ( ( in @ SV605 @ ( binunion @ SV248 @ SV472 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(2052,plain,
! [SV473: $i,SV249: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ ( powerset @ SV249 ) )
| ! [SY1270: $i] :
( ~ ( in @ SY1270 @ SV249 )
| ~ ~ ( in @ SY1270 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SY1270 @ SV473 ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2053,plain,
! [SV474: $i > $o,SV250: $i,SV606: $i] :
( ( ( in @ SV606 @ SV250 )
= $false )
| ( ( ~ ( SV474 @ SV606 )
| ( in @ SV606
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2054,plain,
! [SV476: $i,SV252: $i,SV607: $i] :
( ( ( in @ SV607 @ SV252 )
= $false )
| ( ( ~ ( in @ SV607 @ SV476 )
| ~ ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2055,plain,
! [SV478: $i,SV254: $i,SV608: $i] :
( ( ( in @ SV608 @ ( cartprod @ SV254 @ SV478 ) )
= $false )
| ( ( iskpair @ SV608 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2056,plain,
! [SV480: $i,SV256: $i,SV676: $i] :
( ( ( ! [SY1271: $i] :
( ( SV676 != SY1271 )
| ( ( setadjoin @ SV256 @ SV676 )
= ( setadjoin @ SV480 @ SY1271 ) ) ) )
= $true )
| ( ( SV256 = SV480 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2057,plain,
! [SV482: $i,SV259: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( powerset @ SV259 ) )
| ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV259 )
| ~ ( in @ SY1272 @ SV482 )
| ( in @ SY1272 @ SV677 ) )
| ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2058,plain,
! [SV483: $i,SV260: $i,SV609: $i] :
( ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false )
| ( ( ~ ! [SY1201: $i] :
~ ~ ( ~ ( in @ SY1201 @ SV260 )
| ~ ~ ! [SY1202: $i] :
~ ~ ( ~ ( in @ SY1202 @ SV483 )
| ( SV609
!= ( kpair @ SY1201 @ SY1202 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(2059,plain,
! [SV678: $i > $o,SV484: $i,SV261: $i,SV1: $i] :
( ( ( ~ ! [SY1274: $i] :
( ~ ( in @ SY1274 @ SV1 )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ SV261 )
| ~ ( in @ ( kpair @ SY1274 @ SY1275 ) @ SV484 )
| ( SV678 @ ( kpair @ SY1274 @ SY1275 ) ) ) )
| ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2060,plain,
! [SV262: $i,SV2: $i,SV679: $i,SV625: $i] :
( ( ( ( SV625 != SV679 )
| ~ ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) )
| ~ ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1846]) ).
thf(2061,plain,
! [SV264: $i,SV4: $i,SV485: $i] :
( ( ( SV485 = SV4 )
= $true )
| ( ( SV485 = SV264 )
= $true )
| ( ( in @ SV485 @ ( setadjoin @ SV4 @ ( setadjoin @ SV264 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1847]) ).
thf(2062,plain,
! [SV486: $i,SV265: $i,SV5: $i,SV680: $i] :
( ( ( ~ ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
| ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV5 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV265 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV486 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV680 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2063,plain,
! [SV7: $i,SV610: $i] :
( ( ( in @ SV610 @ SV7 )
= $false )
| ( ( ( setunion @ SV7 )
= SV610 )
= $true )
| ( ( singleton @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2064,plain,
! [SV8: $i,SV266: $i] :
( ( ( ~ ( in @ ( sK8_SY679 @ SV266 @ SV8 ) @ SV8 ) )
= $false )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2065,plain,
! [SV8: $i,SV266: $i] :
( ( ( in @ ( sK8_SY679 @ SV266 @ SV8 ) @ SV266 )
= $false )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1851]) ).
thf(2066,plain,
! [SV9: $i,SV626: $i] :
( ( ( in @ SV626 @ SV9 )
= $false )
| ( ( ~ ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(2067,plain,
! [SV627: $o,SV10: $i,SV267: $i] :
( ( ( ~ ! [SY1219: $i] :
( ~ ( in @ SV267 @ SY1219 )
| ~ ( in @ SY1219 @ SV10 )
| SV627 ) )
= $true )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2068,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1854]) ).
thf(2069,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(2070,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
| ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1856]) ).
thf(2071,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ~ ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
| ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1857]) ).
thf(2072,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY1220: $i] :
~ ( ~ ( ~ ( SV12 @ SY1220 )
| ( SY1220 = SV628 ) )
| ~ ( ( SY1220 != SV628 )
| ( SV12 @ SY1220 ) ) ) )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2073,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ SV629 )
= $false )
| ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2074,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SV681 )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1860]) ).
thf(2075,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $true )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1860]) ).
thf(2076,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $false )
| ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1860]) ).
thf(2077,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ( ( sK9_SY685 @ SV270 @ SV15 )
!= ( sK19_SY1221 @ SV15 @ SV270 ) )
| ~ ( ~ ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
| ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1861]) ).
thf(2078,plain,
! [SV271: $i,SV16: $i,SV489: $i] :
( ( ( in @ SV489 @ SV16 )
= $true )
| ( ( ~ ( in @ SV489 @ ( setminus @ SV16 @ SV271 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1862]) ).
thf(2079,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( ~ ( SV19 @ SV630 )
| ~ ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) ) )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2080,plain,
! [SV272: $i,SV20: $i] :
( ( ( SV20 = SV272 )
= $false )
| ( ( subset @ SV20 @ SV272 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2081,plain,
! [SV273: $i,SV21: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ! [SY1223: $i] :
( ~ ( in @ SY1223 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SY1223 @ SV273 )
| ( in @ SY1223 @ SV631 ) ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(2082,plain,
! [SV274: $i,SV22: $i,SV490: $i] :
( ( ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
= $true )
| ( ( ~ ~ ( in @ SV490 @ SV274 )
| ~ ( in @ SV490 @ SV22 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1866]) ).
thf(2083,plain,
! [SV491: $i,SV276: $i,SV24: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV24 )
| ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SV682 ) @ SV276 ) )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2084,plain,
! [SV611: $i,SV492: $i,SV278: $i,SV26: $i] :
( ( ( ( kpair @ SV26 @ SV278 )
= ( kpair @ SV492 @ SV611 ) )
= $false )
| ( ( SV26 = SV492 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(2085,plain,
! [SV279: $i,SV27: $i,SV612: $i,SV493: $i] :
( ( ( in @ ( kpair @ SV493 @ SV612 ) @ ( cartprod @ SV27 @ SV279 ) )
= $false )
| ( ( in @ SV493 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2086,plain,
! [SV494: $i > $i > $o,SV281: $i,SV29: $i,SV613: $i] :
( ( ( in @ SV613 @ SV29 )
= $false )
| ( ( ! [SY1203: $i] :
( ~ ( in @ SY1203 @ SV281 )
| ~ ( SV494 @ SV613 @ SY1203 )
| ( in @ ( kpair @ SV613 @ SY1203 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2087,plain,
! [SV496: $i,SV283: $i,SV31: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV31 )
| ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV283 )
| ~ ( in @ ( kpair @ SV683 @ SY1281 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SY1281 ) ) )
= $true )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2088,plain,
! [SV285: $i,SV33: $i,SV497: $i] :
( ( ( SV497 = SV33 )
= $true )
| ( ( in @ SV497 @ SV285 )
= $true )
| ( ( in @ SV497 @ ( setadjoin @ SV33 @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1872]) ).
thf(2089,plain,
! [SV498: $i,SV287: $o,SV35: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV35 )
| ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 ) )
= $true )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2090,plain,
! [SV499: $i,SV35: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV35 )
| ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 ) )
= $true )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2091,plain,
! [SV500: $i,SV35: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV35 )
| ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 ) )
= $true )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2092,plain,
! [SV36: $i,SV501: $i > $i,SV288: $i] :
( ( ( ~ ( in @ ( sK20_SY1059 @ SV288 @ SV501 @ SV36 ) @ SV36 )
| ( in @ ( SV501 @ ( sK20_SY1059 @ SV288 @ SV501 @ SV36 ) ) @ SV288 ) )
= $false )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1876]) ).
thf(2093,plain,
! [SV293: $i,SV41: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ ( powerset @ SV41 ) ) )
= $true )
| ( ( ~ ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV41 )
| ~ ( in @ SY1224 @ SV632 )
| ( in @ SY1224 @ ( setminus @ SV41 @ SV293 ) ) ) )
= $true )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1878]) ).
thf(2094,plain,
! [SV295: $i,SV43: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( ! [SY1225: $i] :
( ~ ( in @ SY1225 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY1225 ) @ ( binunion @ SV633 @ SY1225 ) ) ) ) ) )
= $true )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(2095,plain,
! [SV44: $i,SV503: $i > $i,SV296: $i] :
( ( ( ~ ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 )
| ( in @ ( SV503 @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) ) @ SV296 ) )
= $false )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1880]) ).
thf(2096,plain,
! [SV45: $i,SV297: $i,SV504: $i] :
( ( ( ~ ~ ( in @ SV504 @ SV297 ) )
= $true )
| ( ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) )
= $true )
| ( ( in @ SV504 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1881]) ).
thf(2097,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2098,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ! [SY1226: $i] :
~ ~ ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1226 )
| ~ ! [SY1227: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1227 )
| ( SY1226 = SY1227 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1882]) ).
thf(2099,plain,
! [SV300: $i,SV50: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ ( powerset @ SV50 ) ) )
= $true )
| ( ( ! [SY1228: $i] :
( ~ ( in @ SY1228 @ SV50 )
| ~ ~ ( in @ SY1228 @ SV300 )
| ~ ( in @ SY1228 @ ( binintersect @ SV300 @ SV634 ) ) ) )
= $true )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2100,plain,
! [SV301: $i,SV51: $i,SV506: $i] :
( ( ( in @ SV506 @ SV51 )
= $true )
| ( ( ~ ~ ( in @ SV506 @ SV301 )
| ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1885]) ).
thf(2101,plain,
! [SV52: $i,SV635: $i] :
( ( ( in @ SV635 @ SV52 )
= $false )
| ( ( SV52 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2102,plain,
! [SV507: $i,SV302: $i,SV54: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV54 )
| ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SV687 ) @ SV302 ) )
= $true )
| ( ( func @ SV54 @ SV302 @ SV507 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2103,plain,
! [SV303: $i > $o,SV55: $i] :
( ( ( ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV55 )
| ~ ( SV303 @ SY746 ) ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2104,plain,
! [SV304: $i,SV56: $i,SV508: $i] :
( ( ( in @ SV508 @ SV56 )
= $true )
| ( ( in @ SV508 @ SV304 )
= $true )
| ( ( in @ SV508 @ ( binunion @ SV56 @ SV304 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1889]) ).
thf(2105,plain,
! [SV58: $i,SV306: $i] :
( ( ( in @ SV306 @ ( setadjoin @ SV58 @ emptyset ) )
= $false )
| ( ( SV58 = SV306 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2106,plain,
! [SV60: $i,SV308: $i,SV511: $i] :
( ( ( in @ SV511 @ SV308 )
= $false )
| ( ( in @ SV511 @ ( setminus @ SV60 @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2107,plain,
! [SV61: $i,SV309: $i,SV512: $i] :
( ( ( ~ ( in @ SV512 @ SV309 ) )
= $true )
| ( ( in @ SV512 @ ( binintersect @ SV61 @ SV309 ) )
= $true )
| ( ( in @ SV512 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1894]) ).
thf(2108,plain,
! [SV310: $i,SV62: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ! [SY1229: $i] :
( ~ ( in @ SY1229 @ ( powerset @ SV62 ) )
| ! [SY1230: $i] :
( ~ ( in @ SY1230 @ SV62 )
| ~ ( in @ SY1230 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1230 @ ( binintersect @ ( binunion @ SV310 @ SY1229 ) @ ( binunion @ SV636 @ SY1229 ) ) ) ) ) )
= $true )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2109,plain,
! [SV311: $i > $o,SV63: $i,SV688: $i] :
( ( ( ~ ~ ( ~ ( in @ SV688 @ SV63 )
| ~ ~ ( SV311 @ SV688 ) ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2110,plain,
! [SV65: $i] :
( ( ( ~ ( in @ ( sK22_SY170 @ SV65 ) @ SV65 ) )
= $false )
| ( ( SV65 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1897]) ).
thf(2111,plain,
! [SV67: $i,SV312: $i,SV513: $i] :
( ( ( ~ ~ ( in @ SV513 @ SV312 ) )
= $true )
| ( ( ~ ( in @ SV513 @ SV67 ) )
= $true )
| ( ( subset @ SV67 @ SV312 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(2112,plain,
! [SV313: $i,SV68: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ ( powerset @ SV68 ) ) )
= $true )
| ( ( ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV68 )
| ~ ( in @ SY1231 @ SV313 )
| ( in @ SY1231 @ SV637 ) )
| ( subset @ SV313 @ SV637 ) )
= $true )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(2113,plain,
! [SV614: $i,SV515: $i,SV316: $i,SV71: $i] :
( ( ( ( kpair @ SV71 @ SV316 )
= ( kpair @ SV515 @ SV614 ) )
= $false )
| ( ( SV316 = SV614 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2114,plain,
! [SV72: $i,SV516: $i,SV317: $i] :
( ( ( ~ ( subset @ SV317 @ SV516 ) )
= $true )
| ( ( subset @ SV72 @ SV516 )
= $true )
| ( ( subset @ SV72 @ SV317 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2115,plain,
! [SV517: $i,SV318: $i,SV73: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV73 )
| ( ( ap @ SV73 @ SV318 @ SV517 @ SV689 )
= ( ap @ SV73 @ SV318 @ SV517 @ SV689 ) ) )
= $true )
| ( ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2116,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) )
| ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1904]) ).
thf(2117,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2118,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY1232: $i] :
( ~ ( in @ SY1232 @ SV76 )
| ~ ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
| ~ ( SV321 @ SY1232 )
| ( ( sK12_SY769 @ SV321 @ SV76 )
= SY1232 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1905]) ).
thf(2119,plain,
! [SV322: $i,SV77: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SV77 )
| ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SY1233 @ SV638 )
| ~ ( in @ SY1233 @ SV322 ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1906]) ).
thf(2120,plain,
! [SV324: $i,SV79: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ SV79 ) )
= $true )
| ( ( in @ SV324 @ ( setunion @ SV79 ) )
= $true )
| ( ( in @ SV324 @ SV518 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2121,plain,
! [SV82: $i,SV326: $i] :
( ( ( ~ ( in @ SV326 @ ( powerset @ SV82 ) ) )
= $true )
| ( ( ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2122,plain,
! [SV82: $i,SV326: $i] :
( ( ( ~ ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) ) )
= $true )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2123,plain,
! [SV327: $i > $o,SV83: $i,SV690: $i] :
( ( ( ~ ~ ( ~ ( in @ SV690 @ SV83 )
| ~ ( SV327 @ SV690 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2124,plain,
! [SV520: $i,SV328: $o,SV84: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV84 )
| ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1282: $i] :
( ~ ( ~ SV328
| ( SY1282 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1282 != SV691 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) )
= $true )
| ( ( in @ SV520 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2125,plain,
! [SV521: $i,SV84: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV84 )
| ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1283: $i] :
( ~ ( ~ $true
| ( SY1283 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1283 != SV692 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) )
= $true )
| ( ( in @ SV521 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2126,plain,
! [SV522: $i,SV84: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV84 )
| ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1284: $i] :
( ~ ( ~ $false
| ( SY1284 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1284 != SV693 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2127,plain,
! [SV85: $i,SV523: $i,SV329: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ SV329 )
| ( in @ ( kpair @ SV523 @ SV694 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) ) )
= $true )
| ( ( in @ SV523 @ SV85 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2128,plain,
! [SV524: $i,SV330: $i,SV86: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV86 )
| ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV330 )
| ~ ( in @ ( kpair @ SV695 @ SY1285 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SY1285 ) ) )
= $true )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2129,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( ~ ( SV89 @ SV639 )
| ~ ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) ) )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2130,plain,
! [SV525: $i,SV335: $i,SV90: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV90 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1286: $i] : ( in @ ( kpair @ SV696 @ SY1286 ) @ SV525 ) ) )
@ SV335 ) )
= $true )
| ( ( func @ SV90 @ SV335 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2131,plain,
! [SV92: $i,SV526: $i,SV337: $i > $o] :
( ( ( ~ ( SV337 @ SV526 ) )
= $true )
| ( ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset )
= $true )
| ( ( in @ SV526 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1919]) ).
thf(2132,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( ~ ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) )
| ~ ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) )
= $false )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2133,plain,
! [SV341: $i,SV96: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ ( powerset @ SV96 ) ) )
= $true )
| ( ( ! [SY1235: $i] :
( ~ ( in @ SY1235 @ SV96 )
| ~ ( in @ SY1235 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SY1235 @ SV341 ) ) )
= $true )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2134,plain,
! [SV97: $i,SV529: $i,SV342: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV342 )
| ( ( kpair @ SV529 @ SV697 )
= ( kpair @ SV529 @ SV697 ) ) )
= $true )
| ( ( in @ SV529 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2135,plain,
! [SV344: $i,SV100: $i,SV698: $i,SV641: $i] :
( ( ( ( SV641 != SV698 )
| ~ ( in @ SV641 @ SV100 )
| ( in @ SV698 @ SV344 ) )
= $true )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2136,plain,
! [SV345: $i,SV101: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ ( powerset @ SV101 ) ) )
= $true )
| ( ( ~ ( subset @ ( setminus @ SV101 @ SV642 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SV642 ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2137,plain,
! [SV346: $i,SV102: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ! [SY1237: $i] :
( ~ ( in @ SY1237 @ ( powerset @ SV102 ) )
| ! [SY1238: $i] :
( ~ ( in @ SY1238 @ SV102 )
| ~ ( in @ SY1238 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1238 @ ( binunion @ SV346 @ SY1237 ) ) ) ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2138,plain,
! [SV530: $i,SV348: $i,SV104: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV104 )
| ( in @ ( kpair @ SV699 @ ( ap @ SV104 @ SV348 @ SV530 @ SV699 ) ) @ SV530 ) )
= $true )
| ( ( func @ SV104 @ SV348 @ SV530 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2139,plain,
! [SV105: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK23_SY262 @ SV105 ) @ SV105 )
| ~ $true ) )
= $false )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1928]) ).
thf(2140,plain,
! [SV109: $i,SV532: $i,SV351: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV351 )
| ( in @ ( kpair @ SV532 @ SV700 ) @ ( cartprod @ SV109 @ SV351 ) ) )
= $true )
| ( ( in @ SV532 @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2141,plain,
! [SV352: $i,SV110: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ ( powerset @ SV110 ) )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV110 )
| ~ ( in @ SY1240 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1240 @ ( binunion @ SV644 @ SY1239 ) ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2142,plain,
! [SV353: $i,SV111: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ ( powerset @ SV111 ) ) )
= $true )
| ( ( ~ ( subset @ SV353 @ SV645 )
| ( subset @ ( setminus @ SV111 @ SV645 ) @ ( setminus @ SV111 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2143,plain,
! [SV354: $i,SV112: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ~ ( subset @ SV354 @ ( setminus @ SV112 @ SV646 ) )
| ( subset @ SV646 @ ( setminus @ SV112 @ SV354 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1933]) ).
thf(2144,plain,
! [SV113: $i,SV355: $i] :
( ( ( ~ ( in @ ( sK13_SY818 @ SV355 @ SV113 ) @ SV113 ) )
= $false )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2145,plain,
! [SV113: $i,SV355: $i] :
( ( ( in @ ( sK13_SY818 @ SV355 @ SV113 ) @ SV355 )
= $false )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1934]) ).
thf(2146,plain,
! [SV114: $i,SV533: $i,SV356: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV356 )
| ( ( kfst @ ( kpair @ SV533 @ SV701 ) )
= SV533 ) )
= $true )
| ( ( in @ SV533 @ SV114 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2147,plain,
! [SV534: $i,SV358: $o,SV116: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV116 )
| ~ ~ SV358
| ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) ) )
= $true )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2148,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV116 )
| ~ ~ $true
| ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) ) )
= $true )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2149,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV116 )
| ~ ~ $false
| ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) ) )
= $true )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2150,plain,
! [SV117: $i,SV359: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 ) )
= $false )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2151,plain,
! [SV117: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) ) )
= $false )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1939]) ).
thf(2152,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i] :
( ( ( ~ ( func @ SV118 @ SV360 @ SV705 )
| ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1290 )
= ( ap @ SV118 @ SV360 @ SV705 @ SY1290 ) ) )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2153,plain,
! [SV362: $i,SV120: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV120 ) )
= $true )
| ( ( ~ ( in @ SV647 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SV647 @ SV362 ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1941]) ).
thf(2154,plain,
! [SV121: $i,SV538: $i,SV363: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV363 )
| ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SV706 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) ) )
= $true )
| ( ( in @ SV538 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2155,plain,
! [SV364: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK15_SY834 @ SV124 @ SV364 ) @ SV364 ) )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(2156,plain,
! [SV364: $i,SV124: $i] :
( ( ( in @ ( sK15_SY834 @ SV124 @ SV364 ) @ SV124 )
= $false )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(2157,plain,
! [SV540: $i,SV366: $i,SV126: $i,SV707: $i] :
( ( ( ~ ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
| ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV126 )
| ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV366 )
| ~ ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV540 )
| ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV707 ) ) )
| ( subset @ SV540 @ SV707 ) )
= $true )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2158,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i,SV615: $i] :
( ( ( in @ SV615 @ SV128 )
= $false )
| ( ( ! [SY1206: $i] :
( ~ ( in @ SY1206 @ SV368 )
| ~ ( in @ ( kpair @ SV615 @ SY1206 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SY1206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2159,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV129 ) )
= $true )
| ( ( ~ ~ ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SV648 @ SV369 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2160,plain,
! [SV370: $i,SV130: $i,SV616: $i,SV542: $i] :
( ( ( in @ ( kpair @ SV542 @ SV616 ) @ ( cartprod @ SV130 @ SV370 ) )
= $false )
| ( ( in @ SV616 @ SV370 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2161,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2162,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY1241: $i] :
( ~ ( in @ SY1241 @ SV131 )
| ~ ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
| ~ ( SV371 @ SY1241 )
| ( ( sK16_SY848 @ SV371 @ SV131 )
= SY1241 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1950]) ).
thf(2163,plain,
! [SV133: $i,SV373: $i,SV544: $i] :
( ( ( ~ ~ ( in @ SV544 @ SV373 ) )
= $true )
| ( ( SV133 != SV373 )
= $true )
| ( ( in @ SV544 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1952]) ).
thf(2164,plain,
! [SV376: $i,SV136: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( powerset @ SV136 ) ) )
= $true )
| ( ( ! [SY1242: $i] :
( ~ ( in @ SY1242 @ SV136 )
| ~ ( in @ SY1242 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SY1242 @ ( setminus @ SV136 @ SV376 ) ) ) )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2165,plain,
! [SV708: $i > $o,SV650: $i > $o,SV377: $i,SV137: $i] :
( ( ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV137 )
| ! [SY1296: $i] :
( ~ ( in @ SY1296 @ SV377 )
| ( SY1295 != SY1296 )
| ~ ( ~ ( ~ ( SV650 @ SY1295 )
| ( SV708 @ SY1296 ) )
| ~ ( ~ ( SV708 @ SY1296 )
| ( SV650 @ SY1295 ) ) ) ) )
| ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2166,plain,
! [SV138: $i,SV545: $i,SV378: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV378 )
| ( ( ksnd @ ( kpair @ SV545 @ SV709 ) )
= SV709 ) )
= $true )
| ( ( in @ SV545 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2167,plain,
! [SV139: $i,SV379: $i,SV546: $i] :
( ( ( ~ ( subset @ SV546 @ SV379 ) )
= $true )
| ( ( subset @ SV546 @ ( binintersect @ SV139 @ SV379 ) )
= $true )
| ( ( subset @ SV546 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1956]) ).
thf(2168,plain,
! [SV140: $i,SV380: $i,SV547: $i] :
( ( ( ~ ~ ( in @ SV547 @ SV380 ) )
= $true )
| ( ( ~ ( subset @ SV140 @ SV380 ) )
= $true )
| ( ( in @ SV547 @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1957]) ).
thf(2169,plain,
! [SV381: $i,SV141: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV141 ) )
= $true )
| ( ( ~ ( in @ SV651 @ SV381 )
| ( in @ SV651 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1958]) ).
thf(2170,plain,
! [SV383: $i,SV144: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( powerset @ SV144 ) ) )
= $true )
| ( ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SV652 ) ) ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2171,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ( ~ ( SV146 @ SV653 )
| ~ ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) ) )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1960]) ).
thf(2172,plain,
! [SV384: $i,SV147: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ ( powerset @ SV147 ) ) )
= $true )
| ( ( ! [SY1249: $i] :
( ~ ( in @ SY1249 @ SV147 )
| ~ ~ ( in @ SY1249 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SY1249 @ SV654 ) ) )
= $true )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2173,plain,
! [SV385: $i,SV148: $i,SV655: $i] :
( ( ( ~ ( in @ SV655 @ ( powerset @ SV148 ) ) )
= $true )
| ( ( ~ ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV148 )
| ~ ( in @ SY1250 @ SV385 )
| ( in @ SY1250 @ SV655 ) )
| ( in @ SV385 @ ( powerset @ SV655 ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1962]) ).
thf(2174,plain,
! [SV152: $i,SV549: $i > $i,SV389: $i] :
( ( ( ~ ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 )
| ( in @ ( SV549 @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) ) @ SV389 ) )
= $false )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1964]) ).
thf(2175,plain,
! [SV390: $i,SV153: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( powerset @ SV153 ) ) )
= $true )
| ( ( in @ ( setminus @ SV390 @ SV656 ) @ ( powerset @ SV153 ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2176,plain,
! [SV550: $i,SV391: $o,SV154: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV154 )
| ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) ) )
= $true )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2177,plain,
! [SV551: $i,SV154: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ SV154 )
| ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) ) )
= $true )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2178,plain,
! [SV552: $i,SV154: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ SV154 )
| ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) ) )
= $true )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2179,plain,
! [SV553: $i > $i > $o,SV392: $i,SV156: $i,SV657: $i,SV618: $i] :
( ( ( ~ ( in @ ( kpair @ SV618 @ SV657 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SY1118: $i,SY1119: $i] : ( SV553 @ SY1118 @ SY1119 ) ) ) )
= $true )
| ( ( in @ SV657 @ SV392 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1969]) ).
thf(2180,plain,
! [SV554: $i,SV393: $o,SV157: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ SV157 )
| ( in @ ( if @ SV157 @ SV393 @ SV554 @ SV713 ) @ SV157 ) )
= $true )
| ( ( in @ SV554 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2181,plain,
! [SV555: $i,SV157: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV157 )
| ( in @ ( if @ SV157 @ $true @ SV555 @ SV714 ) @ SV157 ) )
= $true )
| ( ( in @ SV555 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2182,plain,
! [SV556: $i,SV157: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV157 )
| ( in @ ( if @ SV157 @ $false @ SV556 @ SV715 ) @ SV157 ) )
= $true )
| ( ( in @ SV556 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2183,plain,
! [SV158: $i] :
( ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ~ ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) )
= $true )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1973]) ).
thf(2184,plain,
! [SV394: $i,SV160: $i,SV557: $i] :
( ( ( SV557 = SV160 )
= $true )
| ( ( SV557 = SV394 )
= $true )
| ( ( in @ SV557 @ ( setadjoin @ SV160 @ ( setadjoin @ SV394 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1974]) ).
thf(2185,plain,
! [SV162: $i,SV559: $i > $i,SV396: $i] :
( ( ( ~ ( in @ ( sK25_SY1125 @ SV396 @ SV559 @ SV162 ) @ SV162 )
| ( in @ ( SV559 @ ( sK25_SY1125 @ SV396 @ SV559 @ SV162 ) ) @ SV396 ) )
= $false )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1975]) ).
thf(2186,plain,
! [SV560: $i > $i > $o,SV398: $i,SV164: $i,SV658: $i,SV619: $i] :
( ( ( ~ ( in @ ( kpair @ SV619 @ SV658 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SY1129: $i,SY1130: $i] : ( SV560 @ SY1129 @ SY1130 ) ) ) )
= $true )
| ( ( SV560 @ SV619 @ SV658 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2187,plain,
! [SV165: $i,SV399: $i] :
( ( ( subset @ SV399 @ SV165 )
= $false )
| ( ( SV165 = SV399 )
= $true )
| ( ( subset @ SV165 @ SV399 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2188,plain,
! [SV402: $i,SV168: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ ( powerset @ SV168 ) ) )
= $true )
| ( ( ! [SY1255: $i] :
( ~ ( in @ SY1255 @ SV168 )
| ~ ( in @ SY1255 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY1255 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) ) )
= $true )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2189,plain,
! [SV403: $i > $o,SV169: $i] :
( ( ( ! [SY905: $i] :
~ ~ ( ~ ( in @ SY905 @ SV169 )
| ~ ( SV403 @ SY905 ) ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2190,plain,
! [SV405: $i,SV171: $i,SV562: $i] :
( ( ( in @ SV562 @ ( setminus @ SV171 @ SV405 ) )
= $false )
| ( ( in @ SV562 @ SV405 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1981]) ).
thf(2191,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY909 @ SV408 @ SV174 ) @ SV174 )
| ~ ( SV408 @ ( sK26_SY909 @ SV408 @ SV174 ) ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1982]) ).
thf(2192,plain,
! [SV563: $i,SV409: $i,SV175: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
| ~ ! [SY1302: $i] :
( ~ ( in @ SY1302 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1302 )
= ( ap @ SV175 @ SV409 @ SV716 @ SY1302 ) ) )
| ( SV563 = SV716 ) )
= $true )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2193,plain,
! [SV410: $i,SV176: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV176 ) )
= $true )
| ( ( ~ ( in @ SV660 @ SV410 )
| ~ ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) ) )
= $true )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1984]) ).
thf(2194,plain,
! [SV180: $i,SV565: $i > $i,SV412: $i] :
( ( ( ~ ( in @ ( sK27_SY1133 @ SV412 @ SV565 @ SV180 ) @ SV180 )
| ( in @ ( SV565 @ ( sK27_SY1133 @ SV412 @ SV565 @ SV180 ) ) @ SV412 ) )
= $false )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1986]) ).
thf(2195,plain,
! [SV413: $i,SV181: $i,SV661: $i] :
( ( ( ~ ( in @ SV661 @ ( powerset @ SV181 ) ) )
= $true )
| ( ( ! [SY1256: $o,SY1257: $i] :
( ~ ( in @ SY1257 @ SV181 )
| ~ ( in @ SY1257 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SY1257 @ SV413 )
| SY1256 )
| ~ ( ~ ( in @ SY1257 @ SV661 )
| SY1256 )
| SY1256 ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2196,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( ~ ( SV182 @ SV662 )
| ~ ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) ) )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2197,plain,
! [SV415: $i,SV184: $i,SV663: $i] :
( ( ( ~ ( in @ SV663 @ ( powerset @ SV184 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV415 @ SV663 ) @ ( powerset @ SV184 ) )
= $true )
| ( ( in @ SV415 @ ( powerset @ SV184 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1989]) ).
thf(2198,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) )
= $true )
| ( ( ~ ( in @ SV566 @ SV185 )
| ( in @ SV566 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2199,plain,
! [SV417: $i,SV187: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ ( powerset @ SV187 ) ) )
= $true )
| ( ( in @ ( binunion @ SV417 @ SV664 ) @ ( powerset @ SV187 ) )
= $true )
| ( ( in @ SV417 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2200,plain,
! [SV567: $i,SV418: $i,SV188: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV188 )
| ( ( ap @ SV188 @ SV418 @ SV567 @ SV717 )
= ( ap @ SV188 @ SV418 @ SV567 @ SV717 ) ) )
= $true )
| ( ( func @ SV188 @ SV418 @ SV567 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2201,plain,
! [SV568: $i,SV420: $i,SV190: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV190 )
| ( in @ ( kpair @ SV718 @ ( ap @ SV190 @ SV420 @ SV568 @ SV718 ) ) @ SV568 ) )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2202,plain,
! [SV421: $i > $o,SV191: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV191 )
| ( SV421 @ SV719 ) )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2203,plain,
! [SV620: $i,SV569: $i,SV422: $i,SV192: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV192 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV192 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV569 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV569 @ ( setadjoin @ SV620 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV192 = SV569 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2204,plain,
! [SV720: $i > $o,SV570: $i,SV423: $i,SV193: $i] :
( ( ( ~ ! [SY1303: $i] :
( ~ ( in @ SY1303 @ SV193 )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV423 )
| ~ ( in @ ( kpair @ SY1303 @ SY1304 ) @ SV570 )
| ( SV720 @ ( kpair @ SY1303 @ SY1304 ) ) ) )
| ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2205,plain,
! [SV424: $i,SV721: $o,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| SV721 )
| ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1997]) ).
thf(2206,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| $true )
| ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1997]) ).
thf(2207,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| $false )
| ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1997]) ).
thf(2208,plain,
! [SV425: $i > $o,SV195: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV195 )
| ( SV425 @ SV722 ) )
= $true )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2209,plain,
! [SV196: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2210,plain,
! [SV196: $i] :
( ( ~ ! [SY1153: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY1153 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1153 ) )
| ~ ! [SY1156: $i] :
~ ~ ! [SY1157: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1156 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1157 @ SY1153 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1156 )
| ~ ( in @ SX5 @ SY1153 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1156 ) )
| ( in @ SY1157 @ SY1159 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1999]) ).
thf(2211,plain,
! [SV199: $i,SV572: $i,SV428: $i > $o] :
( ( ( ~ ( SV428 @ SV572 ) )
= $true )
| ( ( ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) )
= $true )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2000]) ).
thf(2212,plain,
! [SV429: $i,SV200: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ SV200 ) )
= $true )
| ( ( in @ SV573 @ SV429 )
= $true )
| ( ( subset @ SV200 @ SV429 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2001]) ).
thf(2213,plain,
! [SV201: $i,SV430: $i] :
( ( ( ~ ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 ) )
= $false )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2214,plain,
! [SV201: $i,SV430: $i] :
( ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2215,plain,
! [SV202: $i,SV431: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV431 ) )
= $true )
| ( ( in @ SV574 @ SV202 )
= $true )
| ( ( in @ SV431 @ ( powerset @ SV202 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2216,plain,
! [SV433: $i,SV204: $i,SV665: $i] :
( ( ( ~ ( in @ SV665 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SV665 ) ) )
= $true )
| ( ( in @ SV433 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2217,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ( ~ ( SV205 @ SV666 )
| ~ ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) ) )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2006]) ).
thf(2218,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ( ~ ( SV209 @ SV667 )
| ~ ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) ) )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2219,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK28_SY952 @ SV435 @ SV210 ) @ SV210 )
| ~ ( in @ SV435 @ ( sK28_SY952 @ SV435 @ SV210 ) ) ) )
= $false )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2008]) ).
thf(2220,plain,
! [SV576: $i > $i > $o,SV436: $i,SV211: $i,SV668: $i,SV621: $i] :
( ( ( ~ ( in @ ( kpair @ SV621 @ SV668 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SY1166: $i,SY1167: $i] : ( SV576 @ SY1166 @ SY1167 ) ) ) )
= $true )
| ( ( in @ SV621 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2009]) ).
thf(2221,plain,
! [SV577: $i,SV437: $o,SV212: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV212 )
| ( in @ ( if @ SV212 @ SV437 @ SV577 @ SV723 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SV723 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV577 @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2222,plain,
! [SV578: $i,SV212: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV212 )
| ( in @ ( if @ SV212 @ $true @ SV578 @ SV724 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SV724 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV578 @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2223,plain,
! [SV579: $i,SV212: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV212 )
| ( in @ ( if @ SV212 @ $false @ SV579 @ SV725 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SV725 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV579 @ SV212 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2224,plain,
! [SV581: $i,SV439: $i,SV214: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV214 )
| ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1306: $i] : ( in @ ( kpair @ SV726 @ SY1306 ) @ SV581 ) ) ) )
= $true )
| ( ( func @ SV214 @ SV439 @ SV581 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2225,plain,
! [SV215: $i,SV582: $i > $i,SV440: $i] :
( ( ( ~ ( in @ ( sK29_SY1174 @ SV440 @ SV582 @ SV215 ) @ SV215 )
| ( in @ ( SV582 @ ( sK29_SY1174 @ SV440 @ SV582 @ SV215 ) ) @ SV440 ) )
= $false )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2015]) ).
thf(2226,plain,
! [SV216: $i,SV583: $i,SV441: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV441 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SV727 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) ) )
= $true )
| ( ( in @ SV583 @ SV216 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2227,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( setunion @ SV219 ) ) )
= $true )
| ( ( ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2228,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2019]) ).
thf(2229,plain,
! [SV445: $i,SV220: $i] :
( ( ( ! [SY974: $i] :
~ ~ ( ~ ( in @ SY974 @ SV220 )
| ~ ( in @ SY974 @ SV445 ) ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2230,plain,
! [SV447: $i,SV222: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ ( powerset @ SV222 ) ) )
= $true )
| ( ( ! [SY1263: $i] :
( ~ ( in @ SY1263 @ SV222 )
| ~ ( in @ SY1263 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY1263 @ ( binintersect @ SV447 @ SV669 ) ) ) )
= $true )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2231,plain,
! [SV622: $i,SV585: $i,SV448: $i,SV223: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SV622 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV585 != SV622 )
| ( SV448 = SV622 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2232,plain,
! [SV449: $i,SV224: $i,SV670: $i] :
( ( ( ~ ( in @ SV670 @ ( powerset @ SV224 ) ) )
= $true )
| ( ( ! [SY1264: $i] :
( ~ ( in @ SY1264 @ SV224 )
| ~ ~ ( in @ SY1264 @ SV449 )
| ~ ~ ( in @ SY1264 @ SV670 )
| ~ ( in @ SY1264 @ ( binunion @ SV449 @ SV670 ) ) ) )
= $true )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2023]) ).
thf(2233,plain,
( ( in @ sK3_SY3 @ ( powerset @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2024]) ).
thf(2234,plain,
( ( ~ ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2025]) ).
thf(2235,plain,
! [SV586: $i,SV451: $o,SV226: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV226 )
| ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SV728 )
= SV586 ) )
= $true )
| ( ( in @ SV586 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2236,plain,
! [SV587: $i,SV226: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV226 )
| ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SV729 )
= SV587 ) )
= $true )
| ( ( in @ SV587 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2237,plain,
! [SV588: $i,SV226: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ SV226 )
| ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SV730 )
= SV588 ) )
= $true )
| ( ( in @ SV588 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2238,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( SV227 @ SV671 )
| ~ ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) ) )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2239,plain,
! [SV452: $i,SV228: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ ( powerset @ SV228 ) ) )
= $true )
| ( ( ! [SY1266: $i] :
( ~ ( in @ SY1266 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SY1266 @ SV672 )
| ~ ( in @ SY1266 @ SV452 ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2030]) ).
thf(2240,plain,
! [SV589: $i,SV453: $o,SV229: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV229 )
| ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1307: $i] :
( ~ ( ~ SV453
| ( SY1307 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1307 != SV731 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ SV229 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2241,plain,
! [SV590: $i,SV229: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ SV229 )
| ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1308: $i] :
( ~ ( ~ $true
| ( SY1308 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1308 != SV732 ) ) ) ) ) )
= $true )
| ( ( in @ SV590 @ SV229 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2242,plain,
! [SV591: $i,SV229: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV229 )
| ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1309: $i] :
( ~ ( ~ $false
| ( SY1309 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1309 != SV733 ) ) ) ) ) )
= $true )
| ( ( in @ SV591 @ SV229 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2033]) ).
thf(2243,plain,
! [SV623: $o,SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| SV623 )
| ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2244,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $true )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2245,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $false )
| ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2246,plain,
! [SV624: $i,SV596: $i,SV460: $i,SV236: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV236 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV236 @ ( setadjoin @ SV460 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV596 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV596 @ ( setadjoin @ SV624 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV460 = SV624 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2247,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ( ( sK18_SY995 @ SV461 @ SV237 )
!= ( sK30_SY1267 @ SV237 @ SV461 ) )
| ~ ( ~ ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
| ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2040]) ).
thf(2248,plain,
! [SV463: $i > $o,SV239: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV239 ) )
= $true )
| ( ( ! [SY1268: $i] :
( ~ ( in @ SY1268 @ SV239 )
| ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SY1268 )
| ( SV673 = SY1268 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2249,plain,
! [SV240: $i,SV464: $i,SV597: $i] :
( ( ( ~ ~ ( in @ SV597 @ SV464 ) )
= $true )
| ( ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) )
= $true )
| ( ( in @ SV597 @ SV240 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2042]) ).
thf(2250,plain,
! [SV465: $i,SV241: $i,SV598: $i] :
( ( ( in @ SV598 @ SV241 )
= $true )
| ( ( ~ ( in @ SV598 @ SV465 )
| ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2251,plain,
! [SV466: $i,SV242: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ ( powerset @ SV242 ) ) )
= $true )
| ( ( ! [SY1269: $i] :
( ~ ( in @ SY1269 @ SV242 )
| ~ ~ ( in @ SY1269 @ SV674 )
| ~ ( in @ SY1269 @ ( binintersect @ SV466 @ SV674 ) ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2044]) ).
thf(2252,plain,
! [SV599: $i,SV467: $o,SV243: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1310: $i] :
( ~ ( ~ SV467
| ( SY1310 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1310 != SV734 ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2045]) ).
thf(2253,plain,
! [SV600: $i,SV243: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1311: $i] :
( ~ ( ~ $true
| ( SY1311 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1311 != SV735 ) ) ) ) ) )
= $true )
| ( ( in @ SV600 @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2254,plain,
! [SV601: $i,SV243: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV243 )
| ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1312: $i] :
( ~ ( ~ $false
| ( SY1312 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1312 != SV736 ) ) ) ) ) )
= $true )
| ( ( in @ SV601 @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2047]) ).
thf(2255,plain,
! [SV244: $i,SV602: $i,SV468: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV468 )
| ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SV737 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) ) )
= $true )
| ( ( in @ SV602 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2048]) ).
thf(2256,plain,
! [SV246: $i,SV603: $i,SV470: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV470 )
| ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV738 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) ) )
= $true )
| ( ( in @ SV603 @ SV246 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2049]) ).
thf(2257,plain,
! [SV604: $i,SV739: $i,SV471: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV471 @ SV739 )
| ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1313 )
= ( ap @ SV247 @ SV471 @ SV739 @ SY1313 ) ) )
| ( SV604 = SV739 ) )
= $true )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2258,plain,
! [SV473: $i,SV249: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ ( powerset @ SV249 ) ) )
= $true )
| ( ( ! [SY1270: $i] :
( ~ ( in @ SY1270 @ SV249 )
| ~ ~ ( in @ SY1270 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SY1270 @ SV473 ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2052]) ).
thf(2259,plain,
! [SV250: $i,SV606: $i,SV474: $i > $o] :
( ( ( ~ ( SV474 @ SV606 ) )
= $true )
| ( ( in @ SV606
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) )
= $true )
| ( ( in @ SV606 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2053]) ).
thf(2260,plain,
! [SV252: $i,SV476: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV476 ) )
= $true )
| ( ( ~ ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) ) )
= $true )
| ( ( in @ SV607 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2261,plain,
! [SV480: $i,SV256: $i,SV740: $i,SV676: $i] :
( ( ( ( SV676 != SV740 )
| ( ( setadjoin @ SV256 @ SV676 )
= ( setadjoin @ SV480 @ SV740 ) ) )
= $true )
| ( ( SV256 = SV480 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2262,plain,
! [SV482: $i,SV259: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( powerset @ SV259 ) ) )
= $true )
| ( ( ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV259 )
| ~ ( in @ SY1272 @ SV482 )
| ( in @ SY1272 @ SV677 ) )
| ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2263,plain,
! [SV609: $i,SV483: $i,SV260: $i] :
( ( ( ! [SY1201: $i] :
~ ~ ( ~ ( in @ SY1201 @ SV260 )
| ~ ~ ! [SY1202: $i] :
~ ~ ( ~ ( in @ SY1202 @ SV483 )
| ( SV609
!= ( kpair @ SY1201 @ SY1202 ) ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2264,plain,
! [SV678: $i > $o,SV484: $i,SV261: $i,SV1: $i] :
( ( ( ~ ! [SY1274: $i] :
( ~ ( in @ SY1274 @ SV1 )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ SV261 )
| ~ ( in @ ( kpair @ SY1274 @ SY1275 ) @ SV484 )
| ( SV678 @ ( kpair @ SY1274 @ SY1275 ) ) ) ) )
= $true )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2265,plain,
! [SV262: $i,SV2: $i,SV679: $i,SV625: $i] :
( ( ( SV625 != SV679 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) )
| ~ ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2266,plain,
! [SV486: $i,SV265: $i,SV5: $i,SV680: $i] :
( ( ( ~ ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) ) )
= $true )
| ( ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV5 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV265 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV486 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV680 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2267,plain,
! [SV8: $i,SV266: $i] :
( ( ( in @ ( sK8_SY679 @ SV266 @ SV8 ) @ SV8 )
= $true )
| ( ( subset @ SV8 @ SV266 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2064]) ).
thf(2268,plain,
! [SV626: $i,SV9: $i] :
( ( ( ! [SY30: $i] :
~ ~ ( ~ ( in @ SY30 @ SV9 )
| ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SY30 )
| ~ ( in @ SY31 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2269,plain,
! [SV627: $o,SV10: $i,SV267: $i] :
( ( ( ! [SY1219: $i] :
( ~ ( in @ SV267 @ SY1219 )
| ~ ( in @ SY1219 @ SV10 )
| SV627 ) )
= $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2270,plain,
! [SV10: $i,SV267: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2271,plain,
! [SV10: $i,SV267: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV267 @ SX0 )
| ~ ( in @ SX0 @ SV10 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2272,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) ) )
= $true )
| ( ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2070]) ).
thf(2273,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( ~ ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) ) )
= $true )
| ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2274,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
| ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 ) )
| ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) ) )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2072]) ).
thf(2275,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2276,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SV681 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2074]) ).
thf(2277,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2075]) ).
thf(2278,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2279,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ( sK9_SY685 @ SV270 @ SV15 )
!= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2280,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
| ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2281,plain,
! [SV271: $i,SV16: $i,SV489: $i] :
( ( ( in @ SV489 @ ( setminus @ SV16 @ SV271 ) )
= $false )
| ( ( in @ SV489 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2282,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV630 )
| ~ ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2079]) ).
thf(2283,plain,
! [SV273: $i,SV21: $i,SV631: $i] :
( ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( ! [SY1223: $i] :
( ~ ( in @ SY1223 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SY1223 @ SV273 )
| ( in @ SY1223 @ SV631 ) ) )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2284,plain,
! [SV22: $i,SV274: $i,SV490: $i] :
( ( ( ~ ~ ( in @ SV490 @ SV274 ) )
= $true )
| ( ( ~ ( in @ SV490 @ SV22 ) )
= $true )
| ( ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2285,plain,
! [SV491: $i,SV276: $i,SV24: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV24 ) )
= $true )
| ( ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SV682 ) @ SV276 )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2286,plain,
! [SV29: $i,SV613: $i,SV494: $i > $i > $o,SV281: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV281 )
| ~ ( SV494 @ SV613 @ SV741 )
| ( in @ ( kpair @ SV613 @ SV741 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) )
= $true )
| ( ( in @ SV613 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2287,plain,
! [SV496: $i,SV283: $i,SV31: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV31 ) )
= $true )
| ( ( ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV283 )
| ~ ( in @ ( kpair @ SV683 @ SY1281 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SY1281 ) ) )
= $true )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2288,plain,
! [SV498: $i,SV287: $o,SV35: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV35 ) )
= $true )
| ( ( ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 ) )
= $true )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2289,plain,
! [SV499: $i,SV35: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV35 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 ) )
= $true )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2090]) ).
thf(2290,plain,
! [SV500: $i,SV35: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV35 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 ) )
= $true )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2291,plain,
! [SV36: $i,SV501: $i > $i,SV288: $i] :
( ( ( ~ ( in @ ( sK20_SY1059 @ SV288 @ SV501 @ SV36 ) @ SV36 ) )
= $false )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2292,plain,
! [SV36: $i,SV288: $i,SV501: $i > $i] :
( ( ( in @ ( SV501 @ ( sK20_SY1059 @ SV288 @ SV501 @ SV36 ) ) @ SV288 )
= $false )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2092]) ).
thf(2293,plain,
! [SV293: $i,SV41: $i,SV632: $i] :
( ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( ~ ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
| ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV41 )
| ~ ( in @ SY1224 @ SV632 )
| ( in @ SY1224 @ ( setminus @ SV41 @ SV293 ) ) ) )
= $true )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2093]) ).
thf(2294,plain,
! [SV295: $i,SV43: $i,SV633: $i] :
( ( ( in @ SV633 @ ( powerset @ SV43 ) )
= $false )
| ( ( ! [SY1225: $i] :
( ~ ( in @ SY1225 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SY1225 ) @ ( binunion @ SV633 @ SY1225 ) ) ) ) ) )
= $true )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2295,plain,
! [SV44: $i,SV503: $i > $i,SV296: $i] :
( ( ( ~ ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 ) )
= $false )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2296,plain,
! [SV44: $i,SV296: $i,SV503: $i > $i] :
( ( ( in @ ( SV503 @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) ) @ SV296 )
= $false )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2095]) ).
thf(2297,plain,
! [SV45: $i,SV297: $i,SV504: $i] :
( ( ( ~ ( in @ SV504 @ SV297 ) )
= $false )
| ( ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) )
= $true )
| ( ( in @ SV504 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2096]) ).
thf(2298,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2299,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ! [SY1226: $i] :
~ ~ ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1226 )
| ~ ! [SY1227: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1227 )
| ( SY1226 = SY1227 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2300,plain,
! [SV300: $i,SV50: $i,SV634: $i] :
( ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( ! [SY1228: $i] :
( ~ ( in @ SY1228 @ SV50 )
| ~ ~ ( in @ SY1228 @ SV300 )
| ~ ( in @ SY1228 @ ( binintersect @ SV300 @ SV634 ) ) ) )
= $true )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2301,plain,
! [SV51: $i,SV301: $i,SV506: $i] :
( ( ( ~ ~ ( in @ SV506 @ SV301 ) )
= $true )
| ( ( ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true )
| ( ( in @ SV506 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2302,plain,
! [SV635: $i,SV52: $i] :
( ( ( SV52 = emptyset )
= $false )
| ( ( in @ SV635 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2101]) ).
thf(2303,plain,
! [SV507: $i,SV302: $i,SV54: $i,SV687: $i] :
( ( ( ~ ( in @ SV687 @ SV54 ) )
= $true )
| ( ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SV687 ) @ SV302 )
= $true )
| ( ( func @ SV54 @ SV302 @ SV507 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2304,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
| ~ ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) ) ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2103]) ).
thf(2305,plain,
! [SV61: $i,SV309: $i,SV512: $i] :
( ( ( in @ SV512 @ SV309 )
= $false )
| ( ( in @ SV512 @ ( binintersect @ SV61 @ SV309 ) )
= $true )
| ( ( in @ SV512 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2306,plain,
! [SV310: $i,SV62: $i,SV636: $i] :
( ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( ! [SY1229: $i] :
( ~ ( in @ SY1229 @ ( powerset @ SV62 ) )
| ! [SY1230: $i] :
( ~ ( in @ SY1230 @ SV62 )
| ~ ( in @ SY1230 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1230 @ ( binintersect @ ( binunion @ SV310 @ SY1229 ) @ ( binunion @ SV636 @ SY1229 ) ) ) ) ) )
= $true )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2307,plain,
! [SV311: $i > $o,SV63: $i,SV688: $i] :
( ( ( ~ ( ~ ( in @ SV688 @ SV63 )
| ~ ~ ( SV311 @ SV688 ) ) )
= $false )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2308,plain,
! [SV65: $i] :
( ( ( in @ ( sK22_SY170 @ SV65 ) @ SV65 )
= $true )
| ( ( SV65 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2110]) ).
thf(2309,plain,
! [SV67: $i,SV312: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV312 ) )
= $false )
| ( ( ~ ( in @ SV513 @ SV67 ) )
= $true )
| ( ( subset @ SV67 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2310,plain,
! [SV313: $i,SV68: $i,SV637: $i] :
( ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV68 )
| ~ ( in @ SY1231 @ SV313 )
| ( in @ SY1231 @ SV637 ) )
| ( subset @ SV313 @ SV637 ) )
= $true )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2311,plain,
! [SV72: $i,SV516: $i,SV317: $i] :
( ( ( subset @ SV317 @ SV516 )
= $false )
| ( ( subset @ SV72 @ SV516 )
= $true )
| ( ( subset @ SV72 @ SV317 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2114]) ).
thf(2312,plain,
! [SV517: $i,SV318: $i,SV73: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV73 ) )
= $true )
| ( ( ( ap @ SV73 @ SV318 @ SV517 @ SV689 )
= ( ap @ SV73 @ SV318 @ SV517 @ SV689 ) )
= $true )
| ( ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2313,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2314,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2315,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
| ~ ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
| ~ ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
| ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2118]) ).
thf(2316,plain,
! [SV322: $i,SV77: $i,SV638: $i] :
( ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SV77 )
| ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SY1233 @ SV638 )
| ~ ( in @ SY1233 @ SV322 ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2119]) ).
thf(2317,plain,
! [SV324: $i,SV79: $i,SV518: $i] :
( ( ( in @ SV518 @ SV79 )
= $false )
| ( ( in @ SV324 @ ( setunion @ SV79 ) )
= $true )
| ( ( in @ SV324 @ SV518 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2318,plain,
! [SV82: $i,SV326: $i] :
( ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $false )
| ( ( ! [SY777: $i] :
( ~ ( in @ SY777 @ SV326 )
| ( in @ SY777 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2121]) ).
thf(2319,plain,
! [SV82: $i,SV326: $i] :
( ( ( ! [SY778: $i] :
( ~ ( in @ SY778 @ SV326 )
| ( in @ SY778 @ SV82 ) ) )
= $false )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2320,plain,
! [SV327: $i > $o,SV83: $i,SV690: $i] :
( ( ( ~ ( ~ ( in @ SV690 @ SV83 )
| ~ ( SV327 @ SV690 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2123]) ).
thf(2321,plain,
! [SV520: $i,SV328: $o,SV84: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV84 ) )
= $true )
| ( ( ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1282: $i] :
( ~ ( ~ SV328
| ( SY1282 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1282 != SV691 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) )
= $true )
| ( ( in @ SV520 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2322,plain,
! [SV521: $i,SV84: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ SV84 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1283: $i] :
( ~ ( ~ $true
| ( SY1283 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1283 != SV692 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) )
= $true )
| ( ( in @ SV521 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2323,plain,
! [SV522: $i,SV84: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV84 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1284: $i] :
( ~ ( ~ $false
| ( SY1284 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1284 != SV693 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2126]) ).
thf(2324,plain,
! [SV85: $i,SV523: $i,SV329: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ SV329 ) )
= $true )
| ( ( in @ ( kpair @ SV523 @ SV694 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) )
= $true )
| ( ( in @ SV523 @ SV85 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2325,plain,
! [SV524: $i,SV330: $i,SV86: $i,SV695: $i] :
( ( ( ~ ( in @ SV695 @ SV86 ) )
= $true )
| ( ( ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV330 )
| ~ ( in @ ( kpair @ SV695 @ SY1285 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SY1285 ) ) )
= $true )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2128]) ).
thf(2326,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV639 )
| ~ ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2129]) ).
thf(2327,plain,
! [SV525: $i,SV335: $i,SV90: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV90 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1286: $i] : ( in @ ( kpair @ SV696 @ SY1286 ) @ SV525 ) ) )
@ SV335 )
= $true )
| ( ( func @ SV90 @ SV335 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2328,plain,
! [SV92: $i,SV526: $i,SV337: $i > $o] :
( ( ( SV337 @ SV526 )
= $false )
| ( ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
!= emptyset )
= $true )
| ( ( in @ SV526 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2329,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( ~ ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) ) )
= $false )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2330,plain,
! [SV95: $i,SV528: $i,SV340: $i > $o] :
( ( ( ~ ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) ) )
= $false )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2132]) ).
thf(2331,plain,
! [SV341: $i,SV96: $i,SV640: $i] :
( ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( ! [SY1235: $i] :
( ~ ( in @ SY1235 @ SV96 )
| ~ ( in @ SY1235 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SY1235 @ SV341 ) ) )
= $true )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2133]) ).
thf(2332,plain,
! [SV97: $i,SV529: $i,SV342: $i,SV697: $i] :
( ( ( ~ ( in @ SV697 @ SV342 ) )
= $true )
| ( ( ( kpair @ SV529 @ SV697 )
= ( kpair @ SV529 @ SV697 ) )
= $true )
| ( ( in @ SV529 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2134]) ).
thf(2333,plain,
! [SV344: $i,SV100: $i,SV698: $i,SV641: $i] :
( ( ( SV641 != SV698 )
= $true )
| ( ( ~ ( in @ SV641 @ SV100 )
| ( in @ SV698 @ SV344 ) )
= $true )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2135]) ).
thf(2334,plain,
! [SV345: $i,SV101: $i,SV642: $i] :
( ( ( in @ SV642 @ ( powerset @ SV101 ) )
= $false )
| ( ( ~ ( subset @ ( setminus @ SV101 @ SV642 ) @ ( setminus @ SV101 @ SV345 ) )
| ( subset @ SV345 @ SV642 ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2136]) ).
thf(2335,plain,
! [SV346: $i,SV102: $i,SV643: $i] :
( ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( ! [SY1237: $i] :
( ~ ( in @ SY1237 @ ( powerset @ SV102 ) )
| ! [SY1238: $i] :
( ~ ( in @ SY1238 @ SV102 )
| ~ ( in @ SY1238 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1238 @ ( binunion @ SV346 @ SY1237 ) ) ) ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2336,plain,
! [SV530: $i,SV348: $i,SV104: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV104 ) )
= $true )
| ( ( in @ ( kpair @ SV699 @ ( ap @ SV104 @ SV348 @ SV530 @ SV699 ) ) @ SV530 )
= $true )
| ( ( func @ SV104 @ SV348 @ SV530 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2337,plain,
! [SV105: $i] :
( ( ( ~ ( ~ ( in @ ( sK23_SY262 @ SV105 ) @ SV105 )
| ~ $true ) )
= $true )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2338,plain,
! [SV109: $i,SV532: $i,SV351: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV351 ) )
= $true )
| ( ( in @ ( kpair @ SV532 @ SV700 ) @ ( cartprod @ SV109 @ SV351 ) )
= $true )
| ( ( in @ SV532 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2140]) ).
thf(2339,plain,
! [SV352: $i,SV110: $i,SV644: $i] :
( ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( ! [SY1239: $i] :
( ~ ( in @ SY1239 @ ( powerset @ SV110 ) )
| ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV110 )
| ~ ( in @ SY1240 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1240 @ ( binunion @ SV644 @ SY1239 ) ) ) ) )
= $true )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2340,plain,
! [SV353: $i,SV111: $i,SV645: $i] :
( ( ( in @ SV645 @ ( powerset @ SV111 ) )
= $false )
| ( ( ~ ( subset @ SV353 @ SV645 )
| ( subset @ ( setminus @ SV111 @ SV645 ) @ ( setminus @ SV111 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2341,plain,
! [SV354: $i,SV112: $i,SV646: $i] :
( ( ( in @ SV646 @ ( powerset @ SV112 ) )
= $false )
| ( ( ~ ( subset @ SV354 @ ( setminus @ SV112 @ SV646 ) )
| ( subset @ SV646 @ ( setminus @ SV112 @ SV354 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2342,plain,
! [SV113: $i,SV355: $i] :
( ( ( in @ ( sK13_SY818 @ SV355 @ SV113 ) @ SV113 )
= $true )
| ( ( subset @ SV113 @ SV355 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2343,plain,
! [SV114: $i,SV533: $i,SV356: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV356 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV533 @ SV701 ) )
= SV533 )
= $true )
| ( ( in @ SV533 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2344,plain,
! [SV534: $i,SV358: $o,SV116: $i,SV702: $i] :
( ( ( ~ ( in @ SV702 @ SV116 ) )
= $true )
| ( ( ~ ~ SV358
| ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) ) )
= $true )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2147]) ).
thf(2345,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV116 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) ) )
= $true )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2346,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ SV116 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) ) )
= $true )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2149]) ).
thf(2347,plain,
! [SV117: $i,SV359: $i > $o] :
( ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2348,plain,
! [SV117: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true )
| ( ( ~ ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2349,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i] :
( ( ( ~ ( func @ SV118 @ SV360 @ SV705 ) )
= $true )
| ( ( ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1290 )
= ( ap @ SV118 @ SV360 @ SV705 @ SY1290 ) ) )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2350,plain,
! [SV362: $i,SV120: $i,SV647: $i] :
( ( ( in @ SV647 @ SV120 )
= $false )
| ( ( ~ ( in @ SV647 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
| ( in @ SV647 @ SV362 ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2351,plain,
! [SV121: $i,SV538: $i,SV363: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ SV363 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SV706 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) )
= $true )
| ( ( in @ SV538 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2352,plain,
! [SV364: $i,SV124: $i] :
( ( ( in @ ( sK15_SY834 @ SV124 @ SV364 ) @ SV364 )
= $true )
| ( ( in @ SV364 @ ( powerset @ SV124 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2155]) ).
thf(2353,plain,
! [SV540: $i,SV366: $i,SV126: $i,SV707: $i] :
( ( ( ~ ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) ) )
= $true )
| ( ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV126 )
| ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV366 )
| ~ ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV540 )
| ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV707 ) ) )
| ( subset @ SV540 @ SV707 ) )
= $true )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2354,plain,
! [SV541: $i > $i > $o,SV128: $i,SV615: $i,SV368: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ SV368 )
| ~ ( in @ ( kpair @ SV615 @ SV742 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SV742 ) )
= $true )
| ( ( in @ SV615 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2355,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( in @ SV648 @ SV129 )
= $false )
| ( ( ~ ~ ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) )
| ( in @ SV648 @ SV369 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2159]) ).
thf(2356,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2161]) ).
thf(2357,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
| ~ ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
| ~ ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
| ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2162]) ).
thf(2358,plain,
! [SV133: $i,SV373: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV373 ) )
= $false )
| ( ( SV133 != SV373 )
= $true )
| ( ( in @ SV544 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2359,plain,
! [SV376: $i,SV136: $i,SV649: $i] :
( ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( ! [SY1242: $i] :
( ~ ( in @ SY1242 @ SV136 )
| ~ ( in @ SY1242 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SY1242 @ ( setminus @ SV136 @ SV376 ) ) ) )
= $true )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2360,plain,
! [SV708: $i > $o,SV650: $i > $o,SV377: $i,SV137: $i] :
( ( ( ~ ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV137 )
| ! [SY1296: $i] :
( ~ ( in @ SY1296 @ SV377 )
| ( SY1295 != SY1296 )
| ~ ( ~ ( ~ ( SV650 @ SY1295 )
| ( SV708 @ SY1296 ) )
| ~ ( ~ ( SV708 @ SY1296 )
| ( SV650 @ SY1295 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2361,plain,
! [SV138: $i,SV545: $i,SV378: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ SV378 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV545 @ SV709 ) )
= SV709 )
= $true )
| ( ( in @ SV545 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2362,plain,
! [SV139: $i,SV379: $i,SV546: $i] :
( ( ( subset @ SV546 @ SV379 )
= $false )
| ( ( subset @ SV546 @ ( binintersect @ SV139 @ SV379 ) )
= $true )
| ( ( subset @ SV546 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2363,plain,
! [SV140: $i,SV380: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ SV380 ) )
= $false )
| ( ( ~ ( subset @ SV140 @ SV380 ) )
= $true )
| ( ( in @ SV547 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2364,plain,
! [SV381: $i,SV141: $i,SV651: $i] :
( ( ( in @ SV651 @ SV141 )
= $false )
| ( ( ~ ( in @ SV651 @ SV381 )
| ( in @ SV651 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) ) )
= $true )
| ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2365,plain,
! [SV383: $i,SV144: $i,SV652: $i] :
( ( ( in @ SV652 @ ( powerset @ SV144 ) )
= $false )
| ( ( in @ ( setminus @ SV144 @ SV383 ) @ ( powerset @ ( setminus @ SV144 @ ( binintersect @ SV383 @ SV652 ) ) ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV144 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2366,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV653 )
| ~ ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2367,plain,
! [SV384: $i,SV147: $i,SV654: $i] :
( ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( ! [SY1249: $i] :
( ~ ( in @ SY1249 @ SV147 )
| ~ ~ ( in @ SY1249 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SY1249 @ SV654 ) ) )
= $true )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2368,plain,
! [SV385: $i,SV148: $i,SV655: $i] :
( ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( ~ ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV148 )
| ~ ( in @ SY1250 @ SV385 )
| ( in @ SY1250 @ SV655 ) )
| ( in @ SV385 @ ( powerset @ SV655 ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2173]) ).
thf(2369,plain,
! [SV152: $i,SV549: $i > $i,SV389: $i] :
( ( ( ~ ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 ) )
= $false )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2370,plain,
! [SV152: $i,SV389: $i,SV549: $i > $i] :
( ( ( in @ ( SV549 @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) ) @ SV389 )
= $false )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2174]) ).
thf(2371,plain,
! [SV390: $i,SV153: $i,SV656: $i] :
( ( ( in @ SV656 @ ( powerset @ SV153 ) )
= $false )
| ( ( in @ ( setminus @ SV390 @ SV656 ) @ ( powerset @ SV153 ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2175]) ).
thf(2372,plain,
! [SV550: $i,SV391: $o,SV154: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV154 ) )
= $true )
| ( ( ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) ) )
= $true )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2373,plain,
! [SV551: $i,SV154: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ SV154 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) ) )
= $true )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2177]) ).
thf(2374,plain,
! [SV552: $i,SV154: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ SV154 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) ) )
= $true )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2375,plain,
! [SV553: $i > $i > $o,SV392: $i,SV156: $i,SV657: $i,SV618: $i] :
( ( ( in @ ( kpair @ SV618 @ SV657 )
@ ( dpsetconstr @ SV156 @ SV392
@ ^ [SY1118: $i,SY1119: $i] : ( SV553 @ SY1118 @ SY1119 ) ) )
= $false )
| ( ( in @ SV657 @ SV392 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2376,plain,
! [SV554: $i,SV393: $o,SV157: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ SV157 ) )
= $true )
| ( ( in @ ( if @ SV157 @ SV393 @ SV554 @ SV713 ) @ SV157 )
= $true )
| ( ( in @ SV554 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2180]) ).
thf(2377,plain,
! [SV555: $i,SV157: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV157 ) )
= $true )
| ( ( in @ ( if @ SV157 @ $true @ SV555 @ SV714 ) @ SV157 )
= $true )
| ( ( in @ SV555 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2181]) ).
thf(2378,plain,
! [SV556: $i,SV157: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV157 ) )
= $true )
| ( ( in @ ( if @ SV157 @ $false @ SV556 @ SV715 ) @ SV157 )
= $true )
| ( ( in @ SV556 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2379,plain,
! [SV158: $i] :
( ( ( ! [SY395: $i] :
( ~ ~ ( ~ ( in @ SY395 @ omega )
| ~ ( in @ SY395 @ SV158 ) )
| ( in @ ( setadjoin @ SY395 @ SY395 ) @ SV158 ) ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2183]) ).
thf(2380,plain,
! [SV162: $i,SV559: $i > $i,SV396: $i] :
( ( ( ~ ( in @ ( sK25_SY1125 @ SV396 @ SV559 @ SV162 ) @ SV162 ) )
= $false )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2381,plain,
! [SV162: $i,SV396: $i,SV559: $i > $i] :
( ( ( in @ ( SV559 @ ( sK25_SY1125 @ SV396 @ SV559 @ SV162 ) ) @ SV396 )
= $false )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2185]) ).
thf(2382,plain,
! [SV560: $i > $i > $o,SV398: $i,SV164: $i,SV658: $i,SV619: $i] :
( ( ( in @ ( kpair @ SV619 @ SV658 )
@ ( dpsetconstr @ SV164 @ SV398
@ ^ [SY1129: $i,SY1130: $i] : ( SV560 @ SY1129 @ SY1130 ) ) )
= $false )
| ( ( SV560 @ SV619 @ SV658 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2383,plain,
! [SV402: $i,SV168: $i,SV659: $i] :
( ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( ! [SY1255: $i] :
( ~ ( in @ SY1255 @ SV168 )
| ~ ( in @ SY1255 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SY1255 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) ) )
= $true )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2188]) ).
thf(2384,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
| ~ ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) ) ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2189]) ).
thf(2385,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK26_SY909 @ SV408 @ SV174 ) @ SV174 )
| ~ ( SV408 @ ( sK26_SY909 @ SV408 @ SV174 ) ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2386,plain,
! [SV563: $i,SV409: $i,SV175: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) ) )
= $true )
| ( ( ~ ! [SY1302: $i] :
( ~ ( in @ SY1302 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1302 )
= ( ap @ SV175 @ SV409 @ SV716 @ SY1302 ) ) )
| ( SV563 = SV716 ) )
= $true )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2387,plain,
! [SV410: $i,SV176: $i,SV660: $i] :
( ( ( in @ SV660 @ SV176 )
= $false )
| ( ( ~ ( in @ SV660 @ SV410 )
| ~ ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) ) )
= $true )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2388,plain,
! [SV180: $i,SV565: $i > $i,SV412: $i] :
( ( ( ~ ( in @ ( sK27_SY1133 @ SV412 @ SV565 @ SV180 ) @ SV180 ) )
= $false )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2389,plain,
! [SV180: $i,SV412: $i,SV565: $i > $i] :
( ( ( in @ ( SV565 @ ( sK27_SY1133 @ SV412 @ SV565 @ SV180 ) ) @ SV412 )
= $false )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2194]) ).
thf(2390,plain,
! [SV413: $i,SV181: $i,SV661: $i] :
( ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( ! [SY1256: $o,SY1257: $i] :
( ~ ( in @ SY1257 @ SV181 )
| ~ ( in @ SY1257 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SY1257 @ SV413 )
| SY1256 )
| ~ ( ~ ( in @ SY1257 @ SV661 )
| SY1256 )
| SY1256 ) )
= $true )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2391,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ SV662 )
| ~ ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2196]) ).
thf(2392,plain,
! [SV415: $i,SV184: $i,SV663: $i] :
( ( ( in @ SV663 @ ( powerset @ SV184 ) )
= $false )
| ( ( in @ ( binintersect @ SV415 @ SV663 ) @ ( powerset @ SV184 ) )
= $true )
| ( ( in @ SV415 @ ( powerset @ SV184 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2393,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV185 ) )
= $true )
| ( ( in @ SV566 @ SV416 )
= $true )
| ( ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2394,plain,
! [SV417: $i,SV187: $i,SV664: $i] :
( ( ( in @ SV664 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ ( binunion @ SV417 @ SV664 ) @ ( powerset @ SV187 ) )
= $true )
| ( ( in @ SV417 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2395,plain,
! [SV567: $i,SV418: $i,SV188: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ SV188 ) )
= $true )
| ( ( ( ap @ SV188 @ SV418 @ SV567 @ SV717 )
= ( ap @ SV188 @ SV418 @ SV567 @ SV717 ) )
= $true )
| ( ( func @ SV188 @ SV418 @ SV567 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2396,plain,
! [SV568: $i,SV420: $i,SV190: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV190 ) )
= $true )
| ( ( in @ ( kpair @ SV718 @ ( ap @ SV190 @ SV420 @ SV568 @ SV718 ) ) @ SV568 )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2397,plain,
! [SV421: $i > $o,SV191: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV191 ) )
= $true )
| ( ( SV421 @ SV719 )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2398,plain,
! [SV720: $i > $o,SV570: $i,SV423: $i,SV193: $i] :
( ( ( ~ ! [SY1303: $i] :
( ~ ( in @ SY1303 @ SV193 )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV423 )
| ~ ( in @ ( kpair @ SY1303 @ SY1304 ) @ SV570 )
| ( SV720 @ ( kpair @ SY1303 @ SY1304 ) ) ) ) )
= $true )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2399,plain,
! [SV424: $i,SV721: $o,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| SV721 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2400,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2401,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ~ ( ( SV571 != SV194 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2402,plain,
! [SV425: $i > $o,SV195: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ SV195 ) )
= $true )
| ( ( SV425 @ SV722 )
= $true )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2403,plain,
! [SV196: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2209]) ).
thf(2404,plain,
! [SV196: $i] :
( ( ! [SY1153: $i] :
( ~ ~ ( ~ ! [SY495: $i] :
( ~ ( in @ SY495 @ SY1153 )
| ( in @ SY495 @ SV196 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1153 ) )
| ~ ! [SY1156: $i] :
~ ~ ! [SY1157: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1156 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1157 @ SY1153 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1156 )
| ~ ( in @ SX5 @ SY1153 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1156 ) )
| ( in @ SY1157 @ SY1159 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2210]) ).
thf(2405,plain,
! [SV199: $i,SV572: $i,SV428: $i > $o] :
( ( ( SV428 @ SV572 )
= $false )
| ( ( ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) )
| ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) ) )
= $true )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2211]) ).
thf(2406,plain,
! [SV429: $i,SV200: $i,SV573: $i] :
( ( ( in @ SV573 @ SV200 )
= $false )
| ( ( in @ SV573 @ SV429 )
= $true )
| ( ( subset @ SV200 @ SV429 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2407,plain,
! [SV201: $i,SV430: $i] :
( ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true )
| ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) )
| ( SV201 = SV430 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2408,plain,
! [SV201: $i,SV430: $i] :
( ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) ) )
= $true )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2409,plain,
! [SV202: $i,SV431: $i,SV574: $i] :
( ( ( in @ SV574 @ SV431 )
= $false )
| ( ( in @ SV574 @ SV202 )
= $true )
| ( ( in @ SV431 @ ( powerset @ SV202 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2410,plain,
! [SV433: $i,SV204: $i,SV665: $i] :
( ( ( in @ SV665 @ ( powerset @ SV204 ) )
= $false )
| ( ( subset @ ( setminus @ SV204 @ SV433 ) @ ( setminus @ SV204 @ ( binintersect @ SV433 @ SV665 ) ) )
= $true )
| ( ( in @ SV433 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2411,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV666 )
| ~ ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2412,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ( SV209 @ SV667 )
| ~ ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2413,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ( ~ ( in @ ( sK28_SY952 @ SV435 @ SV210 ) @ SV210 )
| ~ ( in @ SV435 @ ( sK28_SY952 @ SV435 @ SV210 ) ) ) )
= $true )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2414,plain,
! [SV576: $i > $i > $o,SV436: $i,SV211: $i,SV668: $i,SV621: $i] :
( ( ( in @ ( kpair @ SV621 @ SV668 )
@ ( dpsetconstr @ SV211 @ SV436
@ ^ [SY1166: $i,SY1167: $i] : ( SV576 @ SY1166 @ SY1167 ) ) )
= $false )
| ( ( in @ SV621 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2415,plain,
! [SV577: $i,SV437: $o,SV212: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV212 ) )
= $true )
| ( ( in @ ( if @ SV212 @ SV437 @ SV577 @ SV723 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SV723 @ emptyset ) ) )
= $true )
| ( ( in @ SV577 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2416,plain,
! [SV578: $i,SV212: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ SV212 ) )
= $true )
| ( ( in @ ( if @ SV212 @ $true @ SV578 @ SV724 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SV724 @ emptyset ) ) )
= $true )
| ( ( in @ SV578 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2417,plain,
! [SV579: $i,SV212: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV212 ) )
= $true )
| ( ( in @ ( if @ SV212 @ $false @ SV579 @ SV725 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SV725 @ emptyset ) ) )
= $true )
| ( ( in @ SV579 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2418,plain,
! [SV581: $i,SV439: $i,SV214: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV214 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1306: $i] : ( in @ ( kpair @ SV726 @ SY1306 ) @ SV581 ) ) )
= $true )
| ( ( func @ SV214 @ SV439 @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2224]) ).
thf(2419,plain,
! [SV215: $i,SV582: $i > $i,SV440: $i] :
( ( ( ~ ( in @ ( sK29_SY1174 @ SV440 @ SV582 @ SV215 ) @ SV215 ) )
= $false )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2420,plain,
! [SV215: $i,SV440: $i,SV582: $i > $i] :
( ( ( in @ ( SV582 @ ( sK29_SY1174 @ SV440 @ SV582 @ SV215 ) ) @ SV440 )
= $false )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2225]) ).
thf(2421,plain,
! [SV216: $i,SV583: $i,SV441: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV441 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SV727 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) )
= $true )
| ( ( in @ SV583 @ SV216 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2422,plain,
! [SV219: $i,SV444: $i] :
( ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false )
| ( ( ~ ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2423,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2424,plain,
! [SV220: $i,SV445: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV220 )
| ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV445 ) ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2229]) ).
thf(2425,plain,
! [SV447: $i,SV222: $i,SV669: $i] :
( ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( ! [SY1263: $i] :
( ~ ( in @ SY1263 @ SV222 )
| ~ ( in @ SY1263 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SY1263 @ ( binintersect @ SV447 @ SV669 ) ) ) )
= $true )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2426,plain,
! [SV223: $i,SV448: $i,SV622: $i,SV585: $i] :
( ( ( SV585 != SV622 )
= $true )
| ( ( SV448 = SV622 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SV622 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2427,plain,
! [SV449: $i,SV224: $i,SV670: $i] :
( ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( ! [SY1264: $i] :
( ~ ( in @ SY1264 @ SV224 )
| ~ ~ ( in @ SY1264 @ SV449 )
| ~ ~ ( in @ SY1264 @ SV670 )
| ~ ( in @ SY1264 @ ( binunion @ SV449 @ SV670 ) ) ) )
= $true )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2428,plain,
( ( ~ ( in @ sK4_SY5 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2429,plain,
! [SV586: $i,SV451: $o,SV226: $i,SV728: $i] :
( ( ( ~ ( in @ SV728 @ SV226 ) )
= $true )
| ( ( ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SV728 )
= SV586 ) )
= $true )
| ( ( in @ SV586 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2430,plain,
! [SV587: $i,SV226: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV226 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SV729 )
= SV587 ) )
= $true )
| ( ( in @ SV587 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2236]) ).
thf(2431,plain,
! [SV588: $i,SV226: $i,SV730: $i] :
( ( ( ~ ( in @ SV730 @ SV226 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SV730 )
= SV588 ) )
= $true )
| ( ( in @ SV588 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2432,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV671 )
| ~ ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2238]) ).
thf(2433,plain,
! [SV452: $i,SV228: $i,SV672: $i] :
( ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( ! [SY1266: $i] :
( ~ ( in @ SY1266 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SY1266 @ SV672 )
| ~ ( in @ SY1266 @ SV452 ) ) )
= $true )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2434,plain,
! [SV589: $i,SV453: $o,SV229: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV229 ) )
= $true )
| ( ( ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1307: $i] :
( ~ ( ~ SV453
| ( SY1307 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1307 != SV731 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2240]) ).
thf(2435,plain,
! [SV590: $i,SV229: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ SV229 ) )
= $true )
| ( ( ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1308: $i] :
( ~ ( ~ $true
| ( SY1308 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1308 != SV732 ) ) ) ) ) )
= $true )
| ( ( in @ SV590 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2436,plain,
! [SV591: $i,SV229: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV229 ) )
= $true )
| ( ( ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1309: $i] :
( ~ ( ~ $false
| ( SY1309 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1309 != SV733 ) ) ) ) ) )
= $true )
| ( ( in @ SV591 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2437,plain,
! [SV459: $i,SV623: $o,SV235: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| SV623 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2243]) ).
thf(2438,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2439,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV235 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2440,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ( sK18_SY995 @ SV461 @ SV237 )
!= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2441,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
| ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2442,plain,
! [SV463: $i > $o,SV239: $i,SV673: $i] :
( ( ( in @ SV673 @ SV239 )
= $false )
| ( ( ! [SY1268: $i] :
( ~ ( in @ SY1268 @ SV239 )
| ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SY1268 )
| ( SV673 = SY1268 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2443,plain,
! [SV240: $i,SV464: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ SV464 ) )
= $false )
| ( ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) )
= $true )
| ( ( in @ SV597 @ SV240 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2444,plain,
! [SV241: $i,SV465: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV465 ) )
= $true )
| ( ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) )
= $true )
| ( ( in @ SV598 @ SV241 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2250]) ).
thf(2445,plain,
! [SV466: $i,SV242: $i,SV674: $i] :
( ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( ! [SY1269: $i] :
( ~ ( in @ SY1269 @ SV242 )
| ~ ~ ( in @ SY1269 @ SV674 )
| ~ ( in @ SY1269 @ ( binintersect @ SV466 @ SV674 ) ) ) )
= $true )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2251]) ).
thf(2446,plain,
! [SV599: $i,SV467: $o,SV243: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ SV243 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1310: $i] :
( ~ ( ~ SV467
| ( SY1310 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1310 != SV734 ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2447,plain,
! [SV600: $i,SV243: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV243 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1311: $i] :
( ~ ( ~ $true
| ( SY1311 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1311 != SV735 ) ) ) ) )
= $true )
| ( ( in @ SV600 @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2448,plain,
! [SV601: $i,SV243: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV243 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1312: $i] :
( ~ ( ~ $false
| ( SY1312 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1312 != SV736 ) ) ) ) )
= $true )
| ( ( in @ SV601 @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2449,plain,
! [SV244: $i,SV602: $i,SV468: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ SV468 ) )
= $true )
| ( ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SV737 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) )
= $true )
| ( ( in @ SV602 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2450,plain,
! [SV246: $i,SV603: $i,SV470: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV470 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV738 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) )
= $true )
| ( ( in @ SV603 @ SV246 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2451,plain,
! [SV604: $i,SV739: $i,SV471: $i,SV247: $i] :
( ( ( ~ ( func @ SV247 @ SV471 @ SV739 ) )
= $true )
| ( ( ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1313 )
= ( ap @ SV247 @ SV471 @ SV739 @ SY1313 ) ) )
| ( SV604 = SV739 ) )
= $true )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2452,plain,
! [SV473: $i,SV249: $i,SV675: $i] :
( ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( ! [SY1270: $i] :
( ~ ( in @ SY1270 @ SV249 )
| ~ ~ ( in @ SY1270 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SY1270 @ SV473 ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2453,plain,
! [SV250: $i,SV606: $i,SV474: $i > $o] :
( ( ( SV474 @ SV606 )
= $false )
| ( ( in @ SV606
@ ( dsetconstr @ SV250
@ ^ [SY1024: $i] : ( SV474 @ SY1024 ) ) )
= $true )
| ( ( in @ SV606 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2454,plain,
! [SV252: $i,SV476: $i,SV607: $i] :
( ( ( in @ SV607 @ SV476 )
= $false )
| ( ( ~ ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) ) )
= $true )
| ( ( in @ SV607 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2455,plain,
! [SV480: $i,SV256: $i,SV740: $i,SV676: $i] :
( ( ( SV676 != SV740 )
= $true )
| ( ( ( setadjoin @ SV256 @ SV676 )
= ( setadjoin @ SV480 @ SV740 ) )
= $true )
| ( ( SV256 = SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2456,plain,
! [SV482: $i,SV259: $i,SV677: $i] :
( ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV259 )
| ~ ( in @ SY1272 @ SV482 )
| ( in @ SY1272 @ SV677 ) )
| ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2262]) ).
thf(2457,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SV260 )
| ~ ~ ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2263]) ).
thf(2458,plain,
! [SV678: $i > $o,SV484: $i,SV261: $i,SV1: $i] :
( ( ( ! [SY1274: $i] :
( ~ ( in @ SY1274 @ SV1 )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ SV261 )
| ~ ( in @ ( kpair @ SY1274 @ SY1275 ) @ SV484 )
| ( SV678 @ ( kpair @ SY1274 @ SY1275 ) ) ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2264]) ).
thf(2459,plain,
! [SV262: $i,SV2: $i,SV679: $i,SV625: $i] :
( ( ( SV625 = SV679 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) )
| ~ ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2460,plain,
! [SV486: $i,SV265: $i,SV5: $i,SV680: $i] :
( ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV5 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV265 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV486 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV680 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2461,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY30 @ SV626 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2268]) ).
thf(2462,plain,
! [SV10: $i,SV627: $o,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) )
| ~ ( in @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) @ SV10 )
| SV627 )
= $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2269]) ).
thf(2463,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK40_SX0 @ SV10 @ SV267 ) )
| ~ ( in @ ( sK40_SX0 @ SV10 @ SV267 ) @ SV10 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2270]) ).
thf(2464,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK41_SX0 @ SV10 @ SV267 ) )
| ~ ( in @ ( sK41_SX0 @ SV10 @ SV267 ) @ SV10 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2271]) ).
thf(2465,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $false )
| ( ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2466,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( ( SV487 = SV11 )
| ( in @ SV487 @ SV268 ) )
= $false )
| ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2467,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
| ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 ) )
| ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2468,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY42: $i,SY43: $i] :
( ~ ( SV13 @ SY42 )
| ~ ( SV13 @ SY43 )
| ( SY42 = SY43 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2469,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2276]) ).
thf(2470,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2471,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 )
| ~ ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2472,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2279]) ).
thf(2473,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
| ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2474,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV630 ) )
= $true )
| ( ( ~ ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2475,plain,
! [SV631: $i,SV273: $i,SV21: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV21 )
| ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SV743 @ SV273 )
| ( in @ SV743 @ SV631 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2476,plain,
! [SV22: $i,SV274: $i,SV490: $i] :
( ( ( ~ ( in @ SV490 @ SV274 ) )
= $false )
| ( ( ~ ( in @ SV490 @ SV22 ) )
= $true )
| ( ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2477,plain,
! [SV491: $i,SV276: $i,SV24: $i,SV682: $i] :
( ( ( in @ SV682 @ SV24 )
= $false )
| ( ( in @ ( ap @ SV24 @ SV276 @ SV491 @ SV682 ) @ SV276 )
= $true )
| ( ( in @ SV491 @ ( funcSet @ SV24 @ SV276 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2478,plain,
! [SV29: $i,SV613: $i,SV494: $i > $i > $o,SV281: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV281 ) )
= $true )
| ( ( ~ ( SV494 @ SV613 @ SV741 )
| ( in @ ( kpair @ SV613 @ SV741 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) )
= $true )
| ( ( in @ SV613 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2479,plain,
! [SV496: $i,SV283: $i,SV31: $i,SV683: $i] :
( ( ( in @ SV683 @ SV31 )
= $false )
| ( ( ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV283 )
| ~ ( in @ ( kpair @ SV683 @ SY1281 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SY1281 ) ) )
= $true )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2480,plain,
! [SV498: $i,SV287: $o,SV35: $i,SV684: $i] :
( ( ( in @ SV684 @ SV35 )
= $false )
| ( ( ~ ~ SV287
| ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 ) )
= $true )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2481,plain,
! [SV499: $i,SV35: $i,SV685: $i] :
( ( ( in @ SV685 @ SV35 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 ) )
= $true )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2482,plain,
! [SV500: $i,SV35: $i,SV686: $i] :
( ( ( in @ SV686 @ SV35 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 ) )
= $true )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2290]) ).
thf(2483,plain,
! [SV36: $i,SV501: $i > $i,SV288: $i] :
( ( ( in @ ( sK20_SY1059 @ SV288 @ SV501 @ SV36 ) @ SV36 )
= $true )
| ( ( func @ SV36 @ SV288
@ ( lam @ SV36 @ SV288
@ ^ [SY1060: $i] : ( SV501 @ SY1060 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2484,plain,
! [SV632: $i,SV41: $i,SV293: $i] :
( ( ( ~ ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) ) )
= $true )
| ( ( ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV41 )
| ~ ( in @ SY1224 @ SV632 )
| ( in @ SY1224 @ ( setminus @ SV41 @ SV293 ) ) ) )
= $true )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2293]) ).
thf(2485,plain,
! [SV633: $i,SV295: $i,SV43: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ ( powerset @ SV43 ) )
| ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SV744 ) @ ( binunion @ SV633 @ SV744 ) ) ) ) )
= $true )
| ( ( in @ SV633 @ ( powerset @ SV43 ) )
= $false )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2486,plain,
! [SV44: $i,SV503: $i > $i,SV296: $i] :
( ( ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 )
= $true )
| ( ( ! [SY1062: $i] :
( ~ ( in @ SY1062 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SY1062 )
= ( SV503 @ SY1062 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2487,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV745 )
= ( SV503 @ SV745 ) ) )
= $true )
| ( ( in @ ( SV503 @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) ) @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2296]) ).
thf(2488,plain,
! [SV45: $i,SV297: $i,SV504: $i] :
( ( ( in @ SV504 @ SV297 )
= $true )
| ( ( in @ SV504 @ ( symdiff @ SV45 @ SV297 ) )
= $true )
| ( ( in @ SV504 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2489,plain,
! [SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2490,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
| ~ ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2491,plain,
! [SV634: $i,SV300: $i,SV50: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ SV50 )
| ~ ~ ( in @ SV747 @ SV300 )
| ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2492,plain,
! [SV51: $i,SV301: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV301 ) )
= $false )
| ( ( ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true )
| ( ( in @ SV506 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2301]) ).
thf(2493,plain,
! [SV507: $i,SV302: $i,SV54: $i,SV687: $i] :
( ( ( in @ SV687 @ SV54 )
= $false )
| ( ( in @ ( ap @ SV54 @ SV302 @ SV507 @ SV687 ) @ SV302 )
= $true )
| ( ( func @ SV54 @ SV302 @ SV507 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2494,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
| ~ ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) ) ) )
= $true )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2495,plain,
! [SV636: $i,SV310: $i,SV62: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV62 ) )
| ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV62 )
| ~ ( in @ SY1322 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1322 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2306]) ).
thf(2496,plain,
! [SV311: $i > $o,SV63: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV63 )
| ~ ~ ( SV311 @ SV688 ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2497,plain,
! [SV67: $i,SV312: $i,SV513: $i] :
( ( ( in @ SV513 @ SV312 )
= $true )
| ( ( ~ ( in @ SV513 @ SV67 ) )
= $true )
| ( ( subset @ SV67 @ SV312 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2498,plain,
! [SV637: $i,SV313: $i,SV68: $i] :
( ( ( ~ ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV68 )
| ~ ( in @ SY1231 @ SV313 )
| ( in @ SY1231 @ SV637 ) ) )
= $true )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2499,plain,
! [SV517: $i,SV318: $i,SV73: $i,SV689: $i] :
( ( ( in @ SV689 @ SV73 )
= $false )
| ( ( ( ap @ SV73 @ SV318 @ SV517 @ SV689 )
= ( ap @ SV73 @ SV318 @ SV517 @ SV689 ) )
= $true )
| ( ( in @ SV517 @ ( funcSet @ SV73 @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2500,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2501,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2502,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2503,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
| ~ ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
| ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2504,plain,
! [SV638: $i,SV322: $i,SV77: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV77 )
| ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SV749 @ SV638 )
| ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2505,plain,
! [SV82: $i,SV326: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ SV326 )
| ( in @ SV750 @ SV82 ) )
= $true )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2318]) ).
thf(2506,plain,
! [SV326: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK42_SY778 @ SV82 @ SV326 ) @ SV326 )
| ( in @ ( sK42_SY778 @ SV82 @ SV326 ) @ SV82 ) )
= $false )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2319]) ).
thf(2507,plain,
! [SV327: $i > $o,SV83: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV83 )
| ~ ( SV327 @ SV690 ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2320]) ).
thf(2508,plain,
! [SV520: $i,SV328: $o,SV84: $i,SV691: $i] :
( ( ( in @ SV691 @ SV84 )
= $false )
| ( ( ~ SV328
| ( ( dsetconstr @ SV84
@ ^ [SY1282: $i] :
( ~ ( ~ SV328
| ( SY1282 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1282 != SV691 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) ) )
= $true )
| ( ( in @ SV520 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2509,plain,
! [SV521: $i,SV84: $i,SV692: $i] :
( ( ( in @ SV692 @ SV84 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV84
@ ^ [SY1283: $i] :
( ~ ( ~ $true
| ( SY1283 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1283 != SV692 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) ) )
= $true )
| ( ( in @ SV521 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2322]) ).
thf(2510,plain,
! [SV522: $i,SV84: $i,SV693: $i] :
( ( ( in @ SV693 @ SV84 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV84
@ ^ [SY1284: $i] :
( ~ ( ~ $false
| ( SY1284 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1284 != SV693 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) ) )
= $true )
| ( ( in @ SV522 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2511,plain,
! [SV85: $i,SV523: $i,SV329: $i,SV694: $i] :
( ( ( in @ SV694 @ SV329 )
= $false )
| ( ( in @ ( kpair @ SV523 @ SV694 ) @ ( powerset @ ( powerset @ ( binunion @ SV85 @ SV329 ) ) ) )
= $true )
| ( ( in @ SV523 @ SV85 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2512,plain,
! [SV524: $i,SV330: $i,SV86: $i,SV695: $i] :
( ( ( in @ SV695 @ SV86 )
= $false )
| ( ( ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV330 )
| ~ ( in @ ( kpair @ SV695 @ SY1285 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SY1285 ) ) )
= $true )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2513,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV639 ) )
= $true )
| ( ( ~ ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2514,plain,
! [SV525: $i,SV335: $i,SV90: $i,SV696: $i] :
( ( ( in @ SV696 @ SV90 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV335
@ ^ [SY1286: $i] : ( in @ ( kpair @ SV696 @ SY1286 ) @ SV525 ) ) )
@ SV335 )
= $true )
| ( ( func @ SV90 @ SV335 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2515,plain,
! [SV526: $i,SV337: $i > $o,SV92: $i] :
( ( ( ( dsetconstr @ SV92
@ ^ [SY793: $i] : ( SV337 @ SY793 ) )
= emptyset )
= $false )
| ( ( SV337 @ SV526 )
= $false )
| ( ( in @ SV526 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2516,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
| ( SV340 @ SV528 ) )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2517,plain,
! [SV95: $i,SV528: $i,SV340: $i > $o] :
( ( ( ~ ( SV340 @ SV528 )
| ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) ) )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2518,plain,
! [SV640: $i,SV341: $i,SV96: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ SV96 )
| ~ ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SV751 @ SV341 ) )
= $true )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2331]) ).
thf(2519,plain,
! [SV97: $i,SV529: $i,SV342: $i,SV697: $i] :
( ( ( in @ SV697 @ SV342 )
= $false )
| ( ( ( kpair @ SV529 @ SV697 )
= ( kpair @ SV529 @ SV697 ) )
= $true )
| ( ( in @ SV529 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2520,plain,
! [SV344: $i,SV100: $i,SV698: $i,SV641: $i] :
( ( ( SV641 = SV698 )
= $false )
| ( ( ~ ( in @ SV641 @ SV100 )
| ( in @ SV698 @ SV344 ) )
= $true )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2333]) ).
thf(2521,plain,
! [SV345: $i,SV642: $i,SV101: $i] :
( ( ( ~ ( subset @ ( setminus @ SV101 @ SV642 ) @ ( setminus @ SV101 @ SV345 ) ) )
= $true )
| ( ( subset @ SV345 @ SV642 )
= $true )
| ( ( in @ SV642 @ ( powerset @ SV101 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2522,plain,
! [SV643: $i,SV346: $i,SV102: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV102 ) )
| ! [SY1323: $i] :
( ~ ( in @ SY1323 @ SV102 )
| ~ ( in @ SY1323 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1323 @ ( binunion @ SV346 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2523,plain,
! [SV530: $i,SV348: $i,SV104: $i,SV699: $i] :
( ( ( in @ SV699 @ SV104 )
= $false )
| ( ( in @ ( kpair @ SV699 @ ( ap @ SV104 @ SV348 @ SV530 @ SV699 ) ) @ SV530 )
= $true )
| ( ( func @ SV104 @ SV348 @ SV530 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2524,plain,
! [SV105: $i] :
( ( ( ~ ( in @ ( sK23_SY262 @ SV105 ) @ SV105 )
| ~ $true )
= $false )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2525,plain,
! [SV109: $i,SV532: $i,SV351: $i,SV700: $i] :
( ( ( in @ SV700 @ SV351 )
= $false )
| ( ( in @ ( kpair @ SV532 @ SV700 ) @ ( cartprod @ SV109 @ SV351 ) )
= $true )
| ( ( in @ SV532 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2338]) ).
thf(2526,plain,
! [SV644: $i,SV352: $i,SV110: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ ( powerset @ SV110 ) )
| ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV110 )
| ~ ( in @ SY1324 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1324 @ ( binunion @ SV644 @ SV753 ) ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2339]) ).
thf(2527,plain,
! [SV111: $i,SV645: $i,SV353: $i] :
( ( ( ~ ( subset @ SV353 @ SV645 ) )
= $true )
| ( ( subset @ ( setminus @ SV111 @ SV645 ) @ ( setminus @ SV111 @ SV353 ) )
= $true )
| ( ( in @ SV645 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2528,plain,
! [SV646: $i,SV112: $i,SV354: $i] :
( ( ( ~ ( subset @ SV354 @ ( setminus @ SV112 @ SV646 ) ) )
= $true )
| ( ( subset @ SV646 @ ( setminus @ SV112 @ SV354 ) )
= $true )
| ( ( in @ SV646 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2341]) ).
thf(2529,plain,
! [SV114: $i,SV533: $i,SV356: $i,SV701: $i] :
( ( ( in @ SV701 @ SV356 )
= $false )
| ( ( ( kfst @ ( kpair @ SV533 @ SV701 ) )
= SV533 )
= $true )
| ( ( in @ SV533 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2343]) ).
thf(2530,plain,
! [SV534: $i,SV358: $o,SV116: $i,SV702: $i] :
( ( ( in @ SV702 @ SV116 )
= $false )
| ( ( ~ ~ SV358
| ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) ) )
= $true )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2531,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( ( in @ SV703 @ SV116 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) ) )
= $true )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2345]) ).
thf(2532,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( ( in @ SV704 @ SV116 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) ) )
= $true )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2533,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $false )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2534,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ~ ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $false )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2535,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i] :
( ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1290 )
= ( ap @ SV118 @ SV360 @ SV705 @ SY1290 ) ) )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2349]) ).
thf(2536,plain,
! [SV362: $i,SV120: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) ) )
= $true )
| ( ( in @ SV647 @ SV362 )
= $true )
| ( ( in @ SV647 @ SV120 )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2537,plain,
! [SV121: $i,SV538: $i,SV363: $i,SV706: $i] :
( ( ( in @ SV706 @ SV363 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV538 @ ( setadjoin @ SV706 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV121 @ SV363 ) ) ) )
= $true )
| ( ( in @ SV538 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2538,plain,
! [SV540: $i,SV366: $i,SV126: $i,SV707: $i] :
( ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV126 )
| ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV366 )
| ~ ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV540 )
| ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV707 ) ) )
| ( subset @ SV540 @ SV707 ) )
= $true )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2353]) ).
thf(2539,plain,
! [SV541: $i > $i > $o,SV128: $i,SV615: $i,SV368: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ SV368 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV615 @ SV742 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SV742 ) )
= $true )
| ( ( in @ SV615 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2540,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( ~ ~ ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) ) )
= $true )
| ( ( in @ SV648 @ SV369 )
= $true )
| ( ( in @ SV648 @ SV129 )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2541,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2542,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2543,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
| ~ ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
| ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2544,plain,
! [SV133: $i,SV373: $i,SV544: $i] :
( ( ( in @ SV544 @ SV373 )
= $true )
| ( ( SV133 != SV373 )
= $true )
| ( ( in @ SV544 @ SV133 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2358]) ).
thf(2545,plain,
! [SV649: $i,SV376: $i,SV136: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV136 )
| ~ ( in @ SV754 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SV754 @ ( setminus @ SV136 @ SV376 ) ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2359]) ).
thf(2546,plain,
! [SV708: $i > $o,SV650: $i > $o,SV377: $i,SV137: $i] :
( ( ( ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV137 )
| ! [SY1296: $i] :
( ~ ( in @ SY1296 @ SV377 )
| ( SY1295 != SY1296 )
| ~ ( ~ ( ~ ( SV650 @ SY1295 )
| ( SV708 @ SY1296 ) )
| ~ ( ~ ( SV708 @ SY1296 )
| ( SV650 @ SY1295 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2360]) ).
thf(2547,plain,
! [SV138: $i,SV545: $i,SV378: $i,SV709: $i] :
( ( ( in @ SV709 @ SV378 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV545 @ SV709 ) )
= SV709 )
= $true )
| ( ( in @ SV545 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2548,plain,
! [SV140: $i,SV380: $i,SV547: $i] :
( ( ( in @ SV547 @ SV380 )
= $true )
| ( ( ~ ( subset @ SV140 @ SV380 ) )
= $true )
| ( ( in @ SV547 @ SV140 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2363]) ).
thf(2549,plain,
! [SV141: $i,SV381: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ SV381 ) )
= $true )
| ( ( in @ SV651 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) )
= $true )
| ( ( in @ SV651 @ SV141 )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2550,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV653 ) )
= $true )
| ( ( ~ ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2551,plain,
! [SV654: $i,SV384: $i,SV147: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV147 )
| ~ ~ ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2552,plain,
! [SV655: $i,SV385: $i,SV148: $i] :
( ( ( ~ ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV148 )
| ~ ( in @ SY1250 @ SV385 )
| ( in @ SY1250 @ SV655 ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2553,plain,
! [SV152: $i,SV549: $i > $i,SV389: $i] :
( ( ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 )
= $true )
| ( ( ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SY1108 )
= ( SV549 @ SY1108 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2554,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV756 )
= ( SV549 @ SV756 ) ) )
= $true )
| ( ( in @ ( SV549 @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) ) @ SV389 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2370]) ).
thf(2555,plain,
! [SV550: $i,SV391: $o,SV154: $i,SV710: $i] :
( ( ( in @ SV710 @ SV154 )
= $false )
| ( ( ~ ~ SV391
| ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) ) )
= $true )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2556,plain,
! [SV551: $i,SV154: $i,SV711: $i] :
( ( ( in @ SV711 @ SV154 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) ) )
= $true )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2557,plain,
! [SV552: $i,SV154: $i,SV712: $i] :
( ( ( in @ SV712 @ SV154 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) ) )
= $true )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2558,plain,
! [SV554: $i,SV393: $o,SV157: $i,SV713: $i] :
( ( ( in @ SV713 @ SV157 )
= $false )
| ( ( in @ ( if @ SV157 @ SV393 @ SV554 @ SV713 ) @ SV157 )
= $true )
| ( ( in @ SV554 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2559,plain,
! [SV555: $i,SV157: $i,SV714: $i] :
( ( ( in @ SV714 @ SV157 )
= $false )
| ( ( in @ ( if @ SV157 @ $true @ SV555 @ SV714 ) @ SV157 )
= $true )
| ( ( in @ SV555 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2560,plain,
! [SV556: $i,SV157: $i,SV715: $i] :
( ( ( in @ SV715 @ SV157 )
= $false )
| ( ( in @ ( if @ SV157 @ $false @ SV556 @ SV715 ) @ SV157 )
= $true )
| ( ( in @ SV556 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2561,plain,
! [SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ omega )
| ~ ( in @ ( sK43_SY395 @ SV158 ) @ SV158 ) )
| ( in @ ( setadjoin @ ( sK43_SY395 @ SV158 ) @ ( sK43_SY395 @ SV158 ) ) @ SV158 ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2379]) ).
thf(2562,plain,
! [SV162: $i,SV559: $i > $i,SV396: $i] :
( ( ( in @ ( sK25_SY1125 @ SV396 @ SV559 @ SV162 ) @ SV162 )
= $true )
| ( ( in
@ ( lam @ SV162 @ SV396
@ ^ [SY1126: $i] : ( SV559 @ SY1126 ) )
@ ( funcSet @ SV162 @ SV396 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2380]) ).
thf(2563,plain,
! [SV659: $i,SV402: $i,SV168: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV168 )
| ~ ( in @ SV757 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SV757 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2383]) ).
thf(2564,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
| ~ ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) ) ) )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2384]) ).
thf(2565,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY909 @ SV408 @ SV174 ) @ SV174 )
| ~ ( SV408 @ ( sK26_SY909 @ SV408 @ SV174 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2566,plain,
! [SV563: $i,SV409: $i,SV175: $i,SV716: $i] :
( ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( ~ ! [SY1302: $i] :
( ~ ( in @ SY1302 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1302 )
= ( ap @ SV175 @ SV409 @ SV716 @ SY1302 ) ) )
| ( SV563 = SV716 ) )
= $true )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2386]) ).
thf(2567,plain,
! [SV176: $i,SV410: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ SV410 ) )
= $true )
| ( ( ~ ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) ) )
= $true )
| ( ( in @ SV660 @ SV176 )
= $false )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2568,plain,
! [SV180: $i,SV565: $i > $i,SV412: $i] :
( ( ( in @ ( sK27_SY1133 @ SV412 @ SV565 @ SV180 ) @ SV180 )
= $true )
| ( ( ( lam @ SV180 @ SV412
@ ^ [SY1134: $i] : ( SV565 @ SY1134 ) )
= ( lam @ SV180 @ SV412
@ ^ [SY1135: $i] : ( SV565 @ SY1135 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2388]) ).
thf(2569,plain,
! [SV758: $o,SV661: $i,SV413: $i,SV181: $i] :
( ( ( ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV181 )
| ~ ( in @ SY1326 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SY1326 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SY1326 @ SV661 )
| SV758 )
| SV758 ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2390]) ).
thf(2570,plain,
! [SV661: $i,SV413: $i,SV181: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV181 )
| ~ ( in @ SX0 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SX0 @ SV413 )
| $true )
| ~ ( ~ ( in @ SX0 @ SV661 )
| $true )
| $true ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2390]) ).
thf(2571,plain,
! [SV661: $i,SV413: $i,SV181: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV181 )
| ~ ( in @ SX0 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SX0 @ SV413 )
| $false )
| ~ ( ~ ( in @ SX0 @ SV661 )
| $false )
| $false ) )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2390]) ).
thf(2572,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ SV662 ) )
= $true )
| ( ( ~ ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2573,plain,
! [SV416: $i,SV185: $i,SV566: $i] :
( ( ( in @ SV566 @ SV185 )
= $false )
| ( ( in @ SV566 @ SV416 )
= $true )
| ( ( in @ SV566 @ ( setminus @ SV185 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2574,plain,
! [SV567: $i,SV418: $i,SV188: $i,SV717: $i] :
( ( ( in @ SV717 @ SV188 )
= $false )
| ( ( ( ap @ SV188 @ SV418 @ SV567 @ SV717 )
= ( ap @ SV188 @ SV418 @ SV567 @ SV717 ) )
= $true )
| ( ( func @ SV188 @ SV418 @ SV567 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2575,plain,
! [SV568: $i,SV420: $i,SV190: $i,SV718: $i] :
( ( ( in @ SV718 @ SV190 )
= $false )
| ( ( in @ ( kpair @ SV718 @ ( ap @ SV190 @ SV420 @ SV568 @ SV718 ) ) @ SV568 )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV190 @ SV420 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2576,plain,
! [SV421: $i > $o,SV191: $i,SV719: $i] :
( ( ( in @ SV719 @ SV191 )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( ~ ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2577,plain,
! [SV720: $i > $o,SV570: $i,SV423: $i,SV193: $i] :
( ( ( ! [SY1303: $i] :
( ~ ( in @ SY1303 @ SV193 )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV423 )
| ~ ( in @ ( kpair @ SY1303 @ SY1304 ) @ SV570 )
| ( SV720 @ ( kpair @ SY1303 @ SY1304 ) ) ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2398]) ).
thf(2578,plain,
! [SV424: $i,SV721: $o,SV194: $i,SV571: $i] :
( ( ( ( SV571 != SV194 )
| SV721 )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2579,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ( SV571 != SV194 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2580,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( ( SV571 != SV194 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2401]) ).
thf(2581,plain,
! [SV425: $i > $o,SV195: $i,SV722: $i] :
( ( ( in @ SV722 @ SV195 )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( ~ ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2582,plain,
! [SV196: $i] :
( ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
| ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2583,plain,
! [SV196: $i,SV759: $i] :
( ( ~ ~ ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) )
| ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
| ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2584,plain,
! [SV572: $i,SV428: $i > $o,SV199: $i] :
( ( ( ~ ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2585,plain,
! [SV201: $i,SV430: $i] :
( ( ( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) ) )
= $true )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2407]) ).
thf(2586,plain,
! [SV201: $i,SV430: $i] :
( ( ( ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2408]) ).
thf(2587,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV666 ) )
= $true )
| ( ( ~ ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2588,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ( SV209 @ SV667 ) )
= $true )
| ( ( ~ ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2589,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ( in @ ( sK28_SY952 @ SV435 @ SV210 ) @ SV210 )
| ~ ( in @ SV435 @ ( sK28_SY952 @ SV435 @ SV210 ) ) )
= $false )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2590,plain,
! [SV577: $i,SV437: $o,SV212: $i,SV723: $i] :
( ( ( in @ SV723 @ SV212 )
= $false )
| ( ( in @ ( if @ SV212 @ SV437 @ SV577 @ SV723 ) @ ( setadjoin @ SV577 @ ( setadjoin @ SV723 @ emptyset ) ) )
= $true )
| ( ( in @ SV577 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2591,plain,
! [SV578: $i,SV212: $i,SV724: $i] :
( ( ( in @ SV724 @ SV212 )
= $false )
| ( ( in @ ( if @ SV212 @ $true @ SV578 @ SV724 ) @ ( setadjoin @ SV578 @ ( setadjoin @ SV724 @ emptyset ) ) )
= $true )
| ( ( in @ SV578 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2592,plain,
! [SV579: $i,SV212: $i,SV725: $i] :
( ( ( in @ SV725 @ SV212 )
= $false )
| ( ( in @ ( if @ SV212 @ $false @ SV579 @ SV725 ) @ ( setadjoin @ SV579 @ ( setadjoin @ SV725 @ emptyset ) ) )
= $true )
| ( ( in @ SV579 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2593,plain,
! [SV581: $i,SV439: $i,SV214: $i,SV726: $i] :
( ( ( in @ SV726 @ SV214 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV439
@ ^ [SY1306: $i] : ( in @ ( kpair @ SV726 @ SY1306 ) @ SV581 ) ) )
= $true )
| ( ( func @ SV214 @ SV439 @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2594,plain,
! [SV215: $i,SV582: $i > $i,SV440: $i] :
( ( ( in @ ( sK29_SY1174 @ SV440 @ SV582 @ SV215 ) @ SV215 )
= $true )
| ( ( func @ SV215 @ SV440
@ ( dpsetconstr @ SV215 @ SV440
@ ^ [SY1175: $i,SY1176: $i] :
( ( SV582 @ SY1175 )
= SY1176 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2595,plain,
! [SV216: $i,SV583: $i,SV441: $i,SV727: $i] :
( ( ( in @ SV727 @ SV441 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV583 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV583 @ ( setadjoin @ SV727 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV216 @ SV441 ) ) )
= $true )
| ( ( in @ SV583 @ SV216 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2596,plain,
! [SV219: $i,SV444: $i] :
( ( ( ! [SY972: $i] :
~ ~ ( ~ ( in @ SV444 @ SY972 )
| ~ ( in @ SY972 @ SV219 ) ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2597,plain,
! [SV219: $i,SV444: $i] :
( ( ( ! [SY973: $i] :
~ ~ ( ~ ( in @ SV444 @ SY973 )
| ~ ( in @ SY973 @ SV219 ) ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2598,plain,
! [SV220: $i,SV445: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV220 )
| ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV445 ) ) )
= $true )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2599,plain,
! [SV669: $i,SV447: $i,SV222: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV222 )
| ~ ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) ) )
= $true )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2600,plain,
! [SV223: $i,SV448: $i,SV622: $i,SV585: $i] :
( ( ( SV585 = SV622 )
= $false )
| ( ( SV448 = SV622 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV223 @ ( setadjoin @ SV448 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV585 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV585 @ ( setadjoin @ SV622 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2426]) ).
thf(2601,plain,
! [SV670: $i,SV449: $i,SV224: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV224 )
| ~ ~ ( in @ SV761 @ SV449 )
| ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2602,plain,
( ( ~ ( in @ sK4_SY5 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2603,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2428]) ).
thf(2604,plain,
! [SV586: $i,SV451: $o,SV226: $i,SV728: $i] :
( ( ( in @ SV728 @ SV226 )
= $false )
| ( ( ~ SV451
| ( ( if @ SV226 @ SV451 @ SV586 @ SV728 )
= SV586 ) )
= $true )
| ( ( in @ SV586 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2605,plain,
! [SV587: $i,SV226: $i,SV729: $i] :
( ( ( in @ SV729 @ SV226 )
= $false )
| ( ( ~ $true
| ( ( if @ SV226 @ $true @ SV587 @ SV729 )
= SV587 ) )
= $true )
| ( ( in @ SV587 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2606,plain,
! [SV588: $i,SV226: $i,SV730: $i] :
( ( ( in @ SV730 @ SV226 )
= $false )
| ( ( ~ $false
| ( ( if @ SV226 @ $false @ SV588 @ SV730 )
= SV588 ) )
= $true )
| ( ( in @ SV588 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2607,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV671 ) )
= $true )
| ( ( ~ ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2608,plain,
! [SV672: $i,SV452: $i,SV228: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV228 )
| ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SV762 @ SV672 )
| ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2609,plain,
! [SV589: $i,SV453: $o,SV229: $i,SV731: $i] :
( ( ( in @ SV731 @ SV229 )
= $false )
| ( ( ~ SV453
| ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1307: $i] :
( ~ ( ~ SV453
| ( SY1307 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1307 != SV731 ) ) ) ) ) )
= $true )
| ( ( in @ SV589 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2610,plain,
! [SV590: $i,SV229: $i,SV732: $i] :
( ( ( in @ SV732 @ SV229 )
= $false )
| ( ( ~ $true
| ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1308: $i] :
( ~ ( ~ $true
| ( SY1308 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1308 != SV732 ) ) ) ) ) )
= $true )
| ( ( in @ SV590 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2611,plain,
! [SV591: $i,SV229: $i,SV733: $i] :
( ( ( in @ SV733 @ SV229 )
= $false )
| ( ( ~ $false
| ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1309: $i] :
( ~ ( ~ $false
| ( SY1309 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1309 != SV733 ) ) ) ) ) )
= $true )
| ( ( in @ SV591 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2436]) ).
thf(2612,plain,
! [SV459: $i,SV623: $o,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 )
| SV623 )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2613,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2614,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2615,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2440]) ).
thf(2616,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
| ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2617,plain,
! [SV673: $i,SV463: $i > $o,SV239: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV239 )
| ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SV763 )
| ( SV673 = SV763 ) )
= $true )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2442]) ).
thf(2618,plain,
! [SV240: $i,SV464: $i,SV597: $i] :
( ( ( in @ SV597 @ SV464 )
= $true )
| ( ( in @ SV597 @ ( setminus @ SV240 @ SV464 ) )
= $true )
| ( ( in @ SV597 @ SV240 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2443]) ).
thf(2619,plain,
! [SV241: $i,SV465: $i,SV598: $i] :
( ( ( in @ SV598 @ SV465 )
= $false )
| ( ( in @ SV598 @ ( symdiff @ SV241 @ SV465 ) )
= $true )
| ( ( in @ SV598 @ SV241 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2444]) ).
thf(2620,plain,
! [SV466: $i,SV674: $i,SV242: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV242 )
| ~ ~ ( in @ SV764 @ SV674 )
| ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2445]) ).
thf(2621,plain,
! [SV599: $i,SV467: $o,SV243: $i,SV734: $i] :
( ( ( in @ SV734 @ SV243 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1310: $i] :
( ~ ( ~ SV467
| ( SY1310 != SV599 ) )
| ~ ( ~ ~ SV467
| ( SY1310 != SV734 ) ) ) ) )
= $true )
| ( ( in @ SV599 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2622,plain,
! [SV600: $i,SV243: $i,SV735: $i] :
( ( ( in @ SV735 @ SV243 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1311: $i] :
( ~ ( ~ $true
| ( SY1311 != SV600 ) )
| ~ ( ~ ~ $true
| ( SY1311 != SV735 ) ) ) ) )
= $true )
| ( ( in @ SV600 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2623,plain,
! [SV601: $i,SV243: $i,SV736: $i] :
( ( ( in @ SV736 @ SV243 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV243
@ ^ [SY1312: $i] :
( ~ ( ~ $false
| ( SY1312 != SV601 ) )
| ~ ( ~ ~ $false
| ( SY1312 != SV736 ) ) ) ) )
= $true )
| ( ( in @ SV601 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2624,plain,
! [SV244: $i,SV602: $i,SV468: $i,SV737: $i] :
( ( ( in @ SV737 @ SV468 )
= $false )
| ( ( in @ ( setadjoin @ SV602 @ ( setadjoin @ SV737 @ emptyset ) ) @ ( powerset @ ( binunion @ SV244 @ SV468 ) ) )
= $true )
| ( ( in @ SV602 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2625,plain,
! [SV246: $i,SV603: $i,SV470: $i,SV738: $i] :
( ( ( in @ SV738 @ SV470 )
= $false )
| ( ( subset @ ( setadjoin @ SV603 @ ( setadjoin @ SV738 @ emptyset ) ) @ ( binunion @ SV246 @ SV470 ) )
= $true )
| ( ( in @ SV603 @ SV246 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2626,plain,
! [SV604: $i,SV739: $i,SV471: $i,SV247: $i] :
( ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1313 )
= ( ap @ SV247 @ SV471 @ SV739 @ SY1313 ) ) )
| ( SV604 = SV739 ) )
= $true )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2627,plain,
! [SV675: $i,SV473: $i,SV249: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV249 )
| ~ ~ ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2452]) ).
thf(2628,plain,
! [SV476: $i,SV252: $i,SV607: $i] :
( ( ( in @ SV607 @ ( symdiff @ SV252 @ SV476 ) )
= $false )
| ( ( in @ SV607 @ SV476 )
= $false )
| ( ( in @ SV607 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2629,plain,
! [SV480: $i,SV256: $i,SV740: $i,SV676: $i] :
( ( ( SV676 = SV740 )
= $false )
| ( ( ( setadjoin @ SV256 @ SV676 )
= ( setadjoin @ SV480 @ SV740 ) )
= $true )
| ( ( SV256 = SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2630,plain,
! [SV677: $i,SV482: $i,SV259: $i] :
( ( ( ~ ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV259 )
| ~ ( in @ SY1272 @ SV482 )
| ( in @ SY1272 @ SV677 ) ) )
= $true )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2631,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( ~ ( ~ ( in @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SV260 )
| ~ ~ ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) ) )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2632,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( ~ ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 )
| ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV261 )
| ~ ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SY1334 ) @ SV484 )
| ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SY1334 ) ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2458]) ).
thf(2633,plain,
! [SV262: $i,SV679: $i,SV2: $i,SV625: $i] :
( ( ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) )
| ~ ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) ) )
= $false )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2634,plain,
! [SV680: $i,SV486: $i,SV265: $i,SV5: $i] :
( ( ( ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV5 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV265 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV486 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV680 ) ) ) )
= $true )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2635,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ( ~ ( in @ ( sK38_SY30 @ SV626 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2461]) ).
thf(2636,plain,
! [SV10: $i,SV627: $o,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) ) )
= $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2637,plain,
! [SV267: $i,SV10: $i,SV627: $o] :
( ( ( ~ ( in @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) @ SV10 )
| SV627 )
= $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2638,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK40_SX0 @ SV10 @ SV267 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2639,plain,
! [SV267: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK40_SX0 @ SV10 @ SV267 ) @ SV10 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2463]) ).
thf(2640,plain,
! [SV10: $i,SV267: $i] :
( ( ( ~ ( in @ SV267 @ ( sK41_SX0 @ SV10 @ SV267 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2641,plain,
! [SV267: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK41_SX0 @ SV10 @ SV267 ) @ SV10 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2464]) ).
thf(2642,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( SV487 = SV11 )
= $true )
| ( ( in @ SV487 @ SV268 )
= $true )
| ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2643,plain,
! [SV268: $i,SV11: $i,SV487: $i] :
( ( ( SV487 = SV11 )
= $false )
| ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2644,plain,
! [SV11: $i,SV268: $i,SV487: $i] :
( ( ( in @ SV487 @ SV268 )
= $false )
| ( ( in @ SV487 @ ( setadjoin @ SV11 @ SV268 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2645,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
| ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 ) ) )
= $true )
| ( ( ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2467]) ).
thf(2646,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY1335: $i] :
( ~ ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
| ~ ( SV13 @ SY1335 )
| ( ( sK45_SY42 @ SV629 @ SV13 )
= SY1335 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2468]) ).
thf(2647,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2648,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2469]) ).
thf(2649,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2650,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2470]) ).
thf(2651,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2652,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2471]) ).
thf(2653,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2654,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2655,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) )
= $true )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2656,plain,
! [SV631: $i,SV273: $i,SV21: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV21 ) )
= $true )
| ( ( ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SV743 @ SV273 )
| ( in @ SV743 @ SV631 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2657,plain,
! [SV22: $i,SV274: $i,SV490: $i] :
( ( ( in @ SV490 @ SV274 )
= $true )
| ( ( ~ ( in @ SV490 @ SV22 ) )
= $true )
| ( ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2658,plain,
! [SV29: $i,SV613: $i,SV494: $i > $i > $o,SV281: $i,SV741: $i] :
( ( ( in @ SV741 @ SV281 )
= $false )
| ( ( ~ ( SV494 @ SV613 @ SV741 )
| ( in @ ( kpair @ SV613 @ SV741 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) ) )
= $true )
| ( ( in @ SV613 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2659,plain,
! [SV31: $i,SV496: $i,SV683: $i,SV283: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV283 )
| ~ ( in @ ( kpair @ SV683 @ SV766 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SV766 ) )
= $true )
| ( ( in @ SV683 @ SV31 )
= $false )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2479]) ).
thf(2660,plain,
! [SV684: $i,SV498: $i,SV35: $i,SV287: $o] :
( ( ( ~ ~ SV287 )
= $true )
| ( ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 )
= $true )
| ( ( in @ SV684 @ SV35 )
= $false )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2661,plain,
! [SV685: $i,SV499: $i,SV35: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 )
= $true )
| ( ( in @ SV685 @ SV35 )
= $false )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2662,plain,
! [SV686: $i,SV500: $i,SV35: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 )
= $true )
| ( ( in @ SV686 @ SV35 )
= $false )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2663,plain,
! [SV632: $i,SV41: $i,SV293: $i] :
( ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( ! [SY1224: $i] :
( ~ ( in @ SY1224 @ SV41 )
| ~ ( in @ SY1224 @ SV632 )
| ( in @ SY1224 @ ( setminus @ SV41 @ SV293 ) ) ) )
= $true )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2664,plain,
! [SV633: $i,SV295: $i,SV43: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ ( powerset @ SV43 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SV744 ) @ ( binunion @ SV633 @ SV744 ) ) ) )
= $true )
| ( ( in @ SV633 @ ( powerset @ SV43 ) )
= $false )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2665,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV44 )
| ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV767 )
= ( SV503 @ SV767 ) ) )
= $true )
| ( ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2666,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV44 ) )
= $true )
| ( ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV745 )
= ( SV503 @ SV745 ) )
= $true )
| ( ( in @ ( SV503 @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) ) @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2667,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ! [SY1337: $i] :
~ ( ~ ( ~ ( in @ SY1337 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1337 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1337 ) )
| ( in @ SY1337 @ ( sK46_SY736 @ SV46 @ SV298 ) ) ) ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2489]) ).
thf(2668,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
| ~ ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) ) )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2669,plain,
! [SV634: $i,SV300: $i,SV50: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ SV50 ) )
= $true )
| ( ( ~ ~ ( in @ SV747 @ SV300 )
| ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2491]) ).
thf(2670,plain,
! [SV51: $i,SV301: $i,SV506: $i] :
( ( ( in @ SV506 @ SV301 )
= $true )
| ( ( ~ ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) ) )
= $true )
| ( ( in @ SV506 @ SV51 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2671,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
| ~ ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2672,plain,
! [SV636: $i,SV310: $i,SV62: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV62 )
| ~ ( in @ SY1322 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1322 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2495]) ).
thf(2673,plain,
! [SV311: $i > $o,SV63: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV63 ) )
= $true )
| ( ( ~ ~ ( SV311 @ SV688 ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2496]) ).
thf(2674,plain,
! [SV312: $i,SV67: $i,SV513: $i] :
( ( ( in @ SV513 @ SV67 )
= $false )
| ( ( in @ SV513 @ SV312 )
= $true )
| ( ( subset @ SV67 @ SV312 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2675,plain,
! [SV637: $i,SV313: $i,SV68: $i] :
( ( ( ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV68 )
| ~ ( in @ SY1231 @ SV313 )
| ( in @ SY1231 @ SV637 ) ) )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2676,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2677,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2500]) ).
thf(2678,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2679,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2502]) ).
thf(2680,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2681,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
| ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2503]) ).
thf(2682,plain,
! [SV638: $i,SV322: $i,SV77: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV77 ) )
= $true )
| ( ( ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SV749 @ SV638 )
| ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2683,plain,
! [SV82: $i,SV326: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ SV326 ) )
= $true )
| ( ( in @ SV750 @ SV82 )
= $true )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2505]) ).
thf(2684,plain,
! [SV326: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK42_SY778 @ SV82 @ SV326 ) @ SV326 ) )
= $false )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2685,plain,
! [SV326: $i,SV82: $i] :
( ( ( in @ ( sK42_SY778 @ SV82 @ SV326 ) @ SV82 )
= $false )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2506]) ).
thf(2686,plain,
! [SV327: $i > $o,SV83: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV83 ) )
= $true )
| ( ( ~ ( SV327 @ SV690 ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2507]) ).
thf(2687,plain,
! [SV691: $i,SV520: $i,SV84: $i,SV328: $o] :
( ( ( ~ SV328 ) = $true )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1282: $i] :
( ~ ( ~ SV328
| ( SY1282 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1282 != SV691 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) )
= $true )
| ( ( in @ SV691 @ SV84 )
= $false )
| ( ( in @ SV520 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2688,plain,
! [SV692: $i,SV521: $i,SV84: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1283: $i] :
( ~ ( ~ $true
| ( SY1283 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1283 != SV692 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $true )
| ( ( in @ SV692 @ SV84 )
= $false )
| ( ( in @ SV521 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2689,plain,
! [SV693: $i,SV522: $i,SV84: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1284: $i] :
( ~ ( ~ $false
| ( SY1284 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1284 != SV693 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) )
= $true )
| ( ( in @ SV693 @ SV84 )
= $false )
| ( ( in @ SV522 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2690,plain,
! [SV86: $i,SV524: $i,SV695: $i,SV330: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ SV330 )
| ~ ( in @ ( kpair @ SV695 @ SV768 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SV768 ) )
= $true )
| ( ( in @ SV695 @ SV86 )
= $false )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2512]) ).
thf(2691,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) )
= $true )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2692,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( ~ ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) ) )
= $true )
| ( ( SV340 @ SV528 )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2693,plain,
! [SV95: $i,SV528: $i,SV340: $i > $o] :
( ( ( ~ ( SV340 @ SV528 ) )
= $true )
| ( ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2694,plain,
! [SV640: $i,SV341: $i,SV96: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ SV96 ) )
= $true )
| ( ( ~ ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SV751 @ SV341 ) )
= $true )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2695,plain,
! [SV344: $i,SV698: $i,SV100: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV100 ) )
= $true )
| ( ( in @ SV698 @ SV344 )
= $true )
| ( ( SV641 = SV698 )
= $false )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2696,plain,
! [SV345: $i,SV642: $i,SV101: $i] :
( ( ( subset @ ( setminus @ SV101 @ SV642 ) @ ( setminus @ SV101 @ SV345 ) )
= $false )
| ( ( subset @ SV345 @ SV642 )
= $true )
| ( ( in @ SV642 @ ( powerset @ SV101 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2697,plain,
! [SV643: $i,SV346: $i,SV102: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ! [SY1323: $i] :
( ~ ( in @ SY1323 @ SV102 )
| ~ ( in @ SY1323 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1323 @ ( binunion @ SV346 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2698,plain,
! [SV105: $i] :
( ( ( ~ ( in @ ( sK23_SY262 @ SV105 ) @ SV105 ) )
= $false )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2699,plain,
! [SV105: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2700,plain,
! [SV644: $i,SV352: $i,SV110: $i,SV753: $i] :
( ( ( ~ ( in @ SV753 @ ( powerset @ SV110 ) ) )
= $true )
| ( ( ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV110 )
| ~ ( in @ SY1324 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1324 @ ( binunion @ SV644 @ SV753 ) ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2701,plain,
! [SV111: $i,SV645: $i,SV353: $i] :
( ( ( subset @ SV353 @ SV645 )
= $false )
| ( ( subset @ ( setminus @ SV111 @ SV645 ) @ ( setminus @ SV111 @ SV353 ) )
= $true )
| ( ( in @ SV645 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2702,plain,
! [SV646: $i,SV112: $i,SV354: $i] :
( ( ( subset @ SV354 @ ( setminus @ SV112 @ SV646 ) )
= $false )
| ( ( subset @ SV646 @ ( setminus @ SV112 @ SV354 ) )
= $true )
| ( ( in @ SV646 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2703,plain,
! [SV534: $i,SV116: $i,SV702: $i,SV358: $o] :
( ( ( ~ ~ SV358 )
= $true )
| ( ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) )
= $true )
| ( ( in @ SV702 @ SV116 )
= $false )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2704,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) )
= $true )
| ( ( in @ SV703 @ SV116 )
= $false )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2705,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) )
= $true )
| ( ( in @ SV704 @ SV116 )
= $false )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2706,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2533]) ).
thf(2707,plain,
! [SV359: $i > $o,SV117: $i] :
( ( ( ! [SY825: $i] :
~ ~ ( ~ ( in @ SY825 @ SV117 )
| ~ ( SV359 @ SY825 ) ) )
= $true )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2534]) ).
thf(2708,plain,
! [SV705: $i,SV537: $i,SV360: $i,SV118: $i] :
( ( ( ~ ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1290 )
= ( ap @ SV118 @ SV360 @ SV705 @ SY1290 ) ) ) )
= $true )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2535]) ).
thf(2709,plain,
! [SV362: $i,SV120: $i,SV647: $i] :
( ( ( in @ SV647 @ ( setminus @ SV120 @ ( setminus @ SV120 @ SV362 ) ) )
= $false )
| ( ( in @ SV647 @ SV362 )
= $true )
| ( ( in @ SV647 @ SV120 )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV120 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2536]) ).
thf(2710,plain,
! [SV707: $i,SV540: $i,SV366: $i,SV126: $i] :
( ( ( ~ ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV126 )
| ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV366 )
| ~ ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV540 )
| ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV707 ) ) ) )
= $true )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2711,plain,
! [SV541: $i > $i > $o,SV128: $i,SV615: $i,SV368: $i,SV742: $i] :
( ( ( in @ SV742 @ SV368 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV615 @ SV742 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
| ( SV541 @ SV615 @ SV742 ) )
= $true )
| ( ( in @ SV615 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2539]) ).
thf(2712,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) ) )
= $false )
| ( ( in @ SV648 @ SV369 )
= $true )
| ( ( in @ SV648 @ SV129 )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2713,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2714,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2715,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2716,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
| ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2543]) ).
thf(2717,plain,
! [SV544: $i,SV373: $i,SV133: $i] :
( ( ( SV133 = SV373 )
= $false )
| ( ( in @ SV544 @ SV373 )
= $true )
| ( ( in @ SV544 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2718,plain,
! [SV649: $i,SV376: $i,SV136: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV136 ) )
= $true )
| ( ( ~ ( in @ SV754 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SV754 @ ( setminus @ SV136 @ SV376 ) ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2545]) ).
thf(2719,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) @ SV137 )
| ! [SY1340: $i] :
( ~ ( in @ SY1340 @ SV377 )
| ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
!= SY1340 )
| ~ ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ SY1340 ) )
| ~ ( ~ ( SV708 @ SY1340 )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2546]) ).
thf(2720,plain,
! [SV547: $i,SV380: $i,SV140: $i] :
( ( ( subset @ SV140 @ SV380 )
= $false )
| ( ( in @ SV547 @ SV380 )
= $true )
| ( ( in @ SV547 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2721,plain,
! [SV141: $i,SV381: $i,SV651: $i] :
( ( ( in @ SV651 @ SV381 )
= $false )
| ( ( in @ SV651 @ ( setminus @ SV141 @ ( setminus @ SV141 @ SV381 ) ) )
= $true )
| ( ( in @ SV651 @ SV141 )
= $false )
| ( ( in @ SV381 @ ( powerset @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2722,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( SV146 @ SV653 )
= $false )
| ( ( ~ ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) )
= $true )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2723,plain,
! [SV654: $i,SV384: $i,SV147: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ SV147 ) )
= $true )
| ( ( ~ ~ ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2724,plain,
! [SV655: $i,SV385: $i,SV148: $i] :
( ( ( ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV148 )
| ~ ( in @ SY1250 @ SV385 )
| ( in @ SY1250 @ SV655 ) ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2725,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV152 )
| ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV769 )
= ( SV549 @ SV769 ) ) )
= $true )
| ( ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2726,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ SV152 ) )
= $true )
| ( ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV756 )
= ( SV549 @ SV756 ) )
= $true )
| ( ( in @ ( SV549 @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) ) @ SV389 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2727,plain,
! [SV710: $i,SV550: $i,SV154: $i,SV391: $o] :
( ( ( ~ ~ SV391 )
= $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) )
= $true )
| ( ( in @ SV710 @ SV154 )
= $false )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2555]) ).
thf(2728,plain,
! [SV711: $i,SV551: $i,SV154: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) )
= $true )
| ( ( in @ SV711 @ SV154 )
= $false )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2729,plain,
! [SV712: $i,SV552: $i,SV154: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) )
= $true )
| ( ( in @ SV712 @ SV154 )
= $false )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2730,plain,
! [SV158: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ omega )
| ~ ( in @ ( sK43_SY395 @ SV158 ) @ SV158 ) ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2731,plain,
! [SV158: $i] :
( ( ( in @ ( setadjoin @ ( sK43_SY395 @ SV158 ) @ ( sK43_SY395 @ SV158 ) ) @ SV158 )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2561]) ).
thf(2732,plain,
! [SV659: $i,SV402: $i,SV168: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV168 ) )
= $true )
| ( ( ~ ( in @ SV757 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SV757 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2733,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
| ~ ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2734,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( ~ ( in @ ( sK26_SY909 @ SV408 @ SV174 ) @ SV174 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2735,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( ~ ( SV408 @ ( sK26_SY909 @ SV408 @ SV174 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2736,plain,
! [SV716: $i,SV563: $i,SV409: $i,SV175: $i] :
( ( ( ~ ! [SY1302: $i] :
( ~ ( in @ SY1302 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1302 )
= ( ap @ SV175 @ SV409 @ SV716 @ SY1302 ) ) ) )
= $true )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2566]) ).
thf(2737,plain,
! [SV176: $i,SV410: $i,SV660: $i] :
( ( ( in @ SV660 @ SV410 )
= $false )
| ( ( ~ ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) ) )
= $true )
| ( ( in @ SV660 @ SV176 )
= $false )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2738,plain,
! [SV758: $o,SV661: $i,SV413: $i,SV181: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV181 )
| ~ ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2569]) ).
thf(2739,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV181 )
| ~ ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV771 @ SV413 )
| $true )
| ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2740,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV181 )
| ~ ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV772 @ SV413 )
| $false )
| ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2741,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) )
= $true )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2572]) ).
thf(2742,plain,
! [SV719: $i,SV421: $i > $o,SV191: $i] :
( ( ( ! [SY930: $i] :
~ ~ ( ~ ( in @ SY930 @ SV191 )
| ~ ~ ( SV421 @ SY930 ) ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2743,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 )
| ! [SY1342: $i] :
( ~ ( in @ SY1342 @ SV423 )
| ~ ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SY1342 ) @ SV570 )
| ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SY1342 ) ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2577]) ).
thf(2744,plain,
! [SV721: $o,SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 != SV194 )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2745,plain,
! [SV194: $i,SV424: $i,SV571: $i,SV721: $o] :
( ( SV721 = $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2578]) ).
thf(2746,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 != SV194 )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2747,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2579]) ).
thf(2748,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 != SV194 )
= $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2749,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2580]) ).
thf(2750,plain,
! [SV722: $i,SV425: $i > $o,SV195: $i] :
( ( ( ! [SY941: $i] :
~ ~ ( ~ ( in @ SY941 @ SV195 )
| ~ ~ ( SV425 @ SY941 ) ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2581]) ).
thf(2751,plain,
! [SV196: $i] :
( ( ~ ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2582]) ).
thf(2752,plain,
! [SV196: $i] :
( ( ~ ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2582]) ).
thf(2753,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ~ ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) )
| ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2754,plain,
! [SV572: $i,SV428: $i > $o,SV199: $i] :
( ( ( ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV199 )
| ~ ( SV428 @ SY1161 )
| ( SY1161 = SV572 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2755,plain,
! [SV201: $i,SV430: $i] :
( ( ( ! [SY947: $i] :
( ~ ( in @ SY947 @ SV430 )
| ( in @ SY947 @ SV201 ) ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2756,plain,
! [SV430: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK49_SY947 @ SV201 @ SV430 ) @ SV430 )
| ( in @ ( sK49_SY947 @ SV201 @ SV430 ) @ SV201 ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2586]) ).
thf(2757,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( SV205 @ SV666 )
= $false )
| ( ( ~ ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) )
= $true )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2758,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( SV209 @ SV667 )
= $false )
| ( ( ~ ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) )
= $true )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2759,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ( in @ ( sK28_SY952 @ SV435 @ SV210 ) @ SV210 ) )
= $false )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2760,plain,
! [SV210: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ ( sK28_SY952 @ SV435 @ SV210 ) ) )
= $false )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2589]) ).
thf(2761,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ~ ( ~ ( in @ SV444 @ ( sK50_SY972 @ SV219 @ SV444 ) )
| ~ ( in @ ( sK50_SY972 @ SV219 @ SV444 ) @ SV219 ) ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2596]) ).
thf(2762,plain,
! [SV219: $i,SV773: $i,SV444: $i] :
( ( ( ~ ~ ( ~ ( in @ SV444 @ SV773 )
| ~ ( in @ SV773 @ SV219 ) ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2597]) ).
thf(2763,plain,
! [SV220: $i,SV445: $i] :
( ( ( ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV220 )
| ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV445 ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2764,plain,
! [SV669: $i,SV447: $i,SV222: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV222 ) )
= $true )
| ( ( ~ ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) ) )
= $true )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2765,plain,
! [SV670: $i,SV449: $i,SV224: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV224 ) )
= $true )
| ( ( ~ ~ ( in @ SV761 @ SV449 )
| ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2766,plain,
( ( in @ sK4_SY5 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2767,plain,
( ( ~ ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2768,plain,
! [SV728: $i,SV586: $i,SV226: $i,SV451: $o] :
( ( ( ~ SV451 ) = $true )
| ( ( ( if @ SV226 @ SV451 @ SV586 @ SV728 )
= SV586 )
= $true )
| ( ( in @ SV728 @ SV226 )
= $false )
| ( ( in @ SV586 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2769,plain,
! [SV729: $i,SV587: $i,SV226: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV226 @ $true @ SV587 @ SV729 )
= SV587 )
= $true )
| ( ( in @ SV729 @ SV226 )
= $false )
| ( ( in @ SV587 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2605]) ).
thf(2770,plain,
! [SV730: $i,SV588: $i,SV226: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV226 @ $false @ SV588 @ SV730 )
= SV588 )
= $true )
| ( ( in @ SV730 @ SV226 )
= $false )
| ( ( in @ SV588 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2771,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) )
= $true )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2772,plain,
! [SV672: $i,SV452: $i,SV228: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV228 ) )
= $true )
| ( ( ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SV762 @ SV672 )
| ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2773,plain,
! [SV731: $i,SV229: $i,SV589: $i,SV453: $o] :
( ( ( ~ SV453 ) = $true )
| ( ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1307: $i] :
( ~ ( ~ SV453
| ( SY1307 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1307 != SV731 ) ) ) ) )
= $true )
| ( ( in @ SV731 @ SV229 )
= $false )
| ( ( in @ SV589 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2609]) ).
thf(2774,plain,
! [SV732: $i,SV229: $i,SV590: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1308: $i] :
( ~ ( ~ $true
| ( SY1308 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1308 != SV732 ) ) ) ) )
= $true )
| ( ( in @ SV732 @ SV229 )
= $false )
| ( ( in @ SV590 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2775,plain,
! [SV733: $i,SV229: $i,SV591: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1309: $i] :
( ~ ( ~ $false
| ( SY1309 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1309 != SV733 ) ) ) ) )
= $true )
| ( ( in @ SV733 @ SV229 )
= $false )
| ( ( in @ SV591 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2611]) ).
thf(2776,plain,
! [SV623: $o,SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2612]) ).
thf(2777,plain,
! [SV235: $i,SV459: $i,SV595: $i,SV623: $o] :
( ( SV623 = $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2612]) ).
thf(2778,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2779,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2780,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV235 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2614]) ).
thf(2781,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2614]) ).
thf(2782,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2783,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2784,plain,
! [SV673: $i,SV463: $i > $o,SV239: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ SV239 ) )
= $true )
| ( ( ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SV763 )
| ( SV673 = SV763 ) )
= $true )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2617]) ).
thf(2785,plain,
! [SV466: $i,SV674: $i,SV242: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV242 ) )
= $true )
| ( ( ~ ~ ( in @ SV764 @ SV674 )
| ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2786,plain,
! [SV739: $i,SV604: $i,SV471: $i,SV247: $i] :
( ( ( ~ ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1313 )
= ( ap @ SV247 @ SV471 @ SV739 @ SY1313 ) ) ) )
= $true )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2787,plain,
! [SV675: $i,SV473: $i,SV249: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ SV249 ) )
= $true )
| ( ( ~ ~ ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2627]) ).
thf(2788,plain,
! [SV677: $i,SV482: $i,SV259: $i] :
( ( ( ! [SY1272: $i] :
( ~ ( in @ SY1272 @ SV259 )
| ~ ( in @ SY1272 @ SV482 )
| ( in @ SY1272 @ SV677 ) ) )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2789,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( ~ ( in @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SV260 )
| ~ ~ ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2790,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( ~ ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2791,plain,
! [SV1: $i,SV484: $i,SV678: $i > $o,SV261: $i] :
( ( ( ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV261 )
| ~ ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SY1334 ) @ SV484 )
| ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SY1334 ) ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2632]) ).
thf(2792,plain,
! [SV262: $i,SV679: $i,SV2: $i,SV625: $i] :
( ( ( ~ ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) ) )
= $false )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2793,plain,
! [SV2: $i,SV625: $i,SV262: $i,SV679: $i] :
( ( ( ~ ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) ) )
= $false )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2633]) ).
thf(2794,plain,
! [SV680: $i,SV486: $i,SV265: $i,SV5: $i] :
( ( ( ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV5 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV265 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV486 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV680 ) ) ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2795,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK38_SY30 @ SV626 @ SV9 ) @ SV9 )
| ~ ~ ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2796,plain,
! [SV10: $i,SV627: $o,SV267: $i] :
( ( ( in @ SV267 @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) )
= $true )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2636]) ).
thf(2797,plain,
! [SV267: $i,SV10: $i,SV627: $o] :
( ( ( ~ ( in @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) @ SV10 ) )
= $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2637]) ).
thf(2798,plain,
! [SV10: $i,SV267: $i,SV627: $o] :
( ( SV627 = $false )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2637]) ).
thf(2799,plain,
! [SV10: $i,SV267: $i] :
( ( ( in @ SV267 @ ( sK40_SX0 @ SV10 @ SV267 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2800,plain,
! [SV267: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK40_SX0 @ SV10 @ SV267 ) @ SV10 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2801,plain,
! [SV10: $i,SV267: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2639]) ).
thf(2802,plain,
! [SV10: $i,SV267: $i] :
( ( ( in @ SV267 @ ( sK41_SX0 @ SV10 @ SV267 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2803,plain,
! [SV267: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK41_SX0 @ SV10 @ SV267 ) @ SV10 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2641]) ).
thf(2804,plain,
! [SV10: $i,SV267: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2641]) ).
thf(2805,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
| ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 ) )
= $false )
| ( ( ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2806,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
| ~ ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
| ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2646]) ).
thf(2807,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2647]) ).
thf(2808,plain,
! [SV681: $o,SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2809,plain,
! [SV269: $i,SV14: $i,SV488: $i,SV681: $o] :
( ( SV681 = $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2648]) ).
thf(2810,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2811,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2650]) ).
thf(2812,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2650]) ).
thf(2813,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2651]) ).
thf(2814,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2815,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2652]) ).
thf(2816,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2653]) ).
thf(2817,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2653]) ).
thf(2818,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
| ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
= $false )
| ( ( ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2819,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ! [SY1222: $i] :
( ~ ( SV19 @ SY1222 )
| ( SV630 = SY1222 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2820,plain,
! [SV631: $i,SV273: $i,SV21: $i,SV743: $i] :
( ( ( in @ SV743 @ SV21 )
= $false )
| ( ( ~ ( in @ SV273 @ ( powerset @ SV631 ) )
| ~ ( in @ SV743 @ SV273 )
| ( in @ SV743 @ SV631 ) )
= $true )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2656]) ).
thf(2821,plain,
! [SV274: $i,SV22: $i,SV490: $i] :
( ( ( in @ SV490 @ SV22 )
= $false )
| ( ( in @ SV490 @ SV274 )
= $true )
| ( ( in @ SV490 @ ( setminus @ SV22 @ SV274 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2822,plain,
! [SV281: $i,SV29: $i,SV741: $i,SV613: $i,SV494: $i > $i > $o] :
( ( ( ~ ( SV494 @ SV613 @ SV741 ) )
= $true )
| ( ( in @ ( kpair @ SV613 @ SV741 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) )
= $true )
| ( ( in @ SV741 @ SV281 )
= $false )
| ( ( in @ SV613 @ SV29 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2823,plain,
! [SV31: $i,SV496: $i,SV683: $i,SV283: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ SV283 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV683 @ SV766 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SV766 ) )
= $true )
| ( ( in @ SV683 @ SV31 )
= $false )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2824,plain,
! [SV684: $i,SV498: $i,SV35: $i,SV287: $o] :
( ( ( ~ SV287 ) = $false )
| ( ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 )
= $true )
| ( ( in @ SV684 @ SV35 )
= $false )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2825,plain,
! [SV685: $i,SV499: $i,SV35: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 )
= $true )
| ( ( in @ SV685 @ SV35 )
= $false )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2826,plain,
! [SV686: $i,SV500: $i,SV35: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 )
= $true )
| ( ( in @ SV686 @ SV35 )
= $false )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2827,plain,
! [SV293: $i,SV632: $i,SV41: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV41 )
| ~ ( in @ SV774 @ SV632 )
| ( in @ SV774 @ ( setminus @ SV41 @ SV293 ) ) )
= $true )
| ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2663]) ).
thf(2828,plain,
! [SV633: $i,SV295: $i,SV43: $i,SV744: $i] :
( ( ( in @ SV744 @ ( powerset @ SV43 ) )
= $false )
| ( ( in @ ( binintersect @ SV295 @ SV633 ) @ ( powerset @ ( binintersect @ ( binunion @ SV295 @ SV744 ) @ ( binunion @ SV633 @ SV744 ) ) ) )
= $true )
| ( ( in @ SV633 @ ( powerset @ SV43 ) )
= $false )
| ( ( in @ SV295 @ ( powerset @ SV43 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2829,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ SV44 ) )
= $true )
| ( ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV767 )
= ( SV503 @ SV767 ) )
= $true )
| ( ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2665]) ).
thf(2830,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV745: $i] :
( ( ( in @ SV745 @ SV44 )
= $false )
| ( ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV745 )
= ( SV503 @ SV745 ) )
= $true )
| ( ( in @ ( SV503 @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) ) @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2831,plain,
! [SV298: $i,SV46: $i > $i > $o] :
( ( ( ! [SY1337: $i] :
~ ( ~ ( ~ ( in @ SY1337 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1337 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1337 ) )
| ( in @ SY1337 @ ( sK46_SY736 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2832,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
| ~ ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2833,plain,
! [SV634: $i,SV300: $i,SV50: $i,SV747: $i] :
( ( ( in @ SV747 @ SV50 )
= $false )
| ( ( ~ ~ ( in @ SV747 @ SV300 )
| ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2834,plain,
! [SV301: $i,SV51: $i,SV506: $i] :
( ( ( in @ SV506 @ ( symdiff @ SV51 @ SV301 ) )
= $false )
| ( ( in @ SV506 @ SV301 )
= $true )
| ( ( in @ SV506 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2835,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2836,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( ~ ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) ) )
= $false )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2671]) ).
thf(2837,plain,
! [SV636: $i,SV310: $i,SV62: $i,SV748: $i] :
( ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV62 )
| ~ ( in @ SY1322 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SY1322 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2838,plain,
! [SV311: $i > $o,SV63: $i,SV688: $i] :
( ( ( in @ SV688 @ SV63 )
= $false )
| ( ( ~ ~ ( SV311 @ SV688 ) )
= $true )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2839,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV68 )
| ~ ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV313 )
| ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV637 ) )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2675]) ).
thf(2840,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) ) )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2676]) ).
thf(2841,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2842,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2843,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2679]) ).
thf(2844,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2680]) ).
thf(2845,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ~ ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2846,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2681]) ).
thf(2847,plain,
! [SV638: $i,SV322: $i,SV77: $i,SV749: $i] :
( ( ( in @ SV749 @ SV77 )
= $false )
| ( ( ~ ( subset @ SV322 @ SV638 )
| ~ ~ ( in @ SV749 @ SV638 )
| ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2682]) ).
thf(2848,plain,
! [SV82: $i,SV326: $i,SV750: $i] :
( ( ( in @ SV750 @ SV326 )
= $false )
| ( ( in @ SV750 @ SV82 )
= $true )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2849,plain,
! [SV326: $i,SV82: $i] :
( ( ( in @ ( sK42_SY778 @ SV82 @ SV326 ) @ SV326 )
= $true )
| ( ( in @ SV326 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2850,plain,
! [SV327: $i > $o,SV83: $i,SV690: $i] :
( ( ( in @ SV690 @ SV83 )
= $false )
| ( ( ~ ( SV327 @ SV690 ) )
= $true )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2686]) ).
thf(2851,plain,
! [SV691: $i,SV520: $i,SV84: $i,SV328: $o] :
( ( SV328 = $false )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1282: $i] :
( ~ ( ~ SV328
| ( SY1282 != SV520 ) )
| ~ ( ~ ~ SV328
| ( SY1282 != SV691 ) ) ) )
= ( setadjoin @ SV520 @ emptyset ) )
= $true )
| ( ( in @ SV691 @ SV84 )
= $false )
| ( ( in @ SV520 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2852,plain,
! [SV692: $i,SV521: $i,SV84: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1283: $i] :
( ~ ( ~ $true
| ( SY1283 != SV521 ) )
| ~ ( ~ ~ $true
| ( SY1283 != SV692 ) ) ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $true )
| ( ( in @ SV692 @ SV84 )
= $false )
| ( ( in @ SV521 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2853,plain,
! [SV693: $i,SV522: $i,SV84: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV84
@ ^ [SY1284: $i] :
( ~ ( ~ $false
| ( SY1284 != SV522 ) )
| ~ ( ~ ~ $false
| ( SY1284 != SV693 ) ) ) )
= ( setadjoin @ SV522 @ emptyset ) )
= $true )
| ( ( in @ SV693 @ SV84 )
= $false )
| ( ( in @ SV522 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2854,plain,
! [SV86: $i,SV524: $i,SV695: $i,SV330: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ SV330 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV695 @ SV768 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SV768 ) )
= $true )
| ( ( in @ SV695 @ SV86 )
= $false )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2690]) ).
thf(2855,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ! [SY1234: $i] :
( ~ ( SV89 @ SY1234 )
| ( SV639 = SY1234 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2856,plain,
! [SV340: $i > $o,SV95: $i,SV528: $i] :
( ( ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY796: $i] : ( SV340 @ SY796 ) ) )
= $false )
| ( ( SV340 @ SV528 )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2857,plain,
! [SV95: $i,SV528: $i,SV340: $i > $o] :
( ( ( SV340 @ SV528 )
= $false )
| ( ( in @ SV528
@ ( dsetconstr @ SV95
@ ^ [SY797: $i] : ( SV340 @ SY797 ) ) )
= $true )
| ( ( in @ SV528 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2858,plain,
! [SV640: $i,SV341: $i,SV96: $i,SV751: $i] :
( ( ( in @ SV751 @ SV96 )
= $false )
| ( ( ~ ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
| ~ ( in @ SV751 @ SV341 ) )
= $true )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2859,plain,
! [SV344: $i,SV698: $i,SV100: $i,SV641: $i] :
( ( ( in @ SV641 @ SV100 )
= $false )
| ( ( in @ SV698 @ SV344 )
= $true )
| ( ( SV641 = SV698 )
= $false )
| ( ( SV100 = SV344 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2860,plain,
! [SV643: $i,SV346: $i,SV102: $i,SV752: $i] :
( ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( ! [SY1323: $i] :
( ~ ( in @ SY1323 @ SV102 )
| ~ ( in @ SY1323 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SY1323 @ ( binunion @ SV346 @ SV752 ) ) ) )
= $true )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2861,plain,
! [SV105: $i] :
( ( ( in @ ( sK23_SY262 @ SV105 ) @ SV105 )
= $true )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2862,plain,
! [SV105: $i] :
( ( $true = $true )
| ( ( SV105 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2699]) ).
thf(2863,plain,
! [SV644: $i,SV352: $i,SV110: $i,SV753: $i] :
( ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( ! [SY1324: $i] :
( ~ ( in @ SY1324 @ SV110 )
| ~ ( in @ SY1324 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SY1324 @ ( binunion @ SV644 @ SV753 ) ) ) )
= $true )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2864,plain,
! [SV534: $i,SV116: $i,SV702: $i,SV358: $o] :
( ( ( ~ SV358 ) = $false )
| ( ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) )
= $true )
| ( ( in @ SV702 @ SV116 )
= $false )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2865,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) )
= $true )
| ( ( in @ SV703 @ SV116 )
= $false )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2866,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) )
= $true )
| ( ( in @ SV704 @ SV116 )
= $false )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2867,plain,
! [SV359: $i > $o,SV117: $i,SV775: $i] :
( ( ( ~ ~ ( ~ ( in @ SV775 @ SV117 )
| ~ ( SV359 @ SV775 ) ) )
= $true )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2868,plain,
! [SV359: $i > $o,SV117: $i,SV776: $i] :
( ( ( ~ ~ ( ~ ( in @ SV776 @ SV117 )
| ~ ( SV359 @ SV776 ) ) )
= $true )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2707]) ).
thf(2869,plain,
! [SV705: $i,SV537: $i,SV360: $i,SV118: $i] :
( ( ( ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ SY1290 )
= ( ap @ SV118 @ SV360 @ SV705 @ SY1290 ) ) ) )
= $false )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2870,plain,
! [SV707: $i,SV540: $i,SV366: $i,SV126: $i] :
( ( ( ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV126 )
| ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV366 )
| ~ ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV540 )
| ( in @ ( kpair @ SY1293 @ SY1294 ) @ SV707 ) ) ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2871,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i,SV742: $i,SV615: $i] :
( ( ( ~ ( in @ ( kpair @ SV615 @ SV742 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) ) )
= $true )
| ( ( SV541 @ SV615 @ SV742 )
= $true )
| ( ( in @ SV742 @ SV368 )
= $false )
| ( ( in @ SV615 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2872,plain,
! [SV369: $i,SV129: $i,SV648: $i] :
( ( ( in @ SV648 @ ( setminus @ SV129 @ SV369 ) )
= $true )
| ( ( in @ SV648 @ SV369 )
= $true )
| ( ( in @ SV648 @ SV129 )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2712]) ).
thf(2873,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2874,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2875,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2715]) ).
thf(2876,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ~ ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2877,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2716]) ).
thf(2878,plain,
! [SV649: $i,SV376: $i,SV136: $i,SV754: $i] :
( ( ( in @ SV754 @ SV136 )
= $false )
| ( ( ~ ( in @ SV754 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
| ( in @ SV754 @ ( setminus @ SV136 @ SV376 ) ) )
= $true )
| ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2879,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) @ SV137 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2880,plain,
! [SV137: $i,SV650: $i > $o,SV708: $i > $o,SV377: $i] :
( ( ( ! [SY1340: $i] :
( ~ ( in @ SY1340 @ SV377 )
| ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
!= SY1340 )
| ~ ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ SY1340 ) )
| ~ ( ~ ( SV708 @ SY1340 )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2719]) ).
thf(2881,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ! [SY1248: $i] :
( ~ ( SV146 @ SY1248 )
| ( SV653 = SY1248 ) ) )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2882,plain,
! [SV654: $i,SV384: $i,SV147: $i,SV755: $i] :
( ( ( in @ SV755 @ SV147 )
= $false )
| ( ( ~ ~ ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) )
| ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2883,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( ~ ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV148 )
| ~ ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV385 )
| ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV655 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2724]) ).
thf(2884,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ SV152 ) )
= $true )
| ( ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV769 )
= ( SV549 @ SV769 ) )
= $true )
| ( ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2885,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV756: $i] :
( ( ( in @ SV756 @ SV152 )
= $false )
| ( ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV756 )
= ( SV549 @ SV756 ) )
= $true )
| ( ( in @ ( SV549 @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) ) @ SV389 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2886,plain,
! [SV710: $i,SV550: $i,SV154: $i,SV391: $o] :
( ( ( ~ SV391 ) = $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) )
= $true )
| ( ( in @ SV710 @ SV154 )
= $false )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2887,plain,
! [SV711: $i,SV551: $i,SV154: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) )
= $true )
| ( ( in @ SV711 @ SV154 )
= $false )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2888,plain,
! [SV712: $i,SV552: $i,SV154: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) )
= $true )
| ( ( in @ SV712 @ SV154 )
= $false )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2889,plain,
! [SV158: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ omega )
| ~ ( in @ ( sK43_SY395 @ SV158 ) @ SV158 ) ) )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2730]) ).
thf(2890,plain,
! [SV158: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ omega )
| ( in @ SV777 @ SV158 ) )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( setadjoin @ ( sK43_SY395 @ SV158 ) @ ( sK43_SY395 @ SV158 ) ) @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2731]) ).
thf(2891,plain,
! [SV659: $i,SV402: $i,SV168: $i,SV757: $i] :
( ( ( in @ SV757 @ SV168 )
= $false )
| ( ( ~ ( in @ SV757 @ ( setminus @ SV168 @ SV402 ) )
| ( in @ SV757 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) ) )
= $true )
| ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2892,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2893,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( ~ ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) ) )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2733]) ).
thf(2894,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( in @ ( sK26_SY909 @ SV408 @ SV174 ) @ SV174 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2734]) ).
thf(2895,plain,
! [SV174: $i,SV408: $i > $o] :
( ( ( SV408 @ ( sK26_SY909 @ SV408 @ SV174 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV174
@ ^ [SY908: $i] : ( SV408 @ SY908 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2735]) ).
thf(2896,plain,
! [SV716: $i,SV563: $i,SV409: $i,SV175: $i] :
( ( ( ! [SY1302: $i] :
( ~ ( in @ SY1302 @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ SY1302 )
= ( ap @ SV175 @ SV409 @ SV716 @ SY1302 ) ) ) )
= $false )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2897,plain,
! [SV410: $i,SV176: $i,SV660: $i] :
( ( ( in @ SV660 @ ( setminus @ SV176 @ SV410 ) )
= $false )
| ( ( in @ SV660 @ SV410 )
= $false )
| ( ( in @ SV660 @ SV176 )
= $false )
| ( ( in @ SV410 @ ( powerset @ SV176 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2898,plain,
! [SV758: $o,SV661: $i,SV413: $i,SV181: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV181 ) )
= $true )
| ( ( ~ ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2738]) ).
thf(2899,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV181 ) )
= $true )
| ( ( ~ ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV771 @ SV413 )
| $true )
| ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2900,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV181 ) )
= $true )
| ( ( ~ ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV772 @ SV413 )
| $false )
| ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2901,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ! [SY1258: $i] :
( ~ ( SV182 @ SY1258 )
| ( SV662 = SY1258 ) ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2902,plain,
! [SV191: $i,SV421: $i > $o,SV719: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) @ SV191 )
| ~ ~ ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) ) ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2742]) ).
thf(2903,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2904,plain,
! [SV193: $i,SV570: $i,SV720: $i > $o,SV423: $i] :
( ( ( ! [SY1342: $i] :
( ~ ( in @ SY1342 @ SV423 )
| ~ ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SY1342 ) @ SV570 )
| ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SY1342 ) ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2743]) ).
thf(2905,plain,
! [SV721: $o,SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 = SV194 )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 )
| SV721 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2906,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 ) )
= $true )
| ( SV721 = $true )
| ( SV721 = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(2907,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 = SV194 )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true )
| $true )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2746]) ).
thf(2908,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2747]) ).
thf(2909,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( ( SV571 = SV194 )
= $true )
| ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false )
| $false )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2910,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2749]) ).
thf(2911,plain,
! [SV195: $i,SV425: $i > $o,SV722: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) @ SV195 )
| ~ ~ ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) ) ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2750]) ).
thf(2912,plain,
! [SV196: $i] :
( ( ~ ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2913,plain,
! [SV196: $i] :
( ( ! [SY1149: $i,SY1150: $i] :
( ~ ~ ( ~ ( in @ SY1149 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1150 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( in @ SX4 @ SY1150 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1150 )
| ( in @ SX4 @ SY1149 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(2914,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) )
| ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) ) )
= $false )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2915,plain,
! [SV199: $i,SV428: $i > $o,SV572: $i] :
( ( ( ~ ( in @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) @ SV199 )
| ~ ( SV428 @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) )
| ( ( sK56_SY1161 @ SV572 @ SV428 @ SV199 )
= SV572 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2754]) ).
thf(2916,plain,
! [SV430: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK57_SY947 @ SV201 @ SV430 ) @ SV430 )
| ( in @ ( sK57_SY947 @ SV201 @ SV430 ) @ SV201 ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2755]) ).
thf(2917,plain,
! [SV430: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK49_SY947 @ SV201 @ SV430 ) @ SV430 ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2918,plain,
! [SV430: $i,SV201: $i] :
( ( ( in @ ( sK49_SY947 @ SV201 @ SV430 ) @ SV201 )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2756]) ).
thf(2919,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ! [SY1259: $i] :
( ~ ( SV205 @ SY1259 )
| ( SV666 = SY1259 ) ) )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2757]) ).
thf(2920,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ! [SY1260: $i] :
( ~ ( SV209 @ SY1260 )
| ( SV667 = SY1260 ) ) )
= $false )
| ( ( SV209 @ SV667 )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2921,plain,
! [SV210: $i,SV435: $i] :
( ( ( in @ ( sK28_SY952 @ SV435 @ SV210 ) @ SV210 )
= $true )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2922,plain,
! [SV210: $i,SV435: $i] :
( ( ( in @ SV435 @ ( sK28_SY952 @ SV435 @ SV210 ) )
= $true )
| ( ( in @ SV435 @ ( setunion @ SV210 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2923,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ( ~ ( in @ SV444 @ ( sK50_SY972 @ SV219 @ SV444 ) )
| ~ ( in @ ( sK50_SY972 @ SV219 @ SV444 ) @ SV219 ) ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2761]) ).
thf(2924,plain,
! [SV219: $i,SV773: $i,SV444: $i] :
( ( ( ~ ( ~ ( in @ SV444 @ SV773 )
| ~ ( in @ SV773 @ SV219 ) ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2925,plain,
! [SV220: $i,SV445: $i] :
( ( ( ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV220 ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2763]) ).
thf(2926,plain,
! [SV220: $i,SV445: $i] :
( ( ( ~ ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV445 ) )
= $false )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2763]) ).
thf(2927,plain,
! [SV669: $i,SV447: $i,SV222: $i,SV760: $i] :
( ( ( in @ SV760 @ SV222 )
= $false )
| ( ( ~ ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) )
| ~ ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) ) )
= $true )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2928,plain,
! [SV670: $i,SV449: $i,SV224: $i,SV761: $i] :
( ( ( in @ SV761 @ SV224 )
= $false )
| ( ( ~ ~ ( in @ SV761 @ SV449 )
| ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2929,plain,
( ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
| ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2930,plain,
! [SV728: $i,SV586: $i,SV226: $i,SV451: $o] :
( ( SV451 = $false )
| ( ( ( if @ SV226 @ SV451 @ SV586 @ SV728 )
= SV586 )
= $true )
| ( ( in @ SV728 @ SV226 )
= $false )
| ( ( in @ SV586 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2931,plain,
! [SV729: $i,SV587: $i,SV226: $i] :
( ( $true = $false )
| ( ( ( if @ SV226 @ $true @ SV587 @ SV729 )
= SV587 )
= $true )
| ( ( in @ SV729 @ SV226 )
= $false )
| ( ( in @ SV587 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2932,plain,
! [SV730: $i,SV588: $i,SV226: $i] :
( ( $false = $false )
| ( ( ( if @ SV226 @ $false @ SV588 @ SV730 )
= SV588 )
= $true )
| ( ( in @ SV730 @ SV226 )
= $false )
| ( ( in @ SV588 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2933,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ! [SY1265: $i] :
( ~ ( SV227 @ SY1265 )
| ( SV671 = SY1265 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2934,plain,
! [SV672: $i,SV452: $i,SV228: $i,SV762: $i] :
( ( ( in @ SV762 @ SV228 )
= $false )
| ( ( ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
| ~ ( in @ SV762 @ SV672 )
| ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2935,plain,
! [SV731: $i,SV229: $i,SV589: $i,SV453: $o] :
( ( SV453 = $false )
| ( ( in @ SV589
@ ( dsetconstr @ SV229
@ ^ [SY1307: $i] :
( ~ ( ~ SV453
| ( SY1307 != SV589 ) )
| ~ ( ~ ~ SV453
| ( SY1307 != SV731 ) ) ) ) )
= $true )
| ( ( in @ SV731 @ SV229 )
= $false )
| ( ( in @ SV589 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2773]) ).
thf(2936,plain,
! [SV732: $i,SV229: $i,SV590: $i] :
( ( $true = $false )
| ( ( in @ SV590
@ ( dsetconstr @ SV229
@ ^ [SY1308: $i] :
( ~ ( ~ $true
| ( SY1308 != SV590 ) )
| ~ ( ~ ~ $true
| ( SY1308 != SV732 ) ) ) ) )
= $true )
| ( ( in @ SV732 @ SV229 )
= $false )
| ( ( in @ SV590 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2774]) ).
thf(2937,plain,
! [SV733: $i,SV229: $i,SV591: $i] :
( ( $false = $false )
| ( ( in @ SV591
@ ( dsetconstr @ SV229
@ ^ [SY1309: $i] :
( ~ ( ~ $false
| ( SY1309 != SV591 ) )
| ~ ( ~ ~ $false
| ( SY1309 != SV733 ) ) ) ) )
= $true )
| ( ( in @ SV733 @ SV229 )
= $false )
| ( ( in @ SV591 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2938,plain,
! [SV623: $o,SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ SV235 )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 )
| SV623 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2939,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 ) )
= $true )
| ( SV623 = $true )
| ( SV623 = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2940,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ SV235 )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true )
| $true )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2778]) ).
thf(2941,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2942,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( ( in @ SV595 @ SV235 )
= $true )
| ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false )
| $false )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2780]) ).
thf(2943,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(2944,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2945,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
| ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
= $false )
| ( ( ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(2946,plain,
! [SV673: $i,SV463: $i > $o,SV239: $i,SV763: $i] :
( ( ( in @ SV763 @ SV239 )
= $false )
| ( ( ~ ( SV463 @ SV673 )
| ~ ( SV463 @ SV763 )
| ( SV673 = SV763 ) )
= $true )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2947,plain,
! [SV466: $i,SV674: $i,SV242: $i,SV764: $i] :
( ( ( in @ SV764 @ SV242 )
= $false )
| ( ( ~ ~ ( in @ SV764 @ SV674 )
| ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2785]) ).
thf(2948,plain,
! [SV739: $i,SV604: $i,SV471: $i,SV247: $i] :
( ( ( ! [SY1313: $i] :
( ~ ( in @ SY1313 @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ SY1313 )
= ( ap @ SV247 @ SV471 @ SV739 @ SY1313 ) ) ) )
= $false )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2949,plain,
! [SV675: $i,SV473: $i,SV249: $i,SV765: $i] :
( ( ( in @ SV765 @ SV249 )
= $false )
| ( ( ~ ~ ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) )
| ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2787]) ).
thf(2950,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( ~ ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
| ~ ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
| ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 ) )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2788]) ).
thf(2951,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( ~ ( in @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SV260 ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2789]) ).
thf(2952,plain,
! [SV260: $i,SV609: $i,SV483: $i] :
( ( ( ~ ~ ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2789]) ).
thf(2953,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 )
= $true )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2790]) ).
thf(2954,plain,
! [SV261: $i,SV678: $i > $o,SV484: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 )
| ~ ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
| ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2791]) ).
thf(2955,plain,
! [SV262: $i,SV679: $i,SV2: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV2 )
| ( in @ SV679 @ SV262 ) )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2956,plain,
! [SV2: $i,SV625: $i,SV262: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV262 )
| ( in @ SV625 @ SV2 ) )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2793]) ).
thf(2957,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( ~ ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
| ! [SY1343: $i] :
( ~ ( in @ SY1343 @ SV265 )
| ~ ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SY1343 ) @ SV486 )
| ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SY1343 ) @ SV680 ) ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2794]) ).
thf(2958,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ( in @ ( sK38_SY30 @ SV626 @ SV9 ) @ SV9 ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2959,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ~ ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2795]) ).
thf(2960,plain,
! [SV267: $i,SV10: $i,SV627: $o] :
( ( ( in @ ( sK39_SY1219 @ SV627 @ SV10 @ SV267 ) @ SV10 )
= $true )
| ( SV627 = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2797]) ).
thf(2961,plain,
! [SV267: $i,SV10: $i] :
( ( ( in @ ( sK40_SX0 @ SV10 @ SV267 ) @ SV10 )
= $true )
| ( $true = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(2962,plain,
! [SV267: $i,SV10: $i] :
( ( ( in @ ( sK41_SX0 @ SV10 @ SV267 ) @ SV10 )
= $true )
| ( $false = $true )
| ( ( in @ SV267 @ ( setunion @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(2963,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) )
= $false )
| ( ( ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2964,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2805]) ).
thf(2965,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2966,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
| ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2806]) ).
thf(2967,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 ) )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(2968,plain,
! [SV681: $o,SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2808]) ).
thf(2969,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 ) )
= $true )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2970,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2971,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2811]) ).
thf(2972,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2973,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2813]) ).
thf(2974,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2814]) ).
thf(2975,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2815]) ).
thf(2976,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2977,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(2978,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) )
= $false )
| ( ( ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2979,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2818]) ).
thf(2980,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
| ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2819]) ).
thf(2981,plain,
! [SV21: $i,SV743: $i,SV631: $i,SV273: $i] :
( ( ( ~ ( in @ SV273 @ ( powerset @ SV631 ) ) )
= $true )
| ( ( ~ ( in @ SV743 @ SV273 )
| ( in @ SV743 @ SV631 ) )
= $true )
| ( ( in @ SV743 @ SV21 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2982,plain,
! [SV281: $i,SV29: $i,SV741: $i,SV613: $i,SV494: $i > $i > $o] :
( ( ( SV494 @ SV613 @ SV741 )
= $false )
| ( ( in @ ( kpair @ SV613 @ SV741 )
@ ( dpsetconstr @ SV29 @ SV281
@ ^ [SY1050: $i,SY1051: $i] : ( SV494 @ SY1050 @ SY1051 ) ) )
= $true )
| ( ( in @ SV741 @ SV281 )
= $false )
| ( ( in @ SV613 @ SV29 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2822]) ).
thf(2983,plain,
! [SV31: $i,SV496: $i,SV683: $i,SV283: $i,SV766: $i] :
( ( ( in @ SV766 @ SV283 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV683 @ SV766 ) @ SV496 )
| ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SV766 ) )
= $true )
| ( ( in @ SV683 @ SV31 )
= $false )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2984,plain,
! [SV684: $i,SV498: $i,SV35: $i,SV287: $o] :
( ( SV287 = $true )
| ( ( ( if @ SV35 @ SV287 @ SV498 @ SV684 )
= SV684 )
= $true )
| ( ( in @ SV684 @ SV35 )
= $false )
| ( ( in @ SV498 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2985,plain,
! [SV685: $i,SV499: $i,SV35: $i] :
( ( $true = $true )
| ( ( ( if @ SV35 @ $true @ SV499 @ SV685 )
= SV685 )
= $true )
| ( ( in @ SV685 @ SV35 )
= $false )
| ( ( in @ SV499 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2986,plain,
! [SV686: $i,SV500: $i,SV35: $i] :
( ( $false = $true )
| ( ( ( if @ SV35 @ $false @ SV500 @ SV686 )
= SV686 )
= $true )
| ( ( in @ SV686 @ SV35 )
= $false )
| ( ( in @ SV500 @ SV35 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2826]) ).
thf(2987,plain,
! [SV293: $i,SV632: $i,SV41: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV41 ) )
= $true )
| ( ( ~ ( in @ SV774 @ SV632 )
| ( in @ SV774 @ ( setminus @ SV41 @ SV293 ) ) )
= $true )
| ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(2988,plain,
! [SV503: $i > $i,SV296: $i,SV44: $i,SV767: $i] :
( ( ( in @ SV767 @ SV44 )
= $false )
| ( ( ( ap @ SV44 @ SV296
@ ( lam @ SV44 @ SV296
@ ^ [SY1063: $i] : ( SV503 @ SY1063 ) )
@ SV767 )
= ( SV503 @ SV767 ) )
= $true )
| ( ( in @ ( sK21_SY1061 @ SV296 @ SV503 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2989,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
| ~ ( ~ ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) )
| ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2831]) ).
thf(2990,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 ) )
= $true )
| ( ( ~ ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2991,plain,
! [SV50: $i,SV634: $i,SV300: $i,SV747: $i] :
( ( ( ~ ~ ( in @ SV747 @ SV300 ) )
= $true )
| ( ( ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV747 @ SV50 )
= $false )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(2992,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
= $true )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2993,plain,
! [SV55: $i,SV303: $i > $o] :
( ( ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) )
= $true )
| ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV55 )
| ~ ( SV303 @ SY747 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(2994,plain,
! [SV748: $i,SV636: $i,SV310: $i,SV62: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV62 )
| ~ ( in @ SV779 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SV779 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2837]) ).
thf(2995,plain,
! [SV63: $i,SV688: $i,SV311: $i > $o] :
( ( ( ~ ( SV311 @ SV688 ) )
= $false )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2996,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV68 ) )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2997,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV313 )
| ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV637 ) )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2839]) ).
thf(2998,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
| ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 ) )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(2999,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(3000,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2841]) ).
thf(3001,plain,
! [SV321: $i > $o,SV76: $i,SV780: $i] :
( ( ( ~ ~ ( ~ ( in @ SV780 @ SV76 )
| ~ ( SV321 @ SV780 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2842]) ).
thf(3002,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3003,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3004,plain,
! [SV76: $i,SV321: $i > $o] :
( ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true )
| ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) )
| ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2845]) ).
thf(3005,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2846]) ).
thf(3006,plain,
! [SV77: $i,SV749: $i,SV638: $i,SV322: $i] :
( ( ( ~ ( subset @ SV322 @ SV638 ) )
= $true )
| ( ( ~ ~ ( in @ SV749 @ SV638 )
| ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2847]) ).
thf(3007,plain,
! [SV83: $i,SV690: $i,SV327: $i > $o] :
( ( ( SV327 @ SV690 )
= $false )
| ( ( in @ SV690 @ SV83 )
= $false )
| ( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(3008,plain,
! [SV86: $i,SV524: $i,SV695: $i,SV330: $i,SV768: $i] :
( ( ( in @ SV768 @ SV330 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV695 @ SV768 ) @ SV524 )
| ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SV768 ) )
= $true )
| ( ( in @ SV695 @ SV86 )
= $false )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3009,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
| ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2855]) ).
thf(3010,plain,
! [SV640: $i,SV341: $i,SV96: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) ) )
= $true )
| ( ( ~ ( in @ SV751 @ SV341 ) )
= $true )
| ( ( in @ SV751 @ SV96 )
= $false )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3011,plain,
! [SV752: $i,SV643: $i,SV346: $i,SV102: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ SV102 )
| ~ ( in @ SV781 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SV781 @ ( binunion @ SV346 @ SV752 ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2860]) ).
thf(3012,plain,
! [SV753: $i,SV644: $i,SV352: $i,SV110: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV110 )
| ~ ( in @ SV782 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SV782 @ ( binunion @ SV644 @ SV753 ) ) )
= $true )
| ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2863]) ).
thf(3013,plain,
! [SV534: $i,SV116: $i,SV702: $i,SV358: $o] :
( ( SV358 = $true )
| ( ( in @ SV702
@ ( dsetconstr @ SV116
@ ^ [SY1287: $i] :
( ~ ( ~ SV358
| ( SY1287 != SV534 ) )
| ~ ( ~ ~ SV358
| ( SY1287 != SV702 ) ) ) ) )
= $true )
| ( ( in @ SV702 @ SV116 )
= $false )
| ( ( in @ SV534 @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2864]) ).
thf(3014,plain,
! [SV535: $i,SV116: $i,SV703: $i] :
( ( $true = $true )
| ( ( in @ SV703
@ ( dsetconstr @ SV116
@ ^ [SY1288: $i] :
( ~ ( ~ $true
| ( SY1288 != SV535 ) )
| ~ ( ~ ~ $true
| ( SY1288 != SV703 ) ) ) ) )
= $true )
| ( ( in @ SV703 @ SV116 )
= $false )
| ( ( in @ SV535 @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2865]) ).
thf(3015,plain,
! [SV536: $i,SV116: $i,SV704: $i] :
( ( $false = $true )
| ( ( in @ SV704
@ ( dsetconstr @ SV116
@ ^ [SY1289: $i] :
( ~ ( ~ $false
| ( SY1289 != SV536 ) )
| ~ ( ~ ~ $false
| ( SY1289 != SV704 ) ) ) ) )
= $true )
| ( ( in @ SV704 @ SV116 )
= $false )
| ( ( in @ SV536 @ SV116 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2866]) ).
thf(3016,plain,
! [SV359: $i > $o,SV117: $i,SV775: $i] :
( ( ( ~ ( ~ ( in @ SV775 @ SV117 )
| ~ ( SV359 @ SV775 ) ) )
= $false )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(3017,plain,
! [SV359: $i > $o,SV117: $i,SV776: $i] :
( ( ( ~ ( ~ ( in @ SV776 @ SV117 )
| ~ ( SV359 @ SV776 ) ) )
= $false )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2868]) ).
thf(3018,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i] :
( ( ( ~ ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
| ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) ) )
= $false )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2869]) ).
thf(3019,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( ~ ( in @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SV126 )
| ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV366 )
| ~ ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SY1346 ) @ SV540 )
| ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SY1346 ) @ SV707 ) ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2870]) ).
thf(3020,plain,
! [SV541: $i > $i > $o,SV368: $i,SV128: $i,SV742: $i,SV615: $i] :
( ( ( in @ ( kpair @ SV615 @ SV742 )
@ ( dpsetconstr @ SV128 @ SV368
@ ^ [SY1102: $i,SY1103: $i] : ( SV541 @ SY1102 @ SY1103 ) ) )
= $false )
| ( ( SV541 @ SV615 @ SV742 )
= $true )
| ( ( in @ SV742 @ SV368 )
= $false )
| ( ( in @ SV615 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2871]) ).
thf(3021,plain,
! [SV371: $i > $o,SV131: $i,SV783: $i] :
( ( ( ~ ~ ( ~ ( in @ SV783 @ SV131 )
| ~ ( SV371 @ SV783 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3022,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2874]) ).
thf(3023,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3024,plain,
! [SV131: $i,SV371: $i > $o] :
( ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true )
| ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) )
| ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2876]) ).
thf(3025,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2877]) ).
thf(3026,plain,
! [SV649: $i,SV376: $i,SV136: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) ) )
= $true )
| ( ( in @ SV754 @ ( setminus @ SV136 @ SV376 ) )
= $true )
| ( ( in @ SV754 @ SV136 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3027,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( in @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) @ SV137 )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(3028,plain,
! [SV377: $i,SV708: $i > $o,SV650: $i > $o,SV137: $i] :
( ( ( ~ ( in @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) @ SV377 )
| ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
!= ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ~ ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
| ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2880]) ).
thf(3029,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
| ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) ) )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2881]) ).
thf(3030,plain,
! [SV147: $i,SV654: $i,SV384: $i,SV755: $i] :
( ( ( ~ ~ ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) ) )
= $true )
| ( ( ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV755 @ SV147 )
= $false )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2882]) ).
thf(3031,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( ~ ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(3032,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( ~ ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV385 )
| ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV655 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2883]) ).
thf(3033,plain,
! [SV549: $i > $i,SV389: $i,SV152: $i,SV769: $i] :
( ( ( in @ SV769 @ SV152 )
= $false )
| ( ( ( ap @ SV152 @ SV389
@ ( lam @ SV152 @ SV389
@ ^ [SY1109: $i] : ( SV549 @ SY1109 ) )
@ SV769 )
= ( SV549 @ SV769 ) )
= $true )
| ( ( in @ ( sK24_SY1107 @ SV389 @ SV549 @ SV152 ) @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3034,plain,
! [SV710: $i,SV550: $i,SV154: $i,SV391: $o] :
( ( SV391 = $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1299: $i] :
( ~ ( ~ SV391
| ( SY1299 != SV550 ) )
| ~ ( ~ ~ SV391
| ( SY1299 != SV710 ) ) ) )
= ( setadjoin @ SV710 @ emptyset ) )
= $true )
| ( ( in @ SV710 @ SV154 )
= $false )
| ( ( in @ SV550 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2886]) ).
thf(3035,plain,
! [SV711: $i,SV551: $i,SV154: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1300: $i] :
( ~ ( ~ $true
| ( SY1300 != SV551 ) )
| ~ ( ~ ~ $true
| ( SY1300 != SV711 ) ) ) )
= ( setadjoin @ SV711 @ emptyset ) )
= $true )
| ( ( in @ SV711 @ SV154 )
= $false )
| ( ( in @ SV551 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2887]) ).
thf(3036,plain,
! [SV712: $i,SV552: $i,SV154: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY1301: $i] :
( ~ ( ~ $false
| ( SY1301 != SV552 ) )
| ~ ( ~ ~ $false
| ( SY1301 != SV712 ) ) ) )
= ( setadjoin @ SV712 @ emptyset ) )
= $true )
| ( ( in @ SV712 @ SV154 )
= $false )
| ( ( in @ SV552 @ SV154 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2888]) ).
thf(3037,plain,
! [SV158: $i] :
( ( ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ omega )
| ~ ( in @ ( sK43_SY395 @ SV158 ) @ SV158 ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3038,plain,
! [SV158: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ omega ) )
= $true )
| ( ( in @ SV777 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( setadjoin @ ( sK43_SY395 @ SV158 ) @ ( sK43_SY395 @ SV158 ) ) @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3039,plain,
! [SV659: $i,SV402: $i,SV168: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ ( setminus @ SV168 @ SV402 ) ) )
= $true )
| ( ( in @ SV757 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) )
= $true )
| ( ( in @ SV757 @ SV168 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2891]) ).
thf(3040,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2892]) ).
thf(3041,plain,
! [SV169: $i,SV403: $i > $o] :
( ( ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV169 )
| ~ ( SV403 @ SY906 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2893]) ).
thf(3042,plain,
! [SV175: $i,SV409: $i,SV563: $i,SV716: $i] :
( ( ( ~ ( in @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) @ SV175 )
| ( ( ap @ SV175 @ SV409 @ SV563 @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) )
= ( ap @ SV175 @ SV409 @ SV716 @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) ) ) )
= $false )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2896]) ).
thf(3043,plain,
! [SV758: $o,SV661: $i,SV413: $i,SV181: $i,SV770: $i] :
( ( ( in @ SV770 @ SV181 )
= $false )
| ( ( ~ ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2898]) ).
thf(3044,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV771: $i] :
( ( ( in @ SV771 @ SV181 )
= $false )
| ( ( ~ ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV771 @ SV413 )
| $true )
| ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2899]) ).
thf(3045,plain,
! [SV661: $i,SV413: $i,SV181: $i,SV772: $i] :
( ( ( in @ SV772 @ SV181 )
= $false )
| ( ( ~ ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
| ~ ( ~ ( in @ SV772 @ SV413 )
| $false )
| ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2900]) ).
thf(3046,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) )
| ( SV662
= ( sK68_SY1258 @ SV662 @ SV182 ) ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2901]) ).
thf(3047,plain,
! [SV191: $i,SV421: $i > $o,SV719: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) @ SV191 )
| ~ ~ ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) ) ) )
= $true )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2902]) ).
thf(3048,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 )
= $true )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2903]) ).
thf(3049,plain,
! [SV423: $i,SV720: $i > $o,SV570: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 )
| ~ ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
| ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2904]) ).
thf(3050,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| SV721 ) )
= $true )
| ( SV721 = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(3051,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| SV721 )
= $false )
| ( SV721 = $true )
| ( SV721 = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3052,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(3053,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3054,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( ~ ( in @ SV571 @ SV424 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3055,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2910]) ).
thf(3056,plain,
! [SV195: $i,SV425: $i > $o,SV722: $i] :
( ( ( ~ ( ~ ( in @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) @ SV195 )
| ~ ~ ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) ) ) )
= $true )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(3057,plain,
! [SV196: $i] :
( ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) )
| ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(3058,plain,
! [SV196: $i,SV784: $i] :
( ( ! [SY1347: $i] :
( ~ ~ ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1347 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SY1348: $i] :
( ~ ( in @ SY1348 @ SV784 )
| ( in @ SY1348 @ SY1347 ) )
| ! [SY1349: $i] :
( ~ ( in @ SY1349 @ SY1347 )
| ( in @ SY1349 @ SV784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3059,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) )
| ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2914]) ).
thf(3060,plain,
! [SV199: $i,SV428: $i > $o,SV572: $i] :
( ( ( ~ ( in @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) @ SV199 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2915]) ).
thf(3061,plain,
! [SV199: $i,SV572: $i,SV428: $i > $o] :
( ( ( ~ ( SV428 @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) )
| ( ( sK56_SY1161 @ SV572 @ SV428 @ SV199 )
= SV572 ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2915]) ).
thf(3062,plain,
! [SV430: $i,SV201: $i] :
( ( ( ~ ( in @ ( sK57_SY947 @ SV201 @ SV430 ) @ SV430 ) )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(3063,plain,
! [SV430: $i,SV201: $i] :
( ( ( in @ ( sK57_SY947 @ SV201 @ SV430 ) @ SV201 )
= $false )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2916]) ).
thf(3064,plain,
! [SV430: $i,SV201: $i] :
( ( ( in @ ( sK49_SY947 @ SV201 @ SV430 ) @ SV430 )
= $true )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV430 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(3065,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
| ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) ) )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2919]) ).
thf(3066,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ( SV209 @ ( sK71_SY1260 @ SV667 @ SV209 ) )
| ( SV667
= ( sK71_SY1260 @ SV667 @ SV209 ) ) )
= $false )
| ( ( SV209 @ SV667 )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2920]) ).
thf(3067,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( sK50_SY972 @ SV219 @ SV444 ) )
| ~ ( in @ ( sK50_SY972 @ SV219 @ SV444 ) @ SV219 ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3068,plain,
! [SV219: $i,SV773: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV773 )
| ~ ( in @ SV773 @ SV219 ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2924]) ).
thf(3069,plain,
! [SV220: $i,SV445: $i] :
( ( ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV220 )
= $true )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2925]) ).
thf(3070,plain,
! [SV220: $i,SV445: $i] :
( ( ( in @ ( sK36_SY974 @ SV445 @ SV220 ) @ SV445 )
= $true )
| ( ( ( binintersect @ SV220 @ SV445 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(3071,plain,
! [SV669: $i,SV447: $i,SV222: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) ) )
= $true )
| ( ( ~ ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) ) )
= $true )
| ( ( in @ SV760 @ SV222 )
= $false )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2927]) ).
thf(3072,plain,
! [SV224: $i,SV670: $i,SV449: $i,SV761: $i] :
( ( ( ~ ~ ( in @ SV761 @ SV449 ) )
= $true )
| ( ( ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2928]) ).
thf(3073,plain,
( ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2929]) ).
thf(3074,plain,
( ( ~ ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2929]) ).
thf(3075,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
| ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2933]) ).
thf(3076,plain,
! [SV762: $i,SV672: $i,SV228: $i,SV452: $i] :
( ( ( ~ ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) ) )
= $true )
| ( ( ~ ( in @ SV762 @ SV672 )
| ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( in @ SV762 @ SV228 )
= $false )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3077,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| SV623 ) )
= $true )
| ( SV623 = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3078,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| SV623 )
= $false )
| ( SV623 = $true )
| ( SV623 = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2939]) ).
thf(3079,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3080,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3081,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( ~ ( in @ SV595 @ SV459 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2942]) ).
thf(3082,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2943]) ).
thf(3083,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(3084,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) )
= $false )
| ( ( ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3085,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2945]) ).
thf(3086,plain,
! [SV239: $i,SV763: $i,SV673: $i,SV463: $i > $o] :
( ( ( ~ ( SV463 @ SV673 ) )
= $true )
| ( ( ~ ( SV463 @ SV763 )
| ( SV673 = SV763 ) )
= $true )
| ( ( in @ SV763 @ SV239 )
= $false )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3087,plain,
! [SV242: $i,SV466: $i,SV674: $i,SV764: $i] :
( ( ( ~ ~ ( in @ SV764 @ SV674 ) )
= $true )
| ( ( ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV764 @ SV242 )
= $false )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3088,plain,
! [SV247: $i,SV471: $i,SV604: $i,SV739: $i] :
( ( ( ~ ( in @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) @ SV247 )
| ( ( ap @ SV247 @ SV471 @ SV604 @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) )
= ( ap @ SV247 @ SV471 @ SV739 @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) ) ) )
= $false )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2948]) ).
thf(3089,plain,
! [SV249: $i,SV675: $i,SV473: $i,SV765: $i] :
( ( ( ~ ~ ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) ) )
= $true )
| ( ( ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV765 @ SV249 )
= $false )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2949]) ).
thf(3090,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( ~ ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 ) )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(3091,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( ~ ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
| ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 ) )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2950]) ).
thf(3092,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( in @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SV260 )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2951]) ).
thf(3093,plain,
! [SV260: $i,SV609: $i,SV483: $i] :
( ( ( ~ ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3094,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV484 )
| ( SV678 @ SV785 ) )
= $true )
| ( ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2953]) ).
thf(3095,plain,
! [SV261: $i,SV678: $i > $o,SV484: $i,SV1: $i] :
( ( ( ~ ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2954]) ).
thf(3096,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
| ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2954]) ).
thf(3097,plain,
! [SV262: $i,SV679: $i,SV2: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ SV2 ) )
= $true )
| ( ( in @ SV679 @ SV262 )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3098,plain,
! [SV2: $i,SV625: $i,SV262: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV262 ) )
= $true )
| ( ( in @ SV625 @ SV2 )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2956]) ).
thf(3099,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( ~ ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3100,plain,
! [SV5: $i,SV486: $i,SV680: $i,SV265: $i] :
( ( ( ! [SY1343: $i] :
( ~ ( in @ SY1343 @ SV265 )
| ~ ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SY1343 ) @ SV486 )
| ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SY1343 ) @ SV680 ) ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2957]) ).
thf(3101,plain,
! [SV9: $i,SV626: $i] :
( ( ( in @ ( sK38_SY30 @ SV626 @ SV9 ) @ SV9 )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(3102,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2959]) ).
thf(3103,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ~ ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3104,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3105,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(3106,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3107,plain,
! [SV13: $i > $o,SV629: $i] :
( ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3108,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3109,plain,
! [SV681: $o,SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
| SV681 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3110,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3111,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3112,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
| $true )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3113,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3114,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3115,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
| $false )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3116,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3117,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3118,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2977]) ).
thf(3119,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2978]) ).
thf(3120,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3121,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2980]) ).
thf(3122,plain,
! [SV19: $i > $o,SV630: $i] :
( ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2980]) ).
thf(3123,plain,
! [SV21: $i,SV743: $i,SV631: $i,SV273: $i] :
( ( ( in @ SV273 @ ( powerset @ SV631 ) )
= $false )
| ( ( ~ ( in @ SV743 @ SV273 )
| ( in @ SV743 @ SV631 ) )
= $true )
| ( ( in @ SV743 @ SV21 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3124,plain,
! [SV283: $i,SV31: $i,SV496: $i,SV766: $i,SV683: $i] :
( ( ( ~ ( in @ ( kpair @ SV683 @ SV766 ) @ SV496 ) )
= $true )
| ( ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SV766 )
= $true )
| ( ( in @ SV766 @ SV283 )
= $false )
| ( ( in @ SV683 @ SV31 )
= $false )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2983]) ).
thf(3125,plain,
! [SV293: $i,SV632: $i,SV41: $i,SV774: $i] :
( ( ( in @ SV774 @ SV41 )
= $false )
| ( ( ~ ( in @ SV774 @ SV632 )
| ( in @ SV774 @ ( setminus @ SV41 @ SV293 ) ) )
= $true )
| ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3126,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( ~ ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
| ~ ( ~ ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) )
| ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3127,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) )
= $true )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3128,plain,
! [SV50: $i,SV634: $i,SV300: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ SV300 ) )
= $false )
| ( ( ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV747 @ SV50 )
= $false )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3129,plain,
! [SV303: $i > $o,SV55: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV55 )
| ~ ( SV303 @ SV786 ) )
= $true )
| ( ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3130,plain,
! [SV303: $i > $o,SV55: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV55 )
| ~ ( SV303 @ SV787 ) )
= $true )
| ( ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3131,plain,
! [SV748: $i,SV636: $i,SV310: $i,SV62: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV779 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SV779 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3132,plain,
! [SV63: $i,SV688: $i,SV311: $i > $o] :
( ( ( SV311 @ SV688 )
= $true )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( ~ ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2995]) ).
thf(3133,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV68 )
= $true )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2996]) ).
thf(3134,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( ~ ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV313 ) )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2997]) ).
thf(3135,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV637 )
= $false )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2997]) ).
thf(3136,plain,
! [SV74: $i,SV319: $i] :
( ( ( ~ ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 ) )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3137,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $false )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2998]) ).
thf(3138,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $true )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $false )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3139,plain,
! [SV321: $i > $o,SV76: $i,SV780: $i] :
( ( ( ~ ( ~ ( in @ SV780 @ SV76 )
| ~ ( SV321 @ SV780 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3140,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3002]) ).
thf(3141,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3142,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3004]) ).
thf(3143,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3005]) ).
thf(3144,plain,
! [SV77: $i,SV749: $i,SV638: $i,SV322: $i] :
( ( ( subset @ SV322 @ SV638 )
= $false )
| ( ( ~ ~ ( in @ SV749 @ SV638 )
| ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3145,plain,
! [SV690: $i,SV327: $i > $o,SV83: $i] :
( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV690 @ SV83 )
= $false )
| ( ( SV327 @ SV690 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3007]) ).
thf(3146,plain,
! [SV330: $i,SV86: $i,SV524: $i,SV768: $i,SV695: $i] :
( ( ( ~ ( in @ ( kpair @ SV695 @ SV768 ) @ SV524 ) )
= $true )
| ( ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SV768 )
= $true )
| ( ( in @ SV768 @ SV330 )
= $false )
| ( ( in @ SV695 @ SV86 )
= $false )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3147,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3148,plain,
! [SV89: $i > $o,SV639: $i] :
( ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3009]) ).
thf(3149,plain,
! [SV640: $i,SV341: $i,SV96: $i,SV751: $i] :
( ( ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
= $false )
| ( ( ~ ( in @ SV751 @ SV341 ) )
= $true )
| ( ( in @ SV751 @ SV96 )
= $false )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3150,plain,
! [SV752: $i,SV643: $i,SV346: $i,SV102: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ SV102 ) )
= $true )
| ( ( ~ ( in @ SV781 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SV781 @ ( binunion @ SV346 @ SV752 ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3011]) ).
thf(3151,plain,
! [SV753: $i,SV644: $i,SV352: $i,SV110: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ SV110 ) )
= $true )
| ( ( ~ ( in @ SV782 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SV782 @ ( binunion @ SV644 @ SV753 ) ) )
= $true )
| ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3152,plain,
! [SV359: $i > $o,SV117: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV117 )
| ~ ( SV359 @ SV775 ) )
= $true )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3153,plain,
! [SV359: $i > $o,SV117: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV117 )
| ~ ( SV359 @ SV776 ) )
= $true )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3017]) ).
thf(3154,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i] :
( ( ( ~ ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3155,plain,
! [SV705: $i,SV537: $i,SV360: $i,SV118: $i] :
( ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3156,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( ~ ( in @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SV126 ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3157,plain,
! [SV126: $i,SV540: $i,SV707: $i,SV366: $i] :
( ( ( ! [SY1346: $i] :
( ~ ( in @ SY1346 @ SV366 )
| ~ ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SY1346 ) @ SV540 )
| ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SY1346 ) @ SV707 ) ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3019]) ).
thf(3158,plain,
! [SV371: $i > $o,SV131: $i,SV783: $i] :
( ( ( ~ ( ~ ( in @ SV783 @ SV131 )
| ~ ( SV371 @ SV783 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3159,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3022]) ).
thf(3160,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3023]) ).
thf(3161,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3024]) ).
thf(3162,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3163,plain,
! [SV649: $i,SV376: $i,SV136: $i,SV754: $i] :
( ( ( in @ SV754 @ ( setminus @ SV136 @ ( binunion @ SV376 @ SV649 ) ) )
= $false )
| ( ( in @ SV754 @ ( setminus @ SV136 @ SV376 ) )
= $true )
| ( ( in @ SV754 @ SV136 )
= $false )
| ( ( in @ SV649 @ ( powerset @ SV136 ) )
= $false )
| ( ( in @ SV376 @ ( powerset @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3164,plain,
! [SV377: $i,SV708: $i > $o,SV650: $i > $o,SV137: $i] :
( ( ( ~ ( in @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3165,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
!= ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ~ ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
| ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3028]) ).
thf(3166,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) ) )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3167,plain,
! [SV146: $i > $o,SV653: $i] :
( ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3168,plain,
! [SV147: $i,SV654: $i,SV384: $i,SV755: $i] :
( ( ( ~ ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) ) )
= $false )
| ( ( ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV755 @ SV147 )
= $false )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3169,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3031]) ).
thf(3170,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( ~ ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV385 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3171,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV655 )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3032]) ).
thf(3172,plain,
! [SV158: $i] :
( ( ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3173,plain,
! [SV158: $i] :
( ( ( ~ ( in @ ( sK43_SY395 @ SV158 ) @ SV158 ) )
= $false )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3174,plain,
! [SV158: $i,SV777: $i] :
( ( ( in @ SV777 @ omega )
= $false )
| ( ( in @ SV777 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( setadjoin @ ( sK43_SY395 @ SV158 ) @ ( sK43_SY395 @ SV158 ) ) @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3175,plain,
! [SV659: $i,SV402: $i,SV168: $i,SV757: $i] :
( ( ( in @ SV757 @ ( setminus @ SV168 @ SV402 ) )
= $false )
| ( ( in @ SV757 @ ( setminus @ SV168 @ ( binintersect @ SV402 @ SV659 ) ) )
= $true )
| ( ( in @ SV757 @ SV168 )
= $false )
| ( ( in @ SV659 @ ( powerset @ SV168 ) )
= $false )
| ( ( in @ SV402 @ ( powerset @ SV168 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3176,plain,
! [SV403: $i > $o,SV169: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV169 )
| ~ ( SV403 @ SV788 ) )
= $true )
| ( ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3040]) ).
thf(3177,plain,
! [SV403: $i > $o,SV169: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV169 )
| ~ ( SV403 @ SV789 ) )
= $true )
| ( ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3178,plain,
! [SV175: $i,SV409: $i,SV563: $i,SV716: $i] :
( ( ( ~ ( in @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) @ SV175 ) )
= $false )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3179,plain,
! [SV716: $i,SV563: $i,SV409: $i,SV175: $i] :
( ( ( ( ap @ SV175 @ SV409 @ SV563 @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) )
= ( ap @ SV175 @ SV409 @ SV716 @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) ) )
= $false )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3042]) ).
thf(3180,plain,
! [SV181: $i,SV758: $o,SV661: $i,SV413: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3181,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV771 @ SV413 )
| $true )
| ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3182,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV772 @ SV413 )
| $false )
| ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3045]) ).
thf(3183,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3184,plain,
! [SV182: $i > $o,SV662: $i] :
( ( ( SV662
= ( sK68_SY1258 @ SV662 @ SV182 ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3046]) ).
thf(3185,plain,
! [SV191: $i,SV421: $i > $o,SV719: $i] :
( ( ( ~ ( in @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) @ SV191 )
| ~ ~ ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3186,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ SV570 )
| ( SV720 @ SV790 ) )
= $true )
| ( ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3187,plain,
! [SV423: $i,SV720: $i > $o,SV570: $i,SV193: $i] :
( ( ( ~ ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3188,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
| ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3049]) ).
thf(3189,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| SV721 )
= $false )
| ( SV721 = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3190,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( SV721 = $true )
| ( SV721 = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3191,plain,
! [SV424: $i,SV194: $i,SV571: $i,SV721: $o] :
( ( SV721 = $false )
| ( SV721 = $true )
| ( SV721 = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3051]) ).
thf(3192,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3193,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3194,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3053]) ).
thf(3195,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3196,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3197,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3198,plain,
! [SV195: $i,SV425: $i > $o,SV722: $i] :
( ( ( ~ ( in @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) @ SV195 )
| ~ ~ ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3199,plain,
! [SV196: $i] :
( ( ~ ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3200,plain,
! [SV196: $i] :
( ( ~ ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3201,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ~ ~ ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) )
| ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3202,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) ) )
= $true )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3059]) ).
thf(3203,plain,
! [SV199: $i,SV428: $i > $o,SV572: $i] :
( ( ( in @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) @ SV199 )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3204,plain,
! [SV199: $i,SV572: $i,SV428: $i > $o] :
( ( ( ~ ( SV428 @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3205,plain,
! [SV199: $i,SV428: $i > $o,SV572: $i] :
( ( ( ( sK56_SY1161 @ SV572 @ SV428 @ SV199 )
= SV572 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3061]) ).
thf(3206,plain,
! [SV430: $i,SV201: $i] :
( ( ( in @ ( sK57_SY947 @ SV201 @ SV430 ) @ SV430 )
= $true )
| ( ( SV201 = SV430 )
= $true )
| ( ( in @ ( sK17_SY946 @ SV430 @ SV201 ) @ SV201 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3062]) ).
thf(3207,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) ) )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3208,plain,
! [SV205: $i > $o,SV666: $i] :
( ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3065]) ).
thf(3209,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( ~ ( SV209 @ ( sK71_SY1260 @ SV667 @ SV209 ) ) )
= $false )
| ( ( SV209 @ SV667 )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3210,plain,
! [SV209: $i > $o,SV667: $i] :
( ( ( SV667
= ( sK71_SY1260 @ SV667 @ SV209 ) )
= $false )
| ( ( SV209 @ SV667 )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3066]) ).
thf(3211,plain,
! [SV219: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ ( sK50_SY972 @ SV219 @ SV444 ) ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3212,plain,
! [SV444: $i,SV219: $i] :
( ( ( ~ ( in @ ( sK50_SY972 @ SV219 @ SV444 ) @ SV219 ) )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3067]) ).
thf(3213,plain,
! [SV219: $i,SV773: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV773 ) )
= $true )
| ( ( ~ ( in @ SV773 @ SV219 ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3068]) ).
thf(3214,plain,
! [SV669: $i,SV447: $i,SV222: $i,SV760: $i] :
( ( ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) )
= $false )
| ( ( ~ ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) ) )
= $true )
| ( ( in @ SV760 @ SV222 )
= $false )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3215,plain,
! [SV224: $i,SV670: $i,SV449: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV449 ) )
= $false )
| ( ( ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3072]) ).
thf(3216,plain,
( ( in @ sK4_SY5 @ ( setminus @ sK1_A @ ( binunion @ sK2_SY0 @ sK3_SY3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3217,plain,
( ( ~ ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3218,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3219,plain,
! [SV227: $i > $o,SV671: $i] :
( ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3220,plain,
! [SV762: $i,SV672: $i,SV228: $i,SV452: $i] :
( ( ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
= $false )
| ( ( ~ ( in @ SV762 @ SV672 )
| ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( in @ SV762 @ SV228 )
= $false )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3221,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| SV623 )
= $false )
| ( SV623 = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3222,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( SV623 = $true )
| ( SV623 = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3223,plain,
! [SV459: $i,SV235: $i,SV595: $i,SV623: $o] :
( ( SV623 = $false )
| ( SV623 = $true )
| ( SV623 = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3078]) ).
thf(3224,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3225,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3226,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3080]) ).
thf(3227,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3228,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3229,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3082]) ).
thf(3230,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( ~ ~ ( ~ ( SV237 @ SV792 )
| ~ ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3231,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( ~ ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3232,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3233,plain,
! [SV239: $i,SV763: $i,SV673: $i,SV463: $i > $o] :
( ( ( SV463 @ SV673 )
= $false )
| ( ( ~ ( SV463 @ SV763 )
| ( SV673 = SV763 ) )
= $true )
| ( ( in @ SV763 @ SV239 )
= $false )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3234,plain,
! [SV242: $i,SV466: $i,SV674: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV674 ) )
= $false )
| ( ( ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV764 @ SV242 )
= $false )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3087]) ).
thf(3235,plain,
! [SV247: $i,SV471: $i,SV604: $i,SV739: $i] :
( ( ( ~ ( in @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) @ SV247 ) )
= $false )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3236,plain,
! [SV739: $i,SV604: $i,SV471: $i,SV247: $i] :
( ( ( ( ap @ SV247 @ SV471 @ SV604 @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) )
= ( ap @ SV247 @ SV471 @ SV739 @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) ) )
= $false )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3088]) ).
thf(3237,plain,
! [SV249: $i,SV675: $i,SV473: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) ) )
= $false )
| ( ( ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV765 @ SV249 )
= $false )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3238,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3090]) ).
thf(3239,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( ~ ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 ) )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3240,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3091]) ).
thf(3241,plain,
! [SV260: $i,SV609: $i,SV483: $i] :
( ( ( ! [SY1318: $i] :
~ ~ ( ~ ( in @ SY1318 @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ SY1318 ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3093]) ).
thf(3242,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV484 ) )
= $true )
| ( ( SV678 @ SV785 )
= $true )
| ( ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3243,plain,
! [SV261: $i,SV678: $i > $o,SV484: $i,SV1: $i] :
( ( ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 )
= $true )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3095]) ).
thf(3244,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3245,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3246,plain,
! [SV262: $i,SV679: $i,SV2: $i,SV625: $i] :
( ( ( in @ SV625 @ SV2 )
= $false )
| ( ( in @ SV679 @ SV262 )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3097]) ).
thf(3247,plain,
! [SV2: $i,SV625: $i,SV262: $i,SV679: $i] :
( ( ( in @ SV679 @ SV262 )
= $false )
| ( ( in @ SV625 @ SV2 )
= $true )
| ( ( SV625 = SV679 )
= $false )
| ( ( SV2 = SV262 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3248,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3099]) ).
thf(3249,plain,
! [SV265: $i,SV680: $i,SV486: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
| ~ ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
| ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3100]) ).
thf(3250,plain,
! [SV9: $i,SV626: $i] :
( ( ( ~ ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3251,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
| ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3252,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3253,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3104]) ).
thf(3254,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $false )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3255,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3106]) ).
thf(3256,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $false )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3257,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3258,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3108]) ).
thf(3259,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 ) )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3260,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3261,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3262,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3263,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3264,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3265,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3113]) ).
thf(3266,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3113]) ).
thf(3267,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3268,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3114]) ).
thf(3269,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3115]) ).
thf(3270,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3271,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3116]) ).
thf(3272,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3273,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3274,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
| ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3119]) ).
thf(3275,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3276,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3120]) ).
thf(3277,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( ~ ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3121]) ).
thf(3278,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3279,plain,
! [SV21: $i,SV631: $i,SV273: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV273 ) )
= $true )
| ( ( in @ SV743 @ SV631 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV631 ) )
= $false )
| ( ( in @ SV743 @ SV21 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3280,plain,
! [SV283: $i,SV31: $i,SV496: $i,SV766: $i,SV683: $i] :
( ( ( in @ ( kpair @ SV683 @ SV766 ) @ SV496 )
= $false )
| ( ( ( ap @ SV31 @ SV283 @ SV496 @ SV683 )
= SV766 )
= $true )
| ( ( in @ SV766 @ SV283 )
= $false )
| ( ( in @ SV683 @ SV31 )
= $false )
| ( ( in @ SV496 @ ( funcSet @ SV31 @ SV283 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3281,plain,
! [SV293: $i,SV41: $i,SV632: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ SV632 ) )
= $true )
| ( ( in @ SV774 @ ( setminus @ SV41 @ SV293 ) )
= $true )
| ( ( in @ SV774 @ SV41 )
= $false )
| ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3125]) ).
thf(3282,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( ~ ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3283,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ( ~ ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) )
| ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3126]) ).
thf(3284,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ! [SY1321: $i] :
( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SY1321 )
| ( SV746 = SY1321 ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3285,plain,
! [SV50: $i,SV634: $i,SV300: $i,SV747: $i] :
( ( ( in @ SV747 @ SV300 )
= $true )
| ( ( ~ ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) ) )
= $true )
| ( ( in @ SV747 @ SV50 )
= $false )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3286,plain,
! [SV303: $i > $o,SV55: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ SV55 ) )
= $true )
| ( ( ~ ( SV303 @ SV786 ) )
= $true )
| ( ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3287,plain,
! [SV303: $i > $o,SV55: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV55 ) )
= $true )
| ( ( ~ ( SV303 @ SV787 ) )
= $true )
| ( ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3288,plain,
! [SV748: $i,SV636: $i,SV310: $i,SV62: $i,SV779: $i] :
( ( ( in @ SV779 @ SV62 )
= $false )
| ( ( ~ ( in @ SV779 @ ( binintersect @ SV310 @ SV636 ) )
| ( in @ SV779 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3289,plain,
! [SV688: $i,SV311: $i > $o,SV63: $i] :
( ( ( ! [SY758: $i] :
( ~ ( in @ SY758 @ SV63 )
| ( SV311 @ SY758 ) ) )
= $false )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( SV311 @ SV688 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3132]) ).
thf(3290,plain,
! [SV68: $i,SV313: $i,SV637: $i] :
( ( ( in @ ( sK52_SY1231 @ SV637 @ SV313 @ SV68 ) @ SV313 )
= $true )
| ( ( subset @ SV313 @ SV637 )
= $true )
| ( ( in @ SV637 @ ( powerset @ SV68 ) )
= $false )
| ( ( in @ SV313 @ ( powerset @ SV68 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3134]) ).
thf(3291,plain,
! [SV74: $i,SV319: $i] :
( ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV319 )
= $true )
| ( ( in @ ( sK11_SY768 @ SV319 @ SV74 ) @ SV74 )
= $true )
| ( ( SV74 = SV319 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3292,plain,
! [SV321: $i > $o,SV76: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV76 )
| ~ ( SV321 @ SV780 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3293,plain,
! [SV321: $i > $o,SV76: $i,SV793: $i] :
( ( ( ~ ~ ( ~ ( in @ SV793 @ SV76 )
| ~ ( SV321 @ SV793 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3140]) ).
thf(3294,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3141]) ).
thf(3295,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ~ ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3296,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3143]) ).
thf(3297,plain,
! [SV77: $i,SV322: $i,SV638: $i,SV749: $i] :
( ( ( ~ ~ ( in @ SV749 @ SV638 ) )
= $true )
| ( ( ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( subset @ SV322 @ SV638 )
= $false )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3298,plain,
! [SV690: $i,SV327: $i > $o,SV83: $i] :
( ( ( ( dsetconstr @ SV83
@ ^ [SY780: $i] : ( SV327 @ SY780 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV690 @ SV83 )
= $false )
| ( ( SV327 @ SV690 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3299,plain,
! [SV330: $i,SV86: $i,SV524: $i,SV768: $i,SV695: $i] :
( ( ( in @ ( kpair @ SV695 @ SV768 ) @ SV524 )
= $false )
| ( ( ( ap @ SV86 @ SV330 @ SV524 @ SV695 )
= SV768 )
= $true )
| ( ( in @ SV768 @ SV330 )
= $false )
| ( ( in @ SV695 @ SV86 )
= $false )
| ( ( func @ SV86 @ SV330 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3146]) ).
thf(3300,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( ~ ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3147]) ).
thf(3301,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3302,plain,
! [SV640: $i,SV96: $i,SV341: $i,SV751: $i] :
( ( ( in @ SV751 @ SV341 )
= $false )
| ( ( in @ SV751 @ ( setminus @ SV96 @ ( binunion @ SV341 @ SV640 ) ) )
= $false )
| ( ( in @ SV751 @ SV96 )
= $false )
| ( ( in @ SV640 @ ( powerset @ SV96 ) )
= $false )
| ( ( in @ SV341 @ ( powerset @ SV96 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3303,plain,
! [SV752: $i,SV643: $i,SV346: $i,SV102: $i,SV781: $i] :
( ( ( in @ SV781 @ SV102 )
= $false )
| ( ( ~ ( in @ SV781 @ ( binintersect @ SV346 @ SV643 ) )
| ( in @ SV781 @ ( binunion @ SV346 @ SV752 ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3304,plain,
! [SV753: $i,SV644: $i,SV352: $i,SV110: $i,SV782: $i] :
( ( ( in @ SV782 @ SV110 )
= $false )
| ( ( ~ ( in @ SV782 @ ( binintersect @ SV352 @ SV644 ) )
| ( in @ SV782 @ ( binunion @ SV644 @ SV753 ) ) )
= $true )
| ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3151]) ).
thf(3305,plain,
! [SV359: $i > $o,SV117: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ SV117 ) )
= $true )
| ( ( ~ ( SV359 @ SV775 ) )
= $true )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3306,plain,
! [SV359: $i > $o,SV117: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ SV117 ) )
= $true )
| ( ( ~ ( SV359 @ SV776 ) )
= $true )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3153]) ).
thf(3307,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i] :
( ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV118 )
| ! [SY1292: $i] :
( ~ ( in @ SY1292 @ SV360 )
| ~ ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV705 )
| ( in @ ( kpair @ SY1291 @ SY1292 ) @ SV537 ) ) ) )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3154]) ).
thf(3308,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV118 )
| ! [SY1353: $i] :
( ~ ( in @ SY1353 @ SV360 )
| ~ ( in @ ( kpair @ SV794 @ SY1353 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SY1353 ) @ SV537 ) ) )
= $true )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3155]) ).
thf(3309,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( in @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ SV126 )
= $true )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3310,plain,
! [SV366: $i,SV707: $i,SV540: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) @ SV366 )
| ~ ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV540 )
| ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV707 ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3157]) ).
thf(3311,plain,
! [SV371: $i > $o,SV131: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV131 )
| ~ ( SV371 @ SV783 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3312,plain,
! [SV371: $i > $o,SV131: $i,SV795: $i] :
( ( ( ~ ~ ( ~ ( in @ SV795 @ SV131 )
| ~ ( SV371 @ SV795 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3159]) ).
thf(3313,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3314,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ~ ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3161]) ).
thf(3315,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3316,plain,
! [SV377: $i,SV708: $i > $o,SV650: $i > $o,SV137: $i] :
( ( ( in @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) @ SV377 )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3317,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
!= ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3318,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
| ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3319,plain,
! [SV653: $i,SV146: $i > $o] :
( ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( ! [SY362: $i,SY363: $i] :
( ~ ( SV146 @ SY362 )
| ~ ( SV146 @ SY363 )
| ( SY362 = SY363 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3320,plain,
! [SV653: $i,SV796: $i,SV146: $i > $o] :
( ( ( ! [SY1354: $i] :
( ~ ( SV146 @ SV796 )
| ~ ( SV146 @ SY1354 )
| ( SV796 = SY1354 ) ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3167]) ).
thf(3321,plain,
! [SV147: $i,SV654: $i,SV384: $i,SV755: $i] :
( ( ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) )
= $true )
| ( ( ~ ( in @ SV755 @ SV654 ) )
= $true )
| ( ( in @ SV755 @ SV147 )
= $false )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3168]) ).
thf(3322,plain,
! [SV148: $i,SV385: $i,SV655: $i] :
( ( ( in @ ( sK53_SY1250 @ SV655 @ SV385 @ SV148 ) @ SV385 )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV655 ) )
= $true )
| ( ( in @ SV655 @ ( powerset @ SV148 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV148 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3170]) ).
thf(3323,plain,
! [SV158: $i] :
( ( ( in @ ( sK43_SY395 @ SV158 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3172]) ).
thf(3324,plain,
! [SV158: $i] :
( ( ( in @ ( sK43_SY395 @ SV158 ) @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( ! [SY396: $i] :
( ~ ( in @ SY396 @ omega )
| ( in @ SY396 @ SV158 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3173]) ).
thf(3325,plain,
! [SV403: $i > $o,SV169: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV169 ) )
= $true )
| ( ( ~ ( SV403 @ SV788 ) )
= $true )
| ( ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3176]) ).
thf(3326,plain,
! [SV403: $i > $o,SV169: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV169 ) )
= $true )
| ( ( ~ ( SV403 @ SV789 ) )
= $true )
| ( ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3327,plain,
! [SV175: $i,SV409: $i,SV563: $i,SV716: $i] :
( ( ( in @ ( sK67_SY1302 @ SV716 @ SV563 @ SV409 @ SV175 ) @ SV175 )
= $true )
| ( ( SV563 = SV716 )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV175 @ SV409 ) )
= $false )
| ( ( in @ SV563 @ ( funcSet @ SV175 @ SV409 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3328,plain,
! [SV181: $i,SV758: $o,SV661: $i,SV413: $i,SV770: $i] :
( ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 )
| ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3329,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV771 @ SV413 )
| $true )
| ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3330,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV772 @ SV413 )
| $false )
| ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3331,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) )
= $true )
| ( ( SV182 @ SV662 )
= $false )
| ( ( ~ ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3332,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV662
= ( sK68_SY1258 @ SV662 @ SV182 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3333,plain,
! [SV191: $i,SV421: $i > $o,SV719: $i] :
( ( ( ~ ( in @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) @ SV191 ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3334,plain,
! [SV191: $i,SV719: $i,SV421: $i > $o] :
( ( ( ~ ~ ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3335,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ SV570 ) )
= $true )
| ( ( SV720 @ SV790 )
= $true )
| ( ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3186]) ).
thf(3336,plain,
! [SV423: $i,SV720: $i > $o,SV570: $i,SV193: $i] :
( ( ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 )
= $true )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3337,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3338,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) )
= $false )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3188]) ).
thf(3339,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( SV721 = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3340,plain,
! [SV424: $i,SV194: $i,SV571: $i,SV721: $o] :
( ( SV721 = $false )
| ( SV721 = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3189]) ).
thf(3341,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( SV721 = $true )
| ( SV721 = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3190]) ).
thf(3342,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( $true = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3343,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3344,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3193]) ).
thf(3345,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ SV424 ) )
= $false )
| ( $false = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3195]) ).
thf(3346,plain,
! [SV424: $i,SV194: $i,SV571: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3195]) ).
thf(3347,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3348,plain,
! [SV195: $i,SV425: $i > $o,SV722: $i] :
( ( ( ~ ( in @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) @ SV195 ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3198]) ).
thf(3349,plain,
! [SV195: $i,SV722: $i,SV425: $i > $o] :
( ( ( ~ ~ ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3198]) ).
thf(3350,plain,
! [SV196: $i] :
( ( ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( sK5_SY484 @ SV196 ) )
| ! [SY486: $i] :
( ~ ( in @ SY486 @ SY1144 )
| ( in @ SY486 @ SV196 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3199]) ).
thf(3351,plain,
! [SV196: $i] :
( ( ! [SY1146: $i,SY1147: $i] :
( ~ ~ ( ~ ( in @ SY1146 @ SV196 )
| ~ ( in @ SY1147 @ SV196 ) )
| ~ ! [SY1148: $i] :
( ~ ( in @ SY1148 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SY1146 @ SY1148 )
| ( in @ SY1147 @ SY1148 ) )
| ~ ( ~ ( in @ SY1147 @ SY1148 )
| ( in @ SY1146 @ SY1148 ) ) ) )
| ( SY1146 = SY1147 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3200]) ).
thf(3352,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ( ~ ~ ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) ) )
= $true )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3201]) ).
thf(3353,plain,
! [SV196: $i,SV759: $i] :
( ( ( ! [SY1327: $i] :
( ~ ( in @ SY1327 @ SV759 )
| ( in @ SY1327 @ SV196 ) ) )
= $false )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3354,plain,
! [SV199: $i,SV572: $i,SV428: $i > $o] :
( ( ( SV428 @ ( sK56_SY1161 @ SV572 @ SV428 @ SV199 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV199
@ ^ [SY944: $i] : ( SV428 @ SY944 ) ) )
= $true )
| ( ( SV428 @ SV572 )
= $false )
| ( ( in @ SV572 @ SV199 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3204]) ).
thf(3355,plain,
! [SV666: $i,SV205: $i > $o] :
( ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( ! [SY522: $i,SY523: $i] :
( ~ ( SV205 @ SY522 )
| ~ ( SV205 @ SY523 )
| ( SY522 = SY523 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3207]) ).
thf(3356,plain,
! [SV666: $i,SV797: $i,SV205: $i > $o] :
( ( ( ! [SY1355: $i] :
( ~ ( SV205 @ SV797 )
| ~ ( SV205 @ SY1355 )
| ( SV797 = SY1355 ) ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3208]) ).
thf(3357,plain,
! [SV667: $i,SV209: $i > $o] :
( ( ( SV209 @ ( sK71_SY1260 @ SV667 @ SV209 ) )
= $true )
| ( ( SV209 @ SV667 )
= $false )
| ( ( SV209
@ ( descr
@ ^ [SY528: $i] : ( SV209 @ SY528 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3358,plain,
! [SV219: $i,SV444: $i] :
( ( ( in @ SV444 @ ( sK50_SY972 @ SV219 @ SV444 ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3211]) ).
thf(3359,plain,
! [SV444: $i,SV219: $i] :
( ( ( in @ ( sK50_SY972 @ SV219 @ SV444 ) @ SV219 )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3212]) ).
thf(3360,plain,
! [SV219: $i,SV773: $i,SV444: $i] :
( ( ( in @ SV444 @ SV773 )
= $false )
| ( ( ~ ( in @ SV773 @ SV219 ) )
= $true )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3361,plain,
! [SV222: $i,SV669: $i,SV447: $i,SV760: $i] :
( ( ( in @ SV760 @ ( binintersect @ SV447 @ SV669 ) )
= $false )
| ( ( in @ SV760 @ ( setminus @ SV222 @ SV447 ) )
= $false )
| ( ( in @ SV760 @ SV222 )
= $false )
| ( ( in @ SV669 @ ( powerset @ SV222 ) )
= $false )
| ( ( in @ SV447 @ ( powerset @ SV222 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3214]) ).
thf(3362,plain,
! [SV224: $i,SV670: $i,SV449: $i,SV761: $i] :
( ( ( in @ SV761 @ SV449 )
= $true )
| ( ( ~ ~ ( in @ SV761 @ SV670 )
| ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3215]) ).
thf(3363,plain,
( ( in @ sK4_SY5 @ ( setminus @ sK1_A @ sK2_SY0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3217]) ).
thf(3364,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( ~ ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3218]) ).
thf(3365,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3219]) ).
thf(3366,plain,
! [SV228: $i,SV452: $i,SV672: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ SV672 ) )
= $true )
| ( ( ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
= $false )
| ( ( in @ SV762 @ SV228 )
= $false )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3367,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( SV623 = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3221]) ).
thf(3368,plain,
! [SV459: $i,SV235: $i,SV595: $i,SV623: $o] :
( ( SV623 = $false )
| ( SV623 = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3221]) ).
thf(3369,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( SV623 = $true )
| ( SV623 = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3222]) ).
thf(3370,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3371,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3372,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3225]) ).
thf(3373,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV459 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3227]) ).
thf(3374,plain,
! [SV459: $i,SV235: $i,SV595: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3227]) ).
thf(3375,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3376,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ SV792 )
| ~ ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3230]) ).
thf(3377,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
| ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3378,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3232]) ).
thf(3379,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3232]) ).
thf(3380,plain,
! [SV239: $i,SV673: $i,SV763: $i,SV463: $i > $o] :
( ( ( ~ ( SV463 @ SV763 ) )
= $true )
| ( ( SV673 = SV763 )
= $true )
| ( ( SV463 @ SV673 )
= $false )
| ( ( in @ SV763 @ SV239 )
= $false )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3381,plain,
! [SV242: $i,SV466: $i,SV674: $i,SV764: $i] :
( ( ( in @ SV764 @ SV674 )
= $true )
| ( ( ~ ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) ) )
= $true )
| ( ( in @ SV764 @ SV242 )
= $false )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3234]) ).
thf(3382,plain,
! [SV247: $i,SV471: $i,SV604: $i,SV739: $i] :
( ( ( in @ ( sK73_SY1313 @ SV739 @ SV604 @ SV471 @ SV247 ) @ SV247 )
= $true )
| ( ( SV604 = SV739 )
= $true )
| ( ( func @ SV247 @ SV471 @ SV739 )
= $false )
| ( ( func @ SV247 @ SV471 @ SV604 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3383,plain,
! [SV249: $i,SV675: $i,SV473: $i,SV765: $i] :
( ( ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) )
= $true )
| ( ( ~ ( in @ SV765 @ SV473 ) )
= $true )
| ( ( in @ SV765 @ SV249 )
= $false )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3237]) ).
thf(3384,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3385,plain,
! [SV259: $i,SV482: $i,SV677: $i] :
( ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) )
| ( SV482 = SV677 ) )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3239]) ).
thf(3386,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3387,plain,
! [SV483: $i,SV609: $i,SV260: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3241]) ).
thf(3388,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV785: $i] :
( ( ( in @ SV785 @ SV484 )
= $false )
| ( ( SV678 @ SV785 )
= $true )
| ( ( in @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ SV1 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3242]) ).
thf(3389,plain,
! [SV261: $i,SV1: $i,SV678: $i > $o,SV484: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV484 )
| ( SV678 @ SV798 ) )
= $true )
| ( ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3390,plain,
! [SV1: $i,SV261: $i,SV484: $i,SV678: $i > $o] :
( ( ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
= $true )
| ( ( ! [SY1276: $i] :
( ~ ( in @ SY1276 @ SV484 )
| ( SV678 @ SY1276 ) ) )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3244]) ).
thf(3391,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV484 )
| ( SV678 @ SV799 ) )
= $true )
| ( ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) )
= $false )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3245]) ).
thf(3392,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3248]) ).
thf(3393,plain,
! [SV265: $i,SV680: $i,SV486: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3394,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
| ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3395,plain,
! [SV9: $i,SV626: $i] :
( ( ( ! [SY1319: $i] :
~ ~ ( ~ ( in @ SY1319 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SY1319 @ SV9 ) ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3250]) ).
thf(3396,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
!= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3397,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3398,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3252]) ).
thf(3399,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3400,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ~ ( ~ ( SV13 @ ( sK77_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1356: $i] :
( ~ ( SV13 @ SY1356 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SY1356 ) ) ) )
= $false )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3254]) ).
thf(3401,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY44: $i] :
~ ~ ( ~ ( SV13 @ SY44 )
| ~ ! [SY45: $i] :
( ~ ( SV13 @ SY45 )
| ( SY44 = SY45 ) ) ) )
= $false )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3402,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ~ ( ~ ( SV13 @ ( sK78_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1357: $i] :
( ~ ( SV13 @ SY1357 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SY1357 ) ) ) )
= $false )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3256]) ).
thf(3403,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3257]) ).
thf(3404,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3258]) ).
thf(3405,plain,
! [SV269: $i,SV14: $i,SV488: $i,SV681: $o] :
( ( SV681 = $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3258]) ).
thf(3406,plain,
! [SV681: $o,SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3407,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3260]) ).
thf(3408,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3409,plain,
! [SV269: $i,SV14: $i,SV488: $i,SV681: $o] :
( ( SV681 = $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3410,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3262]) ).
thf(3411,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3263]) ).
thf(3412,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3263]) ).
thf(3413,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3264]) ).
thf(3414,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3265]) ).
thf(3415,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3266]) ).
thf(3416,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3266]) ).
thf(3417,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3267]) ).
thf(3418,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3419,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3268]) ).
thf(3420,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 )
| ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3269]) ).
thf(3421,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3422,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3423,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3271]) ).
thf(3424,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3272]) ).
thf(3425,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3273]) ).
thf(3426,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3427,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3428,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3275]) ).
thf(3429,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3276]) ).
thf(3430,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ! [SY64: $i] :
~ ~ ( ~ ( SV19 @ SY64 )
| ~ ! [SY65: $i] :
( ~ ( SV19 @ SY65 )
| ( SY64 = SY65 ) ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3277]) ).
thf(3431,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ~ ( ~ ( SV19 @ ( sK79_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1358: $i] :
( ~ ( SV19 @ SY1358 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SY1358 ) ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3278]) ).
thf(3432,plain,
! [SV21: $i,SV631: $i,SV273: $i,SV743: $i] :
( ( ( in @ SV743 @ SV273 )
= $false )
| ( ( in @ SV743 @ SV631 )
= $true )
| ( ( in @ SV273 @ ( powerset @ SV631 ) )
= $false )
| ( ( in @ SV743 @ SV21 )
= $false )
| ( ( in @ SV631 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV273 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3433,plain,
! [SV293: $i,SV41: $i,SV632: $i,SV774: $i] :
( ( ( in @ SV774 @ SV632 )
= $false )
| ( ( in @ SV774 @ ( setminus @ SV41 @ SV293 ) )
= $true )
| ( ( in @ SV774 @ SV41 )
= $false )
| ( ( subset @ SV293 @ ( setminus @ SV41 @ SV632 ) )
= $false )
| ( ( in @ SV632 @ ( powerset @ SV41 ) )
= $false )
| ( ( in @ SV293 @ ( powerset @ SV41 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3281]) ).
thf(3434,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
| ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3282]) ).
thf(3435,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) )
| ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3283]) ).
thf(3436,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
| ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3284]) ).
thf(3437,plain,
! [SV50: $i,SV634: $i,SV300: $i,SV747: $i] :
( ( ( in @ SV747 @ ( binintersect @ SV300 @ SV634 ) )
= $false )
| ( ( in @ SV747 @ SV300 )
= $true )
| ( ( in @ SV747 @ SV50 )
= $false )
| ( ( in @ SV634 @ ( powerset @ SV50 ) )
= $false )
| ( ( in @ SV300 @ ( powerset @ SV50 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3285]) ).
thf(3438,plain,
! [SV303: $i > $o,SV55: $i,SV786: $i] :
( ( ( in @ SV786 @ SV55 )
= $false )
| ( ( ~ ( SV303 @ SV786 ) )
= $true )
| ( ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3286]) ).
thf(3439,plain,
! [SV303: $i > $o,SV55: $i,SV787: $i] :
( ( ( in @ SV787 @ SV55 )
= $false )
| ( ( ~ ( SV303 @ SV787 ) )
= $true )
| ( ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3287]) ).
thf(3440,plain,
! [SV62: $i,SV748: $i,SV636: $i,SV310: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( binintersect @ SV310 @ SV636 ) ) )
= $true )
| ( ( in @ SV779 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) )
= $true )
| ( ( in @ SV779 @ SV62 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3441,plain,
! [SV63: $i,SV311: $i > $o,SV688: $i] :
( ( ( ~ ( in @ ( sK81_SY758 @ SV688 @ SV311 @ SV63 ) @ SV63 )
| ( SV311 @ ( sK81_SY758 @ SV688 @ SV311 @ SV63 ) ) )
= $false )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( SV311 @ SV688 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3289]) ).
thf(3442,plain,
! [SV321: $i > $o,SV76: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV76 ) )
= $true )
| ( ( ~ ( SV321 @ SV780 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3443,plain,
! [SV321: $i > $o,SV76: $i,SV793: $i] :
( ( ( ~ ( ~ ( in @ SV793 @ SV76 )
| ~ ( SV321 @ SV793 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3444,plain,
! [SV321: $i > $o,SV76: $i,SV800: $i] :
( ( ( ~ ~ ( ~ ( in @ SV800 @ SV76 )
| ~ ( SV321 @ SV800 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3294]) ).
thf(3445,plain,
! [SV321: $i > $o,SV76: $i] :
( ( ( ! [SY771: $i] :
~ ~ ( ~ ( in @ SY771 @ SV76 )
| ~ ( SV321 @ SY771 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3446,plain,
! [SV321: $i > $o,SV76: $i,SV801: $i] :
( ( ( ~ ~ ( ~ ( in @ SV801 @ SV76 )
| ~ ( SV321 @ SV801 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3296]) ).
thf(3447,plain,
! [SV77: $i,SV322: $i,SV638: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ SV638 ) )
= $false )
| ( ( ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( subset @ SV322 @ SV638 )
= $false )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3448,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ! [SY225: $i] :
~ ~ ( ~ ( SV89 @ SY225 )
| ~ ! [SY226: $i] :
( ~ ( SV89 @ SY226 )
| ( SY225 = SY226 ) ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3300]) ).
thf(3449,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK82_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1359: $i] :
( ~ ( SV89 @ SY1359 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SY1359 ) ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3301]) ).
thf(3450,plain,
! [SV102: $i,SV752: $i,SV643: $i,SV346: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ ( binintersect @ SV346 @ SV643 ) ) )
= $true )
| ( ( in @ SV781 @ ( binunion @ SV346 @ SV752 ) )
= $true )
| ( ( in @ SV781 @ SV102 )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3303]) ).
thf(3451,plain,
! [SV110: $i,SV753: $i,SV644: $i,SV352: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( binintersect @ SV352 @ SV644 ) ) )
= $true )
| ( ( in @ SV782 @ ( binunion @ SV644 @ SV753 ) )
= $true )
| ( ( in @ SV782 @ SV110 )
= $false )
| ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3452,plain,
! [SV359: $i > $o,SV117: $i,SV775: $i] :
( ( ( in @ SV775 @ SV117 )
= $false )
| ( ( ~ ( SV359 @ SV775 ) )
= $true )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3453,plain,
! [SV359: $i > $o,SV117: $i,SV776: $i] :
( ( ( in @ SV776 @ SV117 )
= $false )
| ( ( ~ ( SV359 @ SV776 ) )
= $true )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3306]) ).
thf(3454,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV118 )
| ! [SY1360: $i] :
( ~ ( in @ SY1360 @ SV360 )
| ~ ( in @ ( kpair @ SV802 @ SY1360 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SY1360 ) @ SV537 ) ) )
= $true )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3455,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV118 ) )
= $true )
| ( ( ! [SY1353: $i] :
( ~ ( in @ SY1353 @ SV360 )
| ~ ( in @ ( kpair @ SV794 @ SY1353 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SY1353 ) @ SV537 ) ) )
= $true )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3308]) ).
thf(3456,plain,
! [SV366: $i,SV707: $i,SV540: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3457,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV540 )
| ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV707 ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3310]) ).
thf(3458,plain,
! [SV371: $i > $o,SV131: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV131 ) )
= $true )
| ( ( ~ ( SV371 @ SV783 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3311]) ).
thf(3459,plain,
! [SV371: $i > $o,SV131: $i,SV795: $i] :
( ( ( ~ ( ~ ( in @ SV795 @ SV131 )
| ~ ( SV371 @ SV795 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3460,plain,
! [SV371: $i > $o,SV131: $i,SV803: $i] :
( ( ( ~ ~ ( ~ ( in @ SV803 @ SV131 )
| ~ ( SV371 @ SV803 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3313]) ).
thf(3461,plain,
! [SV371: $i > $o,SV131: $i] :
( ( ( ! [SY850: $i] :
~ ~ ( ~ ( in @ SY850 @ SV131 )
| ~ ( SV371 @ SY850 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3314]) ).
thf(3462,plain,
! [SV371: $i > $o,SV131: $i,SV804: $i] :
( ( ( ~ ~ ( ~ ( in @ SV804 @ SV131 )
| ~ ( SV371 @ SV804 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3315]) ).
thf(3463,plain,
! [SV137: $i,SV377: $i,SV650: $i > $o,SV708: $i > $o] :
( ( ( ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 )
= ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3464,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
| ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3318]) ).
thf(3465,plain,
! [SV653: $i,SV805: $i,SV146: $i > $o] :
( ( ( ! [SY1361: $i] :
( ~ ( SV146 @ SV805 )
| ~ ( SV146 @ SY1361 )
| ( SV805 = SY1361 ) ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3466,plain,
! [SV653: $i,SV806: $i,SV796: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV796 )
| ~ ( SV146 @ SV806 )
| ( SV796 = SV806 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3467,plain,
! [SV147: $i,SV384: $i,SV654: $i,SV755: $i] :
( ( ( in @ SV755 @ SV654 )
= $false )
| ( ( in @ SV755 @ ( binunion @ SV384 @ SV654 ) )
= $true )
| ( ( in @ SV755 @ SV147 )
= $false )
| ( ( in @ SV654 @ ( powerset @ SV147 ) )
= $false )
| ( ( in @ SV384 @ ( powerset @ SV147 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3321]) ).
thf(3468,plain,
! [SV158: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ omega )
| ( in @ SV807 @ SV158 ) )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3323]) ).
thf(3469,plain,
! [SV158: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ omega )
| ( in @ SV808 @ SV158 ) )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3470,plain,
! [SV403: $i > $o,SV169: $i,SV788: $i] :
( ( ( in @ SV788 @ SV169 )
= $false )
| ( ( ~ ( SV403 @ SV788 ) )
= $true )
| ( ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3471,plain,
! [SV403: $i > $o,SV169: $i,SV789: $i] :
( ( ( in @ SV789 @ SV169 )
= $false )
| ( ( ~ ( SV403 @ SV789 ) )
= $true )
| ( ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3326]) ).
thf(3472,plain,
! [SV181: $i,SV661: $i,SV758: $o,SV413: $i,SV770: $i] :
( ( ( ~ ( ~ ( in @ SV770 @ SV413 )
| SV758 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3473,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( ~ ( ~ ( in @ SV771 @ SV413 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3329]) ).
thf(3474,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( ~ ( ~ ( in @ SV772 @ SV413 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3330]) ).
thf(3475,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ! [SY451: $i] :
~ ( SV182 @ SY451 ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3476,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ ( sK83_SY451 @ SV662 @ SV182 ) ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV662
= ( sK68_SY1258 @ SV662 @ SV182 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3332]) ).
thf(3477,plain,
! [SV191: $i,SV421: $i > $o,SV719: $i] :
( ( ( in @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) @ SV191 )
= $true )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3333]) ).
thf(3478,plain,
! [SV191: $i,SV719: $i,SV421: $i > $o] :
( ( ( ~ ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) ) )
= $true )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3334]) ).
thf(3479,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV790: $i] :
( ( ( in @ SV790 @ SV570 )
= $false )
| ( ( SV720 @ SV790 )
= $true )
| ( ( in @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ SV193 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3480,plain,
! [SV423: $i,SV193: $i,SV720: $i > $o,SV570: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV570 )
| ( SV720 @ SV809 ) )
= $true )
| ( ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3336]) ).
thf(3481,plain,
! [SV193: $i,SV423: $i,SV570: $i,SV720: $i > $o] :
( ( ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
= $true )
| ( ( ! [SY1305: $i] :
( ~ ( in @ SY1305 @ SV570 )
| ( SV720 @ SY1305 ) ) )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3337]) ).
thf(3482,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ SV570 )
| ( SV720 @ SV810 ) )
= $true )
| ( ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3338]) ).
thf(3483,plain,
! [SV194: $i,SV721: $o,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( SV721 = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3339]) ).
thf(3484,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( $true = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3342]) ).
thf(3485,plain,
! [SV194: $i,SV424: $i,SV571: $i] :
( ( ( in @ SV571 @ SV424 )
= $true )
| ( $false = $true )
| ( ( SV571 = SV194 )
= $true )
| ( ( in @ SV571 @ ( setadjoin @ SV194 @ SV424 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3345]) ).
thf(3486,plain,
! [SV195: $i,SV425: $i > $o,SV722: $i] :
( ( ( in @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) @ SV195 )
= $true )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3348]) ).
thf(3487,plain,
! [SV195: $i,SV722: $i,SV425: $i > $o] :
( ( ( ~ ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) ) )
= $true )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3349]) ).
thf(3488,plain,
! [SV196: $i,SV811: $i] :
( ( ~ ( in @ SV811 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV811 )
| ( in @ SY1362 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3350]) ).
thf(3489,plain,
! [SV196: $i,SV812: $i] :
( ( ! [SY1363: $i] :
( ~ ~ ( ~ ( in @ SV812 @ SV196 )
| ~ ( in @ SY1363 @ SV196 ) )
| ~ ! [SY1364: $i] :
( ~ ( in @ SY1364 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1364 )
| ( in @ SY1363 @ SY1364 ) )
| ~ ( ~ ( in @ SY1363 @ SY1364 )
| ( in @ SV812 @ SY1364 ) ) ) )
| ( SV812 = SY1363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3351]) ).
thf(3490,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ( ~ ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) ) )
= $false )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3491,plain,
! [SV759: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
| ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 ) )
= $false )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3353]) ).
thf(3492,plain,
! [SV666: $i,SV813: $i,SV205: $i > $o] :
( ( ( ! [SY1365: $i] :
( ~ ( SV205 @ SV813 )
| ~ ( SV205 @ SY1365 )
| ( SV813 = SY1365 ) ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3493,plain,
! [SV666: $i,SV814: $i,SV797: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV797 )
| ~ ( SV205 @ SV814 )
| ( SV797 = SV814 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3356]) ).
thf(3494,plain,
! [SV444: $i,SV219: $i,SV773: $i] :
( ( ( in @ SV773 @ SV219 )
= $false )
| ( ( in @ SV444 @ SV773 )
= $false )
| ( ( in @ SV444 @ ( setunion @ SV219 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3495,plain,
! [SV224: $i,SV449: $i,SV670: $i,SV761: $i] :
( ( ( ~ ~ ( in @ SV761 @ SV670 ) )
= $true )
| ( ( ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV449 )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3362]) ).
thf(3496,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ! [SY579: $i] :
~ ! [SY580: $i] :
~ ( ~ ( ~ ( SV227 @ SY580 )
| ( SY580 = SY579 ) )
| ~ ( ( SY580 != SY579 )
| ( SV227 @ SY580 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3497,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ! [SY1366: $i] :
~ ( ~ ( ~ ( SV227 @ SY1366 )
| ( SY1366
= ( sK85_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SY1366
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SY1366 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3365]) ).
thf(3498,plain,
! [SV228: $i,SV452: $i,SV672: $i,SV762: $i] :
( ( ( in @ SV762 @ SV672 )
= $false )
| ( ( ~ ( in @ SV762 @ SV452 ) )
= $true )
| ( ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
= $false )
| ( ( in @ SV762 @ SV228 )
= $false )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3499,plain,
! [SV235: $i,SV623: $o,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( SV623 = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3367]) ).
thf(3500,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( $true = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3370]) ).
thf(3501,plain,
! [SV235: $i,SV459: $i,SV595: $i] :
( ( ( in @ SV595 @ SV459 )
= $true )
| ( $false = $true )
| ( ( in @ SV595 @ SV235 )
= $true )
| ( ( in @ SV595 @ ( binunion @ SV235 @ SV459 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3373]) ).
thf(3502,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV792 )
| ~ ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3376]) ).
thf(3503,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3377]) ).
thf(3504,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3377]) ).
thf(3505,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3378]) ).
thf(3506,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3507,plain,
! [SV239: $i,SV673: $i,SV763: $i,SV463: $i > $o] :
( ( ( SV463 @ SV763 )
= $false )
| ( ( SV673 = SV763 )
= $true )
| ( ( SV463 @ SV673 )
= $false )
| ( ( in @ SV763 @ SV239 )
= $false )
| ( ( in @ SV673 @ SV239 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV239
@ ^ [SY1003: $i] : ( SV463 @ SY1003 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3508,plain,
! [SV242: $i,SV674: $i,SV466: $i,SV764: $i] :
( ( ( in @ SV764 @ ( binintersect @ SV466 @ SV674 ) )
= $false )
| ( ( in @ SV764 @ SV674 )
= $true )
| ( ( in @ SV764 @ SV242 )
= $false )
| ( ( in @ SV674 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV466 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3381]) ).
thf(3509,plain,
! [SV249: $i,SV675: $i,SV473: $i,SV765: $i] :
( ( ( in @ SV765 @ SV473 )
= $false )
| ( ( in @ SV765 @ ( binunion @ SV473 @ SV675 ) )
= $true )
| ( ( in @ SV765 @ SV249 )
= $false )
| ( ( in @ SV675 @ ( powerset @ SV249 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV249 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3510,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3511,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ~ ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3512,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3513,plain,
! [SV483: $i,SV609: $i,SV260: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) ) ) ) )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3387]) ).
thf(3514,plain,
! [SV261: $i,SV1: $i,SV678: $i > $o,SV484: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV484 ) )
= $true )
| ( ( SV678 @ SV798 )
= $true )
| ( ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3389]) ).
thf(3515,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV484 )
| ( SV678 @ SV815 ) )
= $true )
| ( ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3390]) ).
thf(3516,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV484 ) )
= $true )
| ( ( SV678 @ SV799 )
= $true )
| ( ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) )
= $false )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3391]) ).
thf(3517,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3392]) ).
thf(3518,plain,
! [SV265: $i,SV680: $i,SV486: $i,SV5: $i] :
( ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3393]) ).
thf(3519,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3520,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3394]) ).
thf(3521,plain,
! [SV9: $i,SV626: $i,SV816: $i] :
( ( ( ~ ~ ( ~ ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SV816 @ SV9 ) ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3395]) ).
thf(3522,plain,
! [SV12: $i > $o,SV628: $i] :
( ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ~ ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3396]) ).
thf(3523,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3524,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3525,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ~ ( ~ ( SV12 @ ( sK86_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1367: $i] :
( ~ ( SV12 @ SY1367 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SY1367 ) ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3399]) ).
thf(3526,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK77_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1356: $i] :
( ~ ( SV13 @ SY1356 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SY1356 ) ) ) )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3400]) ).
thf(3527,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ~ ( ~ ( SV13 @ ( sK87_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1368: $i] :
( ~ ( SV13 @ SY1368 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SY1368 ) ) ) )
= $false )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3401]) ).
thf(3528,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK78_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1357: $i] :
( ~ ( SV13 @ SY1357 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SY1357 ) ) ) )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3402]) ).
thf(3529,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3530,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3531,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3406]) ).
thf(3532,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| SV681 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3406]) ).
thf(3533,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3534,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( SV681 = $true )
| ( SV681 = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3408]) ).
thf(3535,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3536,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3411]) ).
thf(3537,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3413]) ).
thf(3538,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3413]) ).
thf(3539,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3540,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3415]) ).
thf(3541,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3542,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV14 )
= $true )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3418]) ).
thf(3543,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ~ ( in @ SV488 @ SV14 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3420]) ).
thf(3544,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3420]) ).
thf(3545,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3546,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3422]) ).
thf(3547,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ SV817 )
| ~ ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3424]) ).
thf(3548,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ SV818 )
| ~ ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3425]) ).
thf(3549,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3426]) ).
thf(3550,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3551,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3428]) ).
thf(3552,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3553,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3554,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ~ ( ~ ( SV19 @ ( sK88_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1371: $i] :
( ~ ( SV19 @ SY1371 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SY1371 ) ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3430]) ).
thf(3555,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( ~ ( SV19 @ ( sK79_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1358: $i] :
( ~ ( SV19 @ SY1358 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SY1358 ) ) ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3431]) ).
thf(3556,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) ) )
= $true )
| ( ( ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3434]) ).
thf(3557,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3435]) ).
thf(3558,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3436]) ).
thf(3559,plain,
! [SV46: $i > $i > $o,SV298: $i,SV746: $i] :
( ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3436]) ).
thf(3560,plain,
! [SV55: $i,SV786: $i,SV303: $i > $o] :
( ( ( SV303 @ SV786 )
= $false )
| ( ( in @ SV786 @ SV55 )
= $false )
| ( ( in @ ( sK32_SY746 @ SV303 @ SV55 ) @ SV55 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3438]) ).
thf(3561,plain,
! [SV55: $i,SV787: $i,SV303: $i > $o] :
( ( ( SV303 @ SV787 )
= $false )
| ( ( in @ SV787 @ SV55 )
= $false )
| ( ( SV303 @ ( sK32_SY746 @ SV303 @ SV55 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3562,plain,
! [SV62: $i,SV748: $i,SV636: $i,SV310: $i,SV779: $i] :
( ( ( in @ SV779 @ ( binintersect @ SV310 @ SV636 ) )
= $false )
| ( ( in @ SV779 @ ( binintersect @ ( binunion @ SV310 @ SV748 ) @ ( binunion @ SV636 @ SV748 ) ) )
= $true )
| ( ( in @ SV779 @ SV62 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV636 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV310 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3563,plain,
! [SV63: $i,SV311: $i > $o,SV688: $i] :
( ( ( ~ ( in @ ( sK81_SY758 @ SV688 @ SV311 @ SV63 ) @ SV63 ) )
= $false )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( SV311 @ SV688 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3564,plain,
! [SV63: $i,SV688: $i,SV311: $i > $o] :
( ( ( SV311 @ ( sK81_SY758 @ SV688 @ SV311 @ SV63 ) )
= $false )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( SV311 @ SV688 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3441]) ).
thf(3565,plain,
! [SV321: $i > $o,SV76: $i,SV780: $i] :
( ( ( in @ SV780 @ SV76 )
= $false )
| ( ( ~ ( SV321 @ SV780 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3566,plain,
! [SV321: $i > $o,SV76: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV76 )
| ~ ( SV321 @ SV793 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3567,plain,
! [SV321: $i > $o,SV76: $i,SV800: $i] :
( ( ( ~ ( ~ ( in @ SV800 @ SV76 )
| ~ ( SV321 @ SV800 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3568,plain,
! [SV321: $i > $o,SV76: $i,SV819: $i] :
( ( ( ~ ~ ( ~ ( in @ SV819 @ SV76 )
| ~ ( SV321 @ SV819 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3445]) ).
thf(3569,plain,
! [SV321: $i > $o,SV76: $i,SV801: $i] :
( ( ( ~ ( ~ ( in @ SV801 @ SV76 )
| ~ ( SV321 @ SV801 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3570,plain,
! [SV77: $i,SV322: $i,SV638: $i,SV749: $i] :
( ( ( in @ SV749 @ SV638 )
= $true )
| ( ( ~ ( in @ SV749 @ SV322 ) )
= $true )
| ( ( subset @ SV322 @ SV638 )
= $false )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3447]) ).
thf(3571,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ~ ( ~ ( SV89 @ ( sK89_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV89 @ SY1372 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SY1372 ) ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3448]) ).
thf(3572,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( ~ ( SV89 @ ( sK82_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1359: $i] :
( ~ ( SV89 @ SY1359 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SY1359 ) ) ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3573,plain,
! [SV102: $i,SV752: $i,SV643: $i,SV346: $i,SV781: $i] :
( ( ( in @ SV781 @ ( binintersect @ SV346 @ SV643 ) )
= $false )
| ( ( in @ SV781 @ ( binunion @ SV346 @ SV752 ) )
= $true )
| ( ( in @ SV781 @ SV102 )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV643 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3450]) ).
thf(3574,plain,
! [SV110: $i,SV753: $i,SV644: $i,SV352: $i,SV782: $i] :
( ( ( in @ SV782 @ ( binintersect @ SV352 @ SV644 ) )
= $false )
| ( ( in @ SV782 @ ( binunion @ SV644 @ SV753 ) )
= $true )
| ( ( in @ SV782 @ SV110 )
= $false )
| ( ( in @ SV753 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV644 @ ( powerset @ SV110 ) )
= $false )
| ( ( in @ SV352 @ ( powerset @ SV110 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3575,plain,
! [SV117: $i,SV775: $i,SV359: $i > $o] :
( ( ( SV359 @ SV775 )
= $false )
| ( ( in @ SV775 @ SV117 )
= $false )
| ( ( in @ ( sK14_SY824 @ SV359 @ SV117 ) @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3576,plain,
! [SV117: $i,SV776: $i,SV359: $i > $o] :
( ( ( SV359 @ SV776 )
= $false )
| ( ( in @ SV776 @ SV117 )
= $false )
| ( ( SV359 @ ( sK14_SY824 @ SV359 @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3453]) ).
thf(3577,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV118 ) )
= $true )
| ( ( ! [SY1360: $i] :
( ~ ( in @ SY1360 @ SV360 )
| ~ ( in @ ( kpair @ SV802 @ SY1360 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SY1360 ) @ SV537 ) ) )
= $true )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3454]) ).
thf(3578,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV794: $i] :
( ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ! [SY1353: $i] :
( ~ ( in @ SY1353 @ SV360 )
| ~ ( in @ ( kpair @ SV794 @ SY1353 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SY1353 ) @ SV537 ) ) )
= $true )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3579,plain,
! [SV366: $i,SV707: $i,SV540: $i,SV126: $i] :
( ( ( in @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) @ SV366 )
= $true )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3456]) ).
thf(3580,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV540 ) )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3581,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV707 )
= $false )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3582,plain,
! [SV371: $i > $o,SV131: $i,SV783: $i] :
( ( ( in @ SV783 @ SV131 )
= $false )
| ( ( ~ ( SV371 @ SV783 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3583,plain,
! [SV371: $i > $o,SV131: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV131 )
| ~ ( SV371 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3459]) ).
thf(3584,plain,
! [SV371: $i > $o,SV131: $i,SV803: $i] :
( ( ( ~ ( ~ ( in @ SV803 @ SV131 )
| ~ ( SV371 @ SV803 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3585,plain,
! [SV371: $i > $o,SV131: $i,SV820: $i] :
( ( ( ~ ~ ( ~ ( in @ SV820 @ SV131 )
| ~ ( SV371 @ SV820 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3461]) ).
thf(3586,plain,
! [SV371: $i > $o,SV131: $i,SV804: $i] :
( ( ( ~ ( ~ ( in @ SV804 @ SV131 )
| ~ ( SV371 @ SV804 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3587,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( ~ ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3464]) ).
thf(3588,plain,
! [SV653: $i,SV821: $i,SV805: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV805 )
| ~ ( SV146 @ SV821 )
| ( SV805 = SV821 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3465]) ).
thf(3589,plain,
! [SV653: $i,SV806: $i,SV796: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV796 ) )
= $true )
| ( ( ~ ( SV146 @ SV806 )
| ( SV796 = SV806 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3590,plain,
! [SV158: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ omega ) )
= $true )
| ( ( in @ SV807 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3468]) ).
thf(3591,plain,
! [SV158: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ omega ) )
= $true )
| ( ( in @ SV808 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(3592,plain,
! [SV169: $i,SV788: $i,SV403: $i > $o] :
( ( ( SV403 @ SV788 )
= $false )
| ( ( in @ SV788 @ SV169 )
= $false )
| ( ( in @ ( sK35_SY905 @ SV403 @ SV169 ) @ SV169 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3470]) ).
thf(3593,plain,
! [SV169: $i,SV789: $i,SV403: $i > $o] :
( ( ( SV403 @ SV789 )
= $false )
| ( ( in @ SV789 @ SV169 )
= $false )
| ( ( SV403 @ ( sK35_SY905 @ SV403 @ SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3594,plain,
! [SV181: $i,SV661: $i,SV758: $o,SV413: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV413 )
| SV758 )
= $false )
| ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3595,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV413 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3596,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV413 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3597,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( ~ ( SV182 @ ( sK90_SY451 @ SV662 @ SV182 ) ) )
= $false )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3475]) ).
thf(3598,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( SV182 @ ( sK83_SY451 @ SV662 @ SV182 ) )
= $true )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV662
= ( sK68_SY1258 @ SV662 @ SV182 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3476]) ).
thf(3599,plain,
! [SV191: $i,SV719: $i,SV421: $i > $o] :
( ( ( SV421 @ ( sK54_SY930 @ SV719 @ SV421 @ SV191 ) )
= $false )
| ( ( SV421 @ SV719 )
= $true )
| ( ( in @ SV719 @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3600,plain,
! [SV423: $i,SV193: $i,SV720: $i > $o,SV570: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV570 ) )
= $true )
| ( ( SV720 @ SV809 )
= $true )
| ( ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3480]) ).
thf(3601,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV570 )
| ( SV720 @ SV822 ) )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3481]) ).
thf(3602,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ SV570 ) )
= $true )
| ( ( SV720 @ SV810 )
= $true )
| ( ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3482]) ).
thf(3603,plain,
! [SV195: $i,SV722: $i,SV425: $i > $o] :
( ( ( SV425 @ ( sK55_SY941 @ SV722 @ SV425 @ SV195 ) )
= $false )
| ( ( SV425 @ SV722 )
= $true )
| ( ( in @ SV722 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3604,plain,
! [SV196: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV811 )
| ( in @ SY1362 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3488]) ).
thf(3605,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ~ ~ ( ~ ( in @ SV812 @ SV196 )
| ~ ( in @ SV823 @ SV196 ) )
| ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3606,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3490]) ).
thf(3607,plain,
! [SV759: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 ) )
= $false )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3491]) ).
thf(3608,plain,
! [SV759: $i,SV196: $i] :
( ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3491]) ).
thf(3609,plain,
! [SV666: $i,SV824: $i,SV813: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV813 )
| ~ ( SV205 @ SV824 )
| ( SV813 = SV824 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(3610,plain,
! [SV666: $i,SV814: $i,SV797: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV797 ) )
= $true )
| ( ( ~ ( SV205 @ SV814 )
| ( SV797 = SV814 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3611,plain,
! [SV224: $i,SV449: $i,SV670: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ SV670 ) )
= $false )
| ( ( ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV449 )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3495]) ).
thf(3612,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ~ ! [SY1374: $i] :
~ ( ~ ( ~ ( SV227 @ SY1374 )
| ( SY1374
= ( sK91_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SY1374
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SY1374 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3496]) ).
thf(3613,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ! [SY1366: $i] :
~ ( ~ ( ~ ( SV227 @ SY1366 )
| ( SY1366
= ( sK85_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SY1366
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SY1366 ) ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3497]) ).
thf(3614,plain,
! [SV228: $i,SV672: $i,SV452: $i,SV762: $i] :
( ( ( in @ SV762 @ SV452 )
= $false )
| ( ( in @ SV762 @ SV672 )
= $false )
| ( ( subset @ SV452 @ ( setminus @ SV228 @ SV672 ) )
= $false )
| ( ( in @ SV762 @ SV228 )
= $false )
| ( ( in @ SV672 @ ( powerset @ SV228 ) )
= $false )
| ( ( in @ SV452 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3615,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV792 ) )
= $true )
| ( ( ~ ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3502]) ).
thf(3616,plain,
! [SV237: $i > $o,SV461: $i > $o] :
( ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) )
| ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3503]) ).
thf(3617,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3504]) ).
thf(3618,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3505]) ).
thf(3619,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3620,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
| ~ ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3510]) ).
thf(3621,plain,
! [SV482: $i,SV677: $i,SV259: $i] :
( ( ( ! [SY1273: $i] :
( ~ ( in @ SY1273 @ SV259 )
| ~ ( in @ SY1273 @ SV677 )
| ( in @ SY1273 @ SV482 ) ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3511]) ).
thf(3622,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
| ~ ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3512]) ).
thf(3623,plain,
! [SV483: $i,SV609: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) @ SV483 )
| ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3624,plain,
! [SV261: $i,SV1: $i,SV678: $i > $o,SV484: $i,SV798: $i] :
( ( ( in @ SV798 @ SV484 )
= $false )
| ( ( SV678 @ SV798 )
= $true )
| ( ( in @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) @ SV261 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3625,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV484 ) )
= $true )
| ( ( SV678 @ SV815 )
= $true )
| ( ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3626,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV799: $i] :
( ( ( in @ SV799 @ SV484 )
= $false )
| ( ( SV678 @ SV799 )
= $true )
| ( ( SV678 @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) )
= $false )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3627,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
| ! [SY1375: $i] :
( ~ ( in @ SY1375 @ SV265 )
| ~ ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1375 ) @ SV680 )
| ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1375 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3517]) ).
thf(3628,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3629,plain,
! [SV5: $i,SV265: $i,SV486: $i,SV680: $i] :
( ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) )
| ( SV486 = SV680 ) )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3519]) ).
thf(3630,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3631,plain,
! [SV9: $i,SV626: $i,SV816: $i] :
( ( ( ~ ( ~ ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SV816 @ SV9 ) ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3632,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY39: $i] :
~ ~ ( ~ ( SV12 @ SY39 )
| ~ ! [SY40: $i] :
( ~ ( SV12 @ SY40 )
| ( SY39 = SY40 ) ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3633,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ~ ( ~ ( SV12 @ ( sK95_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV12 @ SY1376 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SY1376 ) ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3523]) ).
thf(3634,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ~ ( ~ ( SV12 @ ( sK96_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1377: $i] :
( ~ ( SV12 @ SY1377 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SY1377 ) ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3524]) ).
thf(3635,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK86_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1367: $i] :
( ~ ( SV12 @ SY1367 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SY1367 ) ) ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3636,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK77_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1356: $i] :
( ~ ( SV13 @ SY1356 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SY1356 ) ) )
= $false )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3526]) ).
thf(3637,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( ~ ( SV13 @ ( sK87_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1368: $i] :
( ~ ( SV13 @ SY1368 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SY1368 ) ) ) )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3527]) ).
thf(3638,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK78_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1357: $i] :
( ~ ( SV13 @ SY1357 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SY1357 ) ) )
= $false )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3528]) ).
thf(3639,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3640,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3532]) ).
thf(3641,plain,
! [SV14: $i,SV269: $i,SV488: $i,SV681: $o] :
( ( SV681 = $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3532]) ).
thf(3642,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3537]) ).
thf(3643,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3538]) ).
thf(3644,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3538]) ).
thf(3645,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV14 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3543]) ).
thf(3646,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ SV269 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3544]) ).
thf(3647,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3544]) ).
thf(3648,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ SV817 )
| ~ ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3649,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ SV818 )
| ~ ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3548]) ).
thf(3650,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
| ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3651,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3550]) ).
thf(3652,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3550]) ).
thf(3653,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3654,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3655,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3552]) ).
thf(3656,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(3657,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( ~ ( SV19 @ ( sK88_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1371: $i] :
( ~ ( SV19 @ SY1371 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SY1371 ) ) ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(3658,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK79_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1358: $i] :
( ~ ( SV19 @ SY1358 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SY1358 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3659,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( ~ ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3660,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3661,plain,
! [SV746: $i,SV298: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( ~ ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3558]) ).
thf(3662,plain,
! [SV746: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3663,plain,
! [SV63: $i,SV311: $i > $o,SV688: $i] :
( ( ( in @ ( sK81_SY758 @ SV688 @ SV311 @ SV63 ) @ SV63 )
= $true )
| ( ( in @ SV688 @ SV63 )
= $false )
| ( ( SV311 @ SV688 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3563]) ).
thf(3664,plain,
! [SV76: $i,SV780: $i,SV321: $i > $o] :
( ( ( SV321 @ SV780 )
= $false )
| ( ( in @ SV780 @ SV76 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK12_SY769 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3565]) ).
thf(3665,plain,
! [SV321: $i > $o,SV76: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV76 ) )
= $true )
| ( ( ~ ( SV321 @ SV793 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3566]) ).
thf(3666,plain,
! [SV321: $i > $o,SV76: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV76 )
| ~ ( SV321 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3667,plain,
! [SV321: $i > $o,SV76: $i,SV819: $i] :
( ( ( ~ ( ~ ( in @ SV819 @ SV76 )
| ~ ( SV321 @ SV819 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3568]) ).
thf(3668,plain,
! [SV321: $i > $o,SV76: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV76 )
| ~ ( SV321 @ SV801 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3669,plain,
! [SV77: $i,SV638: $i,SV322: $i,SV749: $i] :
( ( ( in @ SV749 @ SV322 )
= $false )
| ( ( in @ SV749 @ SV638 )
= $true )
| ( ( subset @ SV322 @ SV638 )
= $false )
| ( ( in @ SV749 @ SV77 )
= $false )
| ( ( in @ SV638 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3670,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( ~ ( SV89 @ ( sK89_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV89 @ SY1372 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SY1372 ) ) ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3571]) ).
thf(3671,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK82_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1359: $i] :
( ~ ( SV89 @ SY1359 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SY1359 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3672,plain,
! [SV537: $i,SV705: $i,SV360: $i,SV118: $i,SV802: $i] :
( ( ( in @ SV802 @ SV118 )
= $false )
| ( ( ! [SY1360: $i] :
( ~ ( in @ SY1360 @ SV360 )
| ~ ( in @ ( kpair @ SV802 @ SY1360 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SY1360 ) @ SV537 ) ) )
= $true )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3577]) ).
thf(3673,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV794: $i,SV360: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV360 )
| ~ ( in @ ( kpair @ SV794 @ SV825 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SV825 ) @ SV537 ) )
= $true )
| ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3578]) ).
thf(3674,plain,
! [SV126: $i,SV366: $i,SV540: $i,SV707: $i] :
( ( ( in @ ( kpair @ ( sK64_SY1293 @ SV707 @ SV540 @ SV366 @ SV126 ) @ ( sK75_SY1346 @ SV126 @ SV540 @ SV707 @ SV366 ) ) @ SV540 )
= $true )
| ( ( subset @ SV540 @ SV707 )
= $true )
| ( ( subset @ SV707 @ ( cartprod @ SV126 @ SV366 ) )
= $false )
| ( ( subset @ SV540 @ ( cartprod @ SV126 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3580]) ).
thf(3675,plain,
! [SV131: $i,SV783: $i,SV371: $i > $o] :
( ( ( SV371 @ SV783 )
= $false )
| ( ( in @ SV783 @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK16_SY848 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3676,plain,
! [SV371: $i > $o,SV131: $i,SV795: $i] :
( ( ( ~ ( in @ SV795 @ SV131 ) )
= $true )
| ( ( ~ ( SV371 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3583]) ).
thf(3677,plain,
! [SV371: $i > $o,SV131: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV131 )
| ~ ( SV371 @ SV803 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(3678,plain,
! [SV371: $i > $o,SV131: $i,SV820: $i] :
( ( ( ~ ( ~ ( in @ SV820 @ SV131 )
| ~ ( SV371 @ SV820 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3585]) ).
thf(3679,plain,
! [SV371: $i > $o,SV131: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV131 )
| ~ ( SV371 @ SV804 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3586]) ).
thf(3680,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
| ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
= $false )
| ( ( ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3681,plain,
! [SV653: $i,SV821: $i,SV805: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV805 ) )
= $true )
| ( ( ~ ( SV146 @ SV821 )
| ( SV805 = SV821 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3588]) ).
thf(3682,plain,
! [SV653: $i,SV806: $i,SV796: $i,SV146: $i > $o] :
( ( ( SV146 @ SV796 )
= $false )
| ( ( ~ ( SV146 @ SV806 )
| ( SV796 = SV806 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3683,plain,
! [SV158: $i,SV807: $i] :
( ( ( in @ SV807 @ omega )
= $false )
| ( ( in @ SV807 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3684,plain,
! [SV158: $i,SV808: $i] :
( ( ( in @ SV808 @ omega )
= $false )
| ( ( in @ SV808 @ SV158 )
= $true )
| ( ( in @ emptyset @ SV158 )
= $false )
| ( ( in @ ( sK43_SY395 @ SV158 ) @ SV158 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3685,plain,
! [SV181: $i,SV758: $o,SV661: $i,SV413: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV413 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3594]) ).
thf(3686,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV770: $i,SV758: $o] :
( ( SV758 = $false )
| ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3594]) ).
thf(3687,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV413 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3595]) ).
thf(3688,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3595]) ).
thf(3689,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV413 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3690,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3596]) ).
thf(3691,plain,
! [SV662: $i,SV182: $i > $o] :
( ( ( SV182 @ ( sK90_SY451 @ SV662 @ SV182 ) )
= $true )
| ( ( SV182 @ SV662 )
= $false )
| ( ( SV182 @ ( sK68_SY1258 @ SV662 @ SV182 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3692,plain,
! [SV423: $i,SV193: $i,SV720: $i > $o,SV570: $i,SV809: $i] :
( ( ( in @ SV809 @ SV570 )
= $false )
| ( ( SV720 @ SV809 )
= $true )
| ( ( in @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) @ SV423 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3600]) ).
thf(3693,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV570 ) )
= $true )
| ( ( SV720 @ SV822 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(3694,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV810: $i] :
( ( ( in @ SV810 @ SV570 )
= $false )
| ( ( SV720 @ SV810 )
= $true )
| ( ( SV720 @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) )
= $false )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3602]) ).
thf(3695,plain,
! [SV196: $i,SV811: $i] :
( ( ( in @ SV811 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( ! [SY1362: $i] :
( ~ ( in @ SY1362 @ SV811 )
| ( in @ SY1362 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3604]) ).
thf(3696,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ( ~ ~ ( ~ ( in @ SV812 @ SV196 )
| ~ ( in @ SV823 @ SV196 ) ) )
= $true )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3605]) ).
thf(3697,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3606]) ).
thf(3698,plain,
! [SV759: $i,SV196: $i] :
( ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( ~ ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3607]) ).
thf(3699,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3700,plain,
! [SV666: $i,SV824: $i,SV813: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV813 ) )
= $true )
| ( ( ~ ( SV205 @ SV824 )
| ( SV813 = SV824 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3609]) ).
thf(3701,plain,
! [SV666: $i,SV814: $i,SV797: $i,SV205: $i > $o] :
( ( ( SV205 @ SV797 )
= $false )
| ( ( ~ ( SV205 @ SV814 )
| ( SV797 = SV814 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3702,plain,
! [SV224: $i,SV449: $i,SV670: $i,SV761: $i] :
( ( ( in @ SV761 @ SV670 )
= $true )
| ( ( ~ ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) ) )
= $true )
| ( ( in @ SV761 @ SV449 )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(3703,plain,
! [SV671: $i,SV227: $i > $o] :
( ( ( ! [SY1374: $i] :
~ ( ~ ( ~ ( SV227 @ SY1374 )
| ( SY1374
= ( sK91_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SY1374
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SY1374 ) ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3612]) ).
thf(3704,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV227 @ SV826 )
| ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SV826
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV826 ) ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3613]) ).
thf(3705,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3706,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3616]) ).
thf(3707,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3617]) ).
thf(3708,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3709,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3619]) ).
thf(3710,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3620]) ).
thf(3711,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3620]) ).
thf(3712,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
| ~ ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3621]) ).
thf(3713,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3622]) ).
thf(3714,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3622]) ).
thf(3715,plain,
! [SV483: $i,SV609: $i,SV260: $i] :
( ( ( ~ ( in @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) @ SV483 ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3716,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( SV609
!= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) ) )
= $false )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3623]) ).
thf(3717,plain,
! [SV1: $i,SV261: $i,SV678: $i > $o,SV484: $i,SV815: $i] :
( ( ( in @ SV815 @ SV484 )
= $false )
| ( ( SV678 @ SV815 )
= $true )
| ( ( in @ ( kpair @ ( sK44_SY1274 @ SV678 @ SV484 @ SV261 @ SV1 ) @ ( sK59_SY1334 @ SV1 @ SV484 @ SV678 @ SV261 ) ) @ SV484 )
= $true )
| ( ( subset @ SV484 @ ( cartprod @ SV1 @ SV261 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3718,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3719,plain,
! [SV5: $i,SV680: $i,SV486: $i,SV265: $i] :
( ( ( ! [SY1375: $i] :
( ~ ( in @ SY1375 @ SV265 )
| ~ ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1375 ) @ SV680 )
| ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1375 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3627]) ).
thf(3720,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3628]) ).
thf(3721,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3629]) ).
thf(3722,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3723,plain,
! [SV9: $i,SV626: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) )
| ~ ( in @ SV816 @ SV9 ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3631]) ).
thf(3724,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ~ ( ~ ( SV12 @ ( sK98_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1378: $i] :
( ~ ( SV12 @ SY1378 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SY1378 ) ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3632]) ).
thf(3725,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK95_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV12 @ SY1376 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SY1376 ) ) ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3726,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK96_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1377: $i] :
( ~ ( SV12 @ SY1377 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SY1377 ) ) ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3634]) ).
thf(3727,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK86_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1367: $i] :
( ~ ( SV12 @ SY1367 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SY1367 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3728,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK77_SY44 @ SV629 @ SV13 ) ) )
= $false )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3729,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ! [SY1356: $i] :
( ~ ( SV13 @ SY1356 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SY1356 ) ) )
= $false )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3636]) ).
thf(3730,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK87_SY44 @ SV629 @ SV13 ) )
| ~ ! [SY1368: $i] :
( ~ ( SV13 @ SY1368 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SY1368 ) ) )
= $false )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3731,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK78_SY44 @ SV629 @ SV13 ) ) )
= $false )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3638]) ).
thf(3732,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ! [SY1357: $i] :
( ~ ( SV13 @ SY1357 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SY1357 ) ) )
= $false )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3638]) ).
thf(3733,plain,
! [SV269: $i,SV681: $o,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3734,plain,
! [SV14: $i,SV681: $o,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( SV681 = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3640]) ).
thf(3735,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3736,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $true = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3643]) ).
thf(3737,plain,
! [SV269: $i,SV14: $i,SV488: $i] :
( ( ( in @ SV488 @ SV14 )
= $false )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3645]) ).
thf(3738,plain,
! [SV14: $i,SV269: $i,SV488: $i] :
( ( ( in @ SV488 @ SV269 )
= $true )
| ( $false = $true )
| ( ( in @ SV488 @ SV269 )
= $false )
| ( ( in @ SV488 @ ( symdiff @ SV14 @ SV269 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3646]) ).
thf(3739,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV817 )
| ~ ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(3740,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV818 )
| ~ ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3649]) ).
thf(3741,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3742,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3743,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3651]) ).
thf(3744,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3652]) ).
thf(3745,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(3746,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(3747,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3655]) ).
thf(3748,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3749,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK88_SY64 @ SV630 @ SV19 ) )
| ~ ! [SY1371: $i] :
( ~ ( SV19 @ SY1371 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SY1371 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3750,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK79_SY64 @ SV630 @ SV19 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3658]) ).
thf(3751,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ! [SY1358: $i] :
( ~ ( SV19 @ SY1358 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SY1358 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3658]) ).
thf(3752,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1344: $i] :
~ ~ ( ~ ( in @ SY1344 @ SV298 )
| ~ ( SV46 @ SY1344 @ SV778 ) ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3753,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1345: $i] :
~ ~ ( ~ ( in @ SY1345 @ SV298 )
| ~ ( SV46 @ SY1345 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3660]) ).
thf(3754,plain,
! [SV746: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY736: $i] :
~ ! [SY737: $i] :
~ ( ~ ( ~ ( in @ SY737 @ SY736 )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY737 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY737 ) )
| ( in @ SY737 @ SY736 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(3755,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i] :
( ( ( ~ ! [SY1379: $i] :
~ ( ~ ( ~ ( in @ SY1379 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1379 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1379 ) )
| ( in @ SY1379 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3662]) ).
thf(3756,plain,
! [SV321: $i > $o,SV76: $i,SV793: $i] :
( ( ( in @ SV793 @ SV76 )
= $false )
| ( ( ~ ( SV321 @ SV793 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3757,plain,
! [SV321: $i > $o,SV76: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV76 ) )
= $true )
| ( ( ~ ( SV321 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3758,plain,
! [SV321: $i > $o,SV76: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ SV76 )
| ~ ( SV321 @ SV819 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3667]) ).
thf(3759,plain,
! [SV321: $i > $o,SV76: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV76 ) )
= $true )
| ( ( ~ ( SV321 @ SV801 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3668]) ).
thf(3760,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK89_SY225 @ SV639 @ SV89 ) )
| ~ ! [SY1372: $i] :
( ~ ( SV89 @ SY1372 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SY1372 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3761,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK82_SY225 @ SV639 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3671]) ).
thf(3762,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ! [SY1359: $i] :
( ~ ( SV89 @ SY1359 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SY1359 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3671]) ).
thf(3763,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV802: $i,SV360: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ SV360 )
| ~ ( in @ ( kpair @ SV802 @ SV827 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SV827 ) @ SV537 ) )
= $true )
| ( ( in @ SV802 @ SV118 )
= $false )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(3764,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV794: $i,SV360: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV360 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV794 @ SV825 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SV825 ) @ SV537 ) )
= $true )
| ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3673]) ).
thf(3765,plain,
! [SV371: $i > $o,SV131: $i,SV795: $i] :
( ( ( in @ SV795 @ SV131 )
= $false )
| ( ( ~ ( SV371 @ SV795 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3766,plain,
! [SV371: $i > $o,SV131: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV131 ) )
= $true )
| ( ( ~ ( SV371 @ SV803 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3767,plain,
! [SV371: $i > $o,SV131: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV131 )
| ~ ( SV371 @ SV820 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3768,plain,
! [SV371: $i > $o,SV131: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV131 ) )
= $true )
| ( ( ~ ( SV371 @ SV804 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(3769,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( ~ ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) )
= $false )
| ( ( ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3680]) ).
thf(3770,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3680]) ).
thf(3771,plain,
! [SV653: $i,SV821: $i,SV805: $i,SV146: $i > $o] :
( ( ( SV146 @ SV805 )
= $false )
| ( ( ~ ( SV146 @ SV821 )
| ( SV805 = SV821 ) )
= $true )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3681]) ).
thf(3772,plain,
! [SV653: $i,SV796: $i,SV806: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV806 ) )
= $true )
| ( ( SV796 = SV806 )
= $true )
| ( ( SV146 @ SV796 )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3773,plain,
! [SV181: $i,SV758: $o,SV661: $i,SV413: $i,SV770: $i] :
( ( ( in @ SV770 @ SV413 )
= $true )
| ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 )
| SV758 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3685]) ).
thf(3774,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 ) )
= $true )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3686]) ).
thf(3775,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( ( in @ SV771 @ SV413 )
= $true )
| ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true )
| $true )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3776,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3688]) ).
thf(3777,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( ( in @ SV772 @ SV413 )
= $true )
| ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false )
| $false )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3689]) ).
thf(3778,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3690]) ).
thf(3779,plain,
! [SV193: $i,SV423: $i,SV720: $i > $o,SV570: $i,SV822: $i] :
( ( ( in @ SV822 @ SV570 )
= $false )
| ( ( SV720 @ SV822 )
= $true )
| ( ( in @ ( kpair @ ( sK48_SY1303 @ SV720 @ SV570 @ SV423 @ SV193 ) @ ( sK69_SY1342 @ SV193 @ SV570 @ SV720 @ SV423 ) ) @ SV570 )
= $true )
| ( ( subset @ SV570 @ ( cartprod @ SV193 @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3693]) ).
thf(3780,plain,
! [SV196: $i,SV811: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ SV811 )
| ( in @ SV828 @ SV196 ) )
= $true )
| ( ( in @ SV811 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(3781,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ( ~ ( ~ ( in @ SV812 @ SV196 )
| ~ ( in @ SV823 @ SV196 ) ) )
= $false )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3782,plain,
! [SV791: $i,SV196: $i,SV784: $i] :
( ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( ~ ( in @ SV791 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3783,plain,
! [SV196: $i,SV759: $i] :
( ( ( ~ ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3784,plain,
! [SV196: $i,SV759: $i] :
( ( ( ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3699]) ).
thf(3785,plain,
! [SV666: $i,SV824: $i,SV813: $i,SV205: $i > $o] :
( ( ( SV205 @ SV813 )
= $false )
| ( ( ~ ( SV205 @ SV824 )
| ( SV813 = SV824 ) )
= $true )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3786,plain,
! [SV666: $i,SV797: $i,SV814: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV814 ) )
= $true )
| ( ( SV797 = SV814 )
= $true )
| ( ( SV205 @ SV797 )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3787,plain,
! [SV224: $i,SV670: $i,SV449: $i,SV761: $i] :
( ( ( in @ SV761 @ ( binunion @ SV449 @ SV670 ) )
= $false )
| ( ( in @ SV761 @ SV670 )
= $true )
| ( ( in @ SV761 @ SV449 )
= $true )
| ( ( in @ SV761 @ SV224 )
= $false )
| ( ( in @ SV670 @ ( powerset @ SV224 ) )
= $false )
| ( ( in @ SV449 @ ( powerset @ SV224 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3702]) ).
thf(3788,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV227 @ SV829 )
| ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SV829
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV829 ) ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3703]) ).
thf(3789,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( SV227 @ SV826 )
| ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SV826
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV826 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3704]) ).
thf(3790,plain,
! [SV461: $i > $o,SV792: $i,SV237: $i > $o] :
( ( ( ! [SY1352: $i] :
( ~ ( SV237 @ SY1352 )
| ( SV792 = SY1352 ) ) )
= $false )
| ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3791,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3706]) ).
thf(3792,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3707]) ).
thf(3793,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3708]) ).
thf(3794,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( ~ ~ ( ~ ( SV237 @ SV830 )
| ~ ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3709]) ).
thf(3795,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3796,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3711]) ).
thf(3797,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3711]) ).
thf(3798,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3799,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
| ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3800,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3801,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3802,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3714]) ).
thf(3803,plain,
! [SV483: $i,SV609: $i,SV260: $i] :
( ( ( in @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) @ SV483 )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3715]) ).
thf(3804,plain,
! [SV260: $i,SV483: $i,SV609: $i] :
( ( ( SV609
= ( kpair @ ( sK37_SY1201 @ SV609 @ SV483 @ SV260 ) @ ( sK76_SY1318 @ SV260 @ SV609 @ SV483 ) ) )
= $true )
| ( ( in @ SV609 @ ( cartprod @ SV260 @ SV483 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3716]) ).
thf(3805,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3806,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
| ~ ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3719]) ).
thf(3807,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
| ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV265 )
| ~ ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1383 ) @ SV680 )
| ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1383 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3720]) ).
thf(3808,plain,
! [SV486: $i,SV680: $i,SV265: $i,SV5: $i] :
( ( ( ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV5 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV265 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV680 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV486 ) ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3721]) ).
thf(3809,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
| ! [SY1384: $i] :
( ~ ( in @ SY1384 @ SV265 )
| ~ ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1384 ) @ SV680 )
| ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1384 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3722]) ).
thf(3810,plain,
! [SV9: $i,SV626: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) ) )
= $true )
| ( ( ~ ( in @ SV816 @ SV9 ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(3811,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( ~ ( SV12 @ ( sK98_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1378: $i] :
( ~ ( SV12 @ SY1378 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SY1378 ) ) ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3724]) ).
thf(3812,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK95_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1376: $i] :
( ~ ( SV12 @ SY1376 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SY1376 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3725]) ).
thf(3813,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK96_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1377: $i] :
( ~ ( SV12 @ SY1377 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SY1377 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(3814,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK86_SY39 @ SV628 @ SV12 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3815,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ! [SY1367: $i] :
( ~ ( SV12 @ SY1367 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SY1367 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3816,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK77_SY44 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3728]) ).
thf(3817,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY1356: $i] :
( ~ ( SV13 @ SY1356 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SY1356 ) ) )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3729]) ).
thf(3818,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ ( sK87_SY44 @ SV629 @ SV13 ) ) )
= $false )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3730]) ).
thf(3819,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ~ ! [SY1368: $i] :
( ~ ( SV13 @ SY1368 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SY1368 ) ) )
= $false )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3730]) ).
thf(3820,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK78_SY44 @ SV629 @ SV13 ) )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3731]) ).
thf(3821,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY1357: $i] :
( ~ ( SV13 @ SY1357 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SY1357 ) ) )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(3822,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV817 ) )
= $true )
| ( ( ~ ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(3823,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV818 ) )
= $true )
| ( ( ~ ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3740]) ).
thf(3824,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) )
| ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3741]) ).
thf(3825,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) )
| ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3742]) ).
thf(3826,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3743]) ).
thf(3827,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3744]) ).
thf(3828,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3829,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3830,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3747]) ).
thf(3831,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(3832,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ ( sK88_SY64 @ SV630 @ SV19 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3749]) ).
thf(3833,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ~ ! [SY1371: $i] :
( ~ ( SV19 @ SY1371 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SY1371 ) ) )
= $false )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3749]) ).
thf(3834,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( SV19 @ ( sK79_SY64 @ SV630 @ SV19 ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3835,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ! [SY1358: $i] :
( ~ ( SV19 @ SY1358 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SY1358 ) ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3751]) ).
thf(3836,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV778 ) ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3752]) ).
thf(3837,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i,SV831: $i] :
( ( ( ~ ~ ( ~ ( in @ SV831 @ SV298 )
| ~ ( SV46 @ SV831 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3753]) ).
thf(3838,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i] :
( ( ( ~ ! [SY1385: $i] :
~ ( ~ ( ~ ( in @ SY1385 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1385 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1385 ) )
| ( in @ SY1385 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3754]) ).
thf(3839,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i] :
( ( ( ! [SY1379: $i] :
~ ( ~ ( ~ ( in @ SY1379 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1379 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1379 ) )
| ( in @ SY1379 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(3840,plain,
! [SV76: $i,SV793: $i,SV321: $i > $o] :
( ( ( SV321 @ SV793 )
= $false )
| ( ( in @ SV793 @ SV76 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( in @ ( sK33_SY1232 @ SV321 @ SV76 ) @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3756]) ).
thf(3841,plain,
! [SV321: $i > $o,SV76: $i,SV800: $i] :
( ( ( in @ SV800 @ SV76 )
= $false )
| ( ( ~ ( SV321 @ SV800 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(3842,plain,
! [SV321: $i > $o,SV76: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ SV76 ) )
= $true )
| ( ( ~ ( SV321 @ SV819 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3758]) ).
thf(3843,plain,
! [SV321: $i > $o,SV76: $i,SV801: $i] :
( ( ( in @ SV801 @ SV76 )
= $false )
| ( ( ~ ( SV321 @ SV801 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3844,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ ( sK89_SY225 @ SV639 @ SV89 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3845,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ~ ! [SY1372: $i] :
( ~ ( SV89 @ SY1372 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SY1372 ) ) )
= $false )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3846,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( SV89 @ ( sK82_SY225 @ SV639 @ SV89 ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3761]) ).
thf(3847,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ! [SY1359: $i] :
( ~ ( SV89 @ SY1359 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SY1359 ) ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3762]) ).
thf(3848,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV802: $i,SV360: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ SV360 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV802 @ SV827 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SV827 ) @ SV537 ) )
= $true )
| ( ( in @ SV802 @ SV118 )
= $false )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3849,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV794: $i,SV360: $i,SV825: $i] :
( ( ( in @ SV825 @ SV360 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV794 @ SV825 ) @ SV705 )
| ( in @ ( kpair @ SV794 @ SV825 ) @ SV537 ) )
= $true )
| ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3850,plain,
! [SV131: $i,SV795: $i,SV371: $i > $o] :
( ( ( SV371 @ SV795 )
= $false )
| ( ( in @ SV795 @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( in @ ( sK34_SY1241 @ SV371 @ SV131 ) @ SV131 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3765]) ).
thf(3851,plain,
! [SV371: $i > $o,SV131: $i,SV803: $i] :
( ( ( in @ SV803 @ SV131 )
= $false )
| ( ( ~ ( SV371 @ SV803 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3766]) ).
thf(3852,plain,
! [SV371: $i > $o,SV131: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV131 ) )
= $true )
| ( ( ~ ( SV371 @ SV820 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3767]) ).
thf(3853,plain,
! [SV371: $i > $o,SV131: $i,SV804: $i] :
( ( ( in @ SV804 @ SV131 )
= $false )
| ( ( ~ ( SV371 @ SV804 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3768]) ).
thf(3854,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $true )
| ( ( ~ ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(3855,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) )
= $false )
| ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3856,plain,
! [SV653: $i,SV805: $i,SV821: $i,SV146: $i > $o] :
( ( ( ~ ( SV146 @ SV821 ) )
= $true )
| ( ( SV805 = SV821 )
= $true )
| ( ( SV146 @ SV805 )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(3857,plain,
! [SV653: $i,SV796: $i,SV806: $i,SV146: $i > $o] :
( ( ( SV146 @ SV806 )
= $false )
| ( ( SV796 = SV806 )
= $true )
| ( ( SV146 @ SV796 )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV653
= ( sK66_SY1248 @ SV653 @ SV146 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(3858,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( ~ ( in @ SV770 @ SV661 )
| SV758 ) )
= $true )
| ( SV758 = $true )
| ( ( in @ SV770 @ SV413 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3859,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV661 )
| SV758 )
= $false )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3860,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( ~ ( in @ SV771 @ SV661 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV771 @ SV413 )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3775]) ).
thf(3861,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV661 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3862,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( ~ ( in @ SV772 @ SV661 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV772 @ SV413 )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(3863,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV661 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3864,plain,
! [SV196: $i,SV811: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ SV811 ) )
= $true )
| ( ( in @ SV828 @ SV196 )
= $true )
| ( ( in @ SV811 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3780]) ).
thf(3865,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV196 )
| ~ ( in @ SV823 @ SV196 ) )
= $true )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(3866,plain,
! [SV784: $i,SV196: $i,SV791: $i] :
( ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) )
| ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3867,plain,
! [SV196: $i,SV759: $i] :
( ( ( ! [SY1328: $i] :
~ ( in @ SY1328 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3783]) ).
thf(3868,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( in @ SV832 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3784]) ).
thf(3869,plain,
! [SV666: $i,SV813: $i,SV824: $i,SV205: $i > $o] :
( ( ( ~ ( SV205 @ SV824 ) )
= $true )
| ( ( SV813 = SV824 )
= $true )
| ( ( SV205 @ SV813 )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(3870,plain,
! [SV666: $i,SV797: $i,SV814: $i,SV205: $i > $o] :
( ( ( SV205 @ SV814 )
= $false )
| ( ( SV797 = SV814 )
= $true )
| ( ( SV205 @ SV797 )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV666
= ( sK70_SY1259 @ SV666 @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3786]) ).
thf(3871,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( SV227 @ SV829 )
| ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) ) )
| ~ ( ( SV829
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV829 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3872,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( SV227 @ SV826 )
| ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3873,plain,
! [SV227: $i > $o,SV671: $i,SV826: $i] :
( ( ( ~ ( ( SV826
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV826 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3874,plain,
! [SV792: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
| ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3790]) ).
thf(3875,plain,
! [SV461: $i > $o,SV237: $i > $o] :
( ( ( ! [SY605: $i] :
~ ~ ( ~ ( SV237 @ SY605 )
| ~ ! [SY606: $i] :
( ~ ( SV237 @ SY606 )
| ( SY605 = SY606 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3791]) ).
thf(3876,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( ~ ~ ( ~ ( SV237 @ SV833 )
| ~ ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3792]) ).
thf(3877,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( ~ ~ ( ~ ( SV237 @ SV834 )
| ~ ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3793]) ).
thf(3878,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ SV830 )
| ~ ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3794]) ).
thf(3879,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK92_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV259 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3796]) ).
thf(3880,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV259 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3798]) ).
thf(3881,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( ~ ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 ) )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3799]) ).
thf(3882,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV482 )
= $false )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3799]) ).
thf(3883,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK93_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV677 )
= $false )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3884,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3885,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3806]) ).
thf(3886,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3887,plain,
! [SV5: $i,SV680: $i,SV486: $i,SV265: $i] :
( ( ( ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV265 )
| ~ ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1383 ) @ SV680 )
| ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1383 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3807]) ).
thf(3888,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
| ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV265 )
| ~ ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1390 ) @ SV680 )
| ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1390 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3808]) ).
thf(3889,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3890,plain,
! [SV5: $i,SV680: $i,SV486: $i,SV265: $i] :
( ( ( ! [SY1384: $i] :
( ~ ( in @ SY1384 @ SV265 )
| ~ ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1384 ) @ SV680 )
| ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1384 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3891,plain,
! [SV9: $i,SV626: $i,SV816: $i] :
( ( ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) )
= $false )
| ( ( ~ ( in @ SV816 @ SV9 ) )
= $true )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3810]) ).
thf(3892,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK98_SY39 @ SV628 @ SV12 ) )
| ~ ! [SY1378: $i] :
( ~ ( SV12 @ SY1378 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SY1378 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3811]) ).
thf(3893,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK95_SY39 @ SV628 @ SV12 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3812]) ).
thf(3894,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ! [SY1376: $i] :
( ~ ( SV12 @ SY1376 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SY1376 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3812]) ).
thf(3895,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK96_SY39 @ SV628 @ SV12 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3813]) ).
thf(3896,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ! [SY1377: $i] :
( ~ ( SV12 @ SY1377 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SY1377 ) ) )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3813]) ).
thf(3897,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK86_SY39 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(3898,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY1367: $i] :
( ~ ( SV12 @ SY1367 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SY1367 ) ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3815]) ).
thf(3899,plain,
! [SV629: $i,SV835: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV835 )
| ( ( sK77_SY44 @ SV629 @ SV13 )
= SV835 ) )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3817]) ).
thf(3900,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( SV13 @ ( sK87_SY44 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3818]) ).
thf(3901,plain,
! [SV629: $i,SV13: $i > $o] :
( ( ( ! [SY1368: $i] :
( ~ ( SV13 @ SY1368 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SY1368 ) ) )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3819]) ).
thf(3902,plain,
! [SV629: $i,SV836: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV836 )
| ( ( sK78_SY44 @ SV629 @ SV13 )
= SV836 ) )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3821]) ).
thf(3903,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3904,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3823]) ).
thf(3905,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(3906,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(3907,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3908,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(3909,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3828]) ).
thf(3910,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(3911,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(3912,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3831]) ).
thf(3913,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( SV19 @ ( sK88_SY64 @ SV630 @ SV19 ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3832]) ).
thf(3914,plain,
! [SV630: $i,SV19: $i > $o] :
( ( ( ! [SY1371: $i] :
( ~ ( SV19 @ SY1371 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SY1371 ) ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3833]) ).
thf(3915,plain,
! [SV630: $i,SV837: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV837 )
| ( ( sK79_SY64 @ SV630 @ SV19 )
= SV837 ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3835]) ).
thf(3916,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( ~ ( in @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3836]) ).
thf(3917,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i,SV831: $i] :
( ( ( ~ ( ~ ( in @ SV831 @ SV298 )
| ~ ( SV46 @ SV831 @ SV778 ) ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3837]) ).
thf(3918,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i] :
( ( ( ! [SY1385: $i] :
~ ( ~ ( ~ ( in @ SY1385 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY738: $i] :
~ ~ ( ~ ( in @ SY738 @ SV298 )
| ~ ( SV46 @ SY738 @ SY1385 ) ) )
| ~ ( ~ ~ ! [SY739: $i] :
~ ~ ( ~ ( in @ SY739 @ SV298 )
| ~ ( SV46 @ SY739 @ SY1385 ) )
| ( in @ SY1385 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3838]) ).
thf(3919,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
| ~ ( ~ ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) )
| ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3839]) ).
thf(3920,plain,
! [SV76: $i,SV800: $i,SV321: $i > $o] :
( ( ( SV321 @ SV800 )
= $false )
| ( ( in @ SV800 @ SV76 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK12_SY769 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3841]) ).
thf(3921,plain,
! [SV321: $i > $o,SV76: $i,SV819: $i] :
( ( ( in @ SV819 @ SV76 )
= $false )
| ( ( ~ ( SV321 @ SV819 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(3922,plain,
! [SV76: $i,SV801: $i,SV321: $i > $o] :
( ( ( SV321 @ SV801 )
= $false )
| ( ( in @ SV801 @ SV76 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( ( sK12_SY769 @ SV321 @ SV76 )
= ( sK33_SY1232 @ SV321 @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(3923,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( SV89 @ ( sK89_SY225 @ SV639 @ SV89 ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3844]) ).
thf(3924,plain,
! [SV639: $i,SV89: $i > $o] :
( ( ( ! [SY1372: $i] :
( ~ ( SV89 @ SY1372 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SY1372 ) ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3845]) ).
thf(3925,plain,
! [SV639: $i,SV839: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV839 )
| ( ( sK82_SY225 @ SV639 @ SV89 )
= SV839 ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3847]) ).
thf(3926,plain,
! [SV118: $i,SV537: $i,SV705: $i,SV802: $i,SV360: $i,SV827: $i] :
( ( ( in @ SV827 @ SV360 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV802 @ SV827 ) @ SV705 )
| ( in @ ( kpair @ SV802 @ SV827 ) @ SV537 ) )
= $true )
| ( ( in @ SV802 @ SV118 )
= $false )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3848]) ).
thf(3927,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i,SV825: $i,SV794: $i] :
( ( ( ~ ( in @ ( kpair @ SV794 @ SV825 ) @ SV705 ) )
= $true )
| ( ( in @ ( kpair @ SV794 @ SV825 ) @ SV537 )
= $true )
| ( ( in @ SV825 @ SV360 )
= $false )
| ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3849]) ).
thf(3928,plain,
! [SV131: $i,SV803: $i,SV371: $i > $o] :
( ( ( SV371 @ SV803 )
= $false )
| ( ( in @ SV803 @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK16_SY848 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3851]) ).
thf(3929,plain,
! [SV371: $i > $o,SV131: $i,SV820: $i] :
( ( ( in @ SV820 @ SV131 )
= $false )
| ( ( ~ ( SV371 @ SV820 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(3930,plain,
! [SV131: $i,SV804: $i,SV371: $i > $o] :
( ( ( SV371 @ SV804 )
= $false )
| ( ( in @ SV804 @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( ( sK16_SY848 @ SV371 @ SV131 )
= ( sK34_SY1241 @ SV371 @ SV131 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(3931,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
| ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) ) )
= $false )
| ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(3932,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
= $false )
| ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3933,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $false )
| ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3855]) ).
thf(3934,plain,
! [SV653: $i,SV805: $i,SV821: $i,SV146: $i > $o] :
( ( ( SV146 @ SV821 )
= $false )
| ( ( SV805 = SV821 )
= $true )
| ( ( SV146 @ SV805 )
= $false )
| ( ( SV146 @ SV653 )
= $false )
| ( ( SV146 @ ( sK66_SY1248 @ SV653 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(3935,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV661 )
| SV758 )
= $false )
| ( SV758 = $true )
| ( ( in @ SV770 @ SV413 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3858]) ).
thf(3936,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV661 ) )
= $false )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(3937,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV770: $i,SV758: $o] :
( ( SV758 = $false )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(3938,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV661 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV771 @ SV413 )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(3939,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV661 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3861]) ).
thf(3940,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3861]) ).
thf(3941,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV661 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV772 @ SV413 )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(3942,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV661 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3863]) ).
thf(3943,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3863]) ).
thf(3944,plain,
! [SV196: $i,SV811: $i,SV828: $i] :
( ( ( in @ SV828 @ SV811 )
= $false )
| ( ( in @ SV828 @ SV196 )
= $true )
| ( ( in @ SV811 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(3945,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV196 ) )
= $true )
| ( ( ~ ( in @ SV823 @ SV196 ) )
= $true )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(3946,plain,
! [SV196: $i,SV791: $i,SV784: $i] :
( ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ SV784 )
| ( in @ SY1350 @ SV791 ) ) )
= $true )
| ( ( ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3866]) ).
thf(3947,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3867]) ).
thf(3948,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( in @ SV832 @ SV759 )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3868]) ).
thf(3949,plain,
! [SV666: $i,SV813: $i,SV824: $i,SV205: $i > $o] :
( ( ( SV205 @ SV824 )
= $false )
| ( ( SV813 = SV824 )
= $true )
| ( ( SV205 @ SV813 )
= $false )
| ( ( SV205 @ SV666 )
= $false )
| ( ( SV205 @ ( sK70_SY1259 @ SV666 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(3950,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( ~ ( ~ ( SV227 @ SV829 )
| ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3871]) ).
thf(3951,plain,
! [SV227: $i > $o,SV671: $i,SV829: $i] :
( ( ( ~ ( ( SV829
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV829 ) ) )
= $false )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3871]) ).
thf(3952,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV826 )
| ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3872]) ).
thf(3953,plain,
! [SV227: $i > $o,SV671: $i,SV826: $i] :
( ( ( ( SV826
!= ( sK85_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV826 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3873]) ).
thf(3954,plain,
! [SV792: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3874]) ).
thf(3955,plain,
! [SV237: $i > $o,SV461: $i > $o,SV792: $i] :
( ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3874]) ).
thf(3956,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( ~ ~ ( ~ ( SV237 @ SV841 )
| ~ ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3875]) ).
thf(3957,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ SV833 )
| ~ ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(3958,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ SV834 )
| ~ ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3877]) ).
thf(3959,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV830 )
| ~ ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3878]) ).
thf(3960,plain,
! [SV259: $i,SV677: $i,SV482: $i] :
( ( ( in @ ( sK97_SY1273 @ SV482 @ SV677 @ SV259 ) @ SV677 )
= $true )
| ( ( SV482 = SV677 )
= $true )
| ( ( in @ ( sK58_SY1272 @ SV677 @ SV482 @ SV259 ) @ SV482 )
= $true )
| ( ( in @ SV677 @ ( powerset @ SV259 ) )
= $false )
| ( ( in @ SV482 @ ( powerset @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3881]) ).
thf(3961,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( in @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3884]) ).
thf(3962,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3885]) ).
thf(3963,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3885]) ).
thf(3964,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3886]) ).
thf(3965,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
| ~ ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3887]) ).
thf(3966,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3888]) ).
thf(3967,plain,
! [SV5: $i,SV680: $i,SV486: $i,SV265: $i] :
( ( ( ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV265 )
| ~ ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1390 ) @ SV680 )
| ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SY1390 ) @ SV486 ) ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3888]) ).
thf(3968,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3889]) ).
thf(3969,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
| ~ ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3890]) ).
thf(3970,plain,
! [SV626: $i,SV9: $i,SV816: $i] :
( ( ( in @ SV816 @ SV9 )
= $false )
| ( ( in @ SV816 @ ( sK38_SY30 @ SV626 @ SV9 ) )
= $false )
| ( ( in @ SV626 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(3971,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ ( sK98_SY39 @ SV628 @ SV12 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(3972,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ~ ! [SY1378: $i] :
( ~ ( SV12 @ SY1378 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SY1378 ) ) )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(3973,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK95_SY39 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3893]) ).
thf(3974,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY1376: $i] :
( ~ ( SV12 @ SY1376 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SY1376 ) ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3894]) ).
thf(3975,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK96_SY39 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3895]) ).
thf(3976,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY1377: $i] :
( ~ ( SV12 @ SY1377 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SY1377 ) ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(3977,plain,
! [SV628: $i,SV842: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV842 )
| ( ( sK86_SY39 @ SV628 @ SV12 )
= SV842 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3898]) ).
thf(3978,plain,
! [SV629: $i,SV835: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV835 ) )
= $true )
| ( ( ( sK77_SY44 @ SV629 @ SV13 )
= SV835 )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3899]) ).
thf(3979,plain,
! [SV629: $i,SV843: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV843 )
| ( ( sK87_SY44 @ SV629 @ SV13 )
= SV843 ) )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3901]) ).
thf(3980,plain,
! [SV629: $i,SV836: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV836 ) )
= $true )
| ( ( ( sK78_SY44 @ SV629 @ SV13 )
= SV836 )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3902]) ).
thf(3981,plain,
! [SV270: $i > $o,SV817: $i,SV15: $i > $o] :
( ( ( ! [SY1369: $i] :
( ~ ( SV15 @ SY1369 )
| ( SV817 = SY1369 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3903]) ).
thf(3982,plain,
! [SV15: $i > $o,SV818: $i,SV270: $i > $o] :
( ( ( ! [SY1370: $i] :
( ~ ( SV270 @ SY1370 )
| ( SV818 = SY1370 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3904]) ).
thf(3983,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(3984,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(3985,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3907]) ).
thf(3986,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3908]) ).
thf(3987,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3909]) ).
thf(3988,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3910]) ).
thf(3989,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ SV844 )
| ~ ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3911]) ).
thf(3990,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ SV845 )
| ~ ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3912]) ).
thf(3991,plain,
! [SV630: $i,SV846: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV846 )
| ( ( sK88_SY64 @ SV630 @ SV19 )
= SV846 ) )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3914]) ).
thf(3992,plain,
! [SV630: $i,SV837: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV837 ) )
= $true )
| ( ( ( sK79_SY64 @ SV630 @ SV19 )
= SV837 )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3915]) ).
thf(3993,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( in @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV778 ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3916]) ).
thf(3994,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ SV298 )
| ~ ( SV46 @ SV831 @ SV778 ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3917]) ).
thf(3995,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
| ~ ( ~ ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) )
| ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3918]) ).
thf(3996,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( ~ ( ~ ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
| ~ ( ~ ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) )
| ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3919]) ).
thf(3997,plain,
! [SV76: $i,SV819: $i,SV321: $i > $o] :
( ( ( SV321 @ SV819 )
= $false )
| ( ( in @ SV819 @ SV76 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV76
@ ^ [SY772: $i] : ( SV321 @ SY772 ) ) )
= $true )
| ( ( SV321 @ ( sK33_SY1232 @ SV321 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3921]) ).
thf(3998,plain,
! [SV639: $i,SV848: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV848 )
| ( ( sK89_SY225 @ SV639 @ SV89 )
= SV848 ) )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(3999,plain,
! [SV639: $i,SV839: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV839 ) )
= $true )
| ( ( ( sK82_SY225 @ SV639 @ SV89 )
= SV839 )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4000,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i,SV827: $i,SV802: $i] :
( ( ( ~ ( in @ ( kpair @ SV802 @ SV827 ) @ SV705 ) )
= $true )
| ( ( in @ ( kpair @ SV802 @ SV827 ) @ SV537 )
= $true )
| ( ( in @ SV827 @ SV360 )
= $false )
| ( ( in @ SV802 @ SV118 )
= $false )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4001,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i,SV825: $i,SV794: $i] :
( ( ( in @ ( kpair @ SV794 @ SV825 ) @ SV705 )
= $false )
| ( ( in @ ( kpair @ SV794 @ SV825 ) @ SV537 )
= $true )
| ( ( in @ SV825 @ SV360 )
= $false )
| ( ( in @ SV794 @ SV118 )
= $false )
| ( ( ( ap @ SV118 @ SV360 @ SV537 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) )
= ( ap @ SV118 @ SV360 @ SV705 @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) ) )
= $false )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4002,plain,
! [SV131: $i,SV820: $i,SV371: $i > $o] :
( ( ( SV371 @ SV820 )
= $false )
| ( ( in @ SV820 @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV131
@ ^ [SY851: $i] : ( SV371 @ SY851 ) ) )
= $true )
| ( ( SV371 @ ( sK34_SY1241 @ SV371 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3929]) ).
thf(4003,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( ~ ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) ) )
= $false )
| ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4004,plain,
! [SV137: $i,SV377: $i,SV708: $i > $o,SV650: $i > $o] :
( ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $false )
| ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3931]) ).
thf(4005,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $true )
| ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $false )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3932]) ).
thf(4006,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ SV661 ) )
= $false )
| ( SV758 = $true )
| ( ( in @ SV770 @ SV413 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4007,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV770: $i,SV758: $o] :
( ( SV758 = $false )
| ( SV758 = $true )
| ( ( in @ SV770 @ SV413 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4008,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( in @ SV770 @ SV661 )
= $true )
| ( SV758 = $true )
| ( SV758 = $false )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3936]) ).
thf(4009,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ SV661 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV771 @ SV413 )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3938]) ).
thf(4010,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV771: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV771 @ SV413 )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3938]) ).
thf(4011,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( in @ SV771 @ SV661 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3939]) ).
thf(4012,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV661 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV772 @ SV413 )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3941]) ).
thf(4013,plain,
! [SV181: $i,SV661: $i,SV413: $i,SV772: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV772 @ SV413 )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3941]) ).
thf(4014,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( in @ SV772 @ SV661 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3942]) ).
thf(4015,plain,
! [SV823: $i,SV196: $i,SV812: $i] :
( ( ( in @ SV812 @ SV196 )
= $false )
| ( ( ~ ( in @ SV823 @ SV196 ) )
= $true )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3945]) ).
thf(4016,plain,
! [SV196: $i,SV791: $i,SV784: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ SV784 )
| ( in @ SV849 @ SV791 ) )
= $true )
| ( ( ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3946]) ).
thf(4017,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( in @ SV840 @ SV759 )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( ~ ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3947]) ).
thf(4018,plain,
! [SV832: $i,SV759: $i,SV196: $i] :
( ( ( ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3948]) ).
thf(4019,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV829 )
| ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3950]) ).
thf(4020,plain,
! [SV227: $i > $o,SV671: $i,SV829: $i] :
( ( ( ( SV829
!= ( sK91_SY579 @ SV671 @ SV227 ) )
| ( SV227 @ SV829 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(4021,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV826 ) )
= $true )
| ( ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3952]) ).
thf(4022,plain,
! [SV227: $i > $o,SV671: $i,SV826: $i] :
( ( ( SV826
!= ( sK85_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV826 )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(4023,plain,
! [SV792: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3954]) ).
thf(4024,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3955]) ).
thf(4025,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( ~ ( ~ ( SV237 @ SV841 )
| ~ ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4026,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV833 )
| ~ ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3957]) ).
thf(4027,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV834 )
| ~ ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3958]) ).
thf(4028,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV830 ) )
= $true )
| ( ( ~ ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4029,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK94_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK100_SY1375 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3962]) ).
thf(4030,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3965]) ).
thf(4031,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3965]) ).
thf(4032,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ SV5 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3966]) ).
thf(4033,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
| ~ ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3967]) ).
thf(4034,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4035,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4036,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( SV12 @ ( sK98_SY39 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3971]) ).
thf(4037,plain,
! [SV628: $i,SV12: $i > $o] :
( ( ( ! [SY1378: $i] :
( ~ ( SV12 @ SY1378 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SY1378 ) ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3972]) ).
thf(4038,plain,
! [SV628: $i,SV850: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV850 )
| ( ( sK95_SY39 @ SV628 @ SV12 )
= SV850 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3974]) ).
thf(4039,plain,
! [SV628: $i,SV851: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV851 )
| ( ( sK96_SY39 @ SV628 @ SV12 )
= SV851 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3976]) ).
thf(4040,plain,
! [SV628: $i,SV842: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV842 ) )
= $true )
| ( ( ( sK86_SY39 @ SV628 @ SV12 )
= SV842 )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3977]) ).
thf(4041,plain,
! [SV629: $i,SV835: $i,SV13: $i > $o] :
( ( ( SV13 @ SV835 )
= $false )
| ( ( ( sK77_SY44 @ SV629 @ SV13 )
= SV835 )
= $true )
| ( ( SV13 @ ( sK45_SY42 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3978]) ).
thf(4042,plain,
! [SV629: $i,SV843: $i,SV13: $i > $o] :
( ( ( ~ ( SV13 @ SV843 ) )
= $true )
| ( ( ( sK87_SY44 @ SV629 @ SV13 )
= SV843 )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3979]) ).
thf(4043,plain,
! [SV629: $i,SV836: $i,SV13: $i > $o] :
( ( ( SV13 @ SV836 )
= $false )
| ( ( ( sK78_SY44 @ SV629 @ SV13 )
= SV836 )
= $true )
| ( ( ( sK45_SY42 @ SV629 @ SV13 )
= ( sK51_SY1335 @ SV629 @ SV13 ) )
= $false )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3980]) ).
thf(4044,plain,
! [SV817: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
| ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3981]) ).
thf(4045,plain,
! [SV818: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
| ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3982]) ).
thf(4046,plain,
! [SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY52: $i] :
~ ~ ( ~ ( SV15 @ SY52 )
| ~ ! [SY53: $i] :
( ~ ( SV15 @ SY53 )
| ( SY52 = SY53 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3983]) ).
thf(4047,plain,
! [SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY691: $i] :
~ ~ ( ~ ( SV270 @ SY691 )
| ~ ! [SY692: $i] :
( ~ ( SV270 @ SY692 )
| ( SY691 = SY692 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3984]) ).
thf(4048,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ SV852 )
| ~ ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3985]) ).
thf(4049,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ SV853 )
| ~ ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3986]) ).
thf(4050,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ SV854 )
| ~ ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3987]) ).
thf(4051,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ SV855 )
| ~ ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4052,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ SV844 )
| ~ ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4053,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ SV845 )
| ~ ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4054,plain,
! [SV630: $i,SV846: $i,SV19: $i > $o] :
( ( ( ~ ( SV19 @ SV846 ) )
= $true )
| ( ( ( sK88_SY64 @ SV630 @ SV19 )
= SV846 )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3991]) ).
thf(4055,plain,
! [SV630: $i,SV837: $i,SV19: $i > $o] :
( ( ( SV19 @ SV837 )
= $false )
| ( ( ( sK79_SY64 @ SV630 @ SV19 )
= SV837 )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV630
= ( sK61_SY1222 @ SV630 @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3992]) ).
thf(4056,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( ~ ( in @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV298 ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4057,plain,
! [SV298: $i,SV778: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV778 ) )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3993]) ).
thf(4058,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ SV298 ) )
= $true )
| ( ( ~ ( SV46 @ SV831 @ SV778 ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3994]) ).
thf(4059,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( ~ ( ~ ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
| ~ ( ~ ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) )
| ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4060,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( ~ ( ~ ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3996]) ).
thf(4061,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ( ~ ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) )
| ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3996]) ).
thf(4062,plain,
! [SV639: $i,SV848: $i,SV89: $i > $o] :
( ( ( ~ ( SV89 @ SV848 ) )
= $true )
| ( ( ( sK89_SY225 @ SV639 @ SV89 )
= SV848 )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3998]) ).
thf(4063,plain,
! [SV639: $i,SV839: $i,SV89: $i > $o] :
( ( ( SV89 @ SV839 )
= $false )
| ( ( ( sK82_SY225 @ SV639 @ SV89 )
= SV839 )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV639
= ( sK62_SY1234 @ SV639 @ SV89 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3999]) ).
thf(4064,plain,
! [SV118: $i,SV360: $i,SV537: $i,SV705: $i,SV827: $i,SV802: $i] :
( ( ( in @ ( kpair @ SV802 @ SV827 ) @ SV705 )
= $false )
| ( ( in @ ( kpair @ SV802 @ SV827 ) @ SV537 )
= $true )
| ( ( in @ SV827 @ SV360 )
= $false )
| ( ( in @ SV802 @ SV118 )
= $false )
| ( ( in @ ( sK63_SY1290 @ SV705 @ SV537 @ SV360 @ SV118 ) @ SV118 )
= $true )
| ( ( func @ SV118 @ SV360 @ SV705 )
= $false )
| ( ( func @ SV118 @ SV360 @ SV537 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4000]) ).
thf(4065,plain,
! [SV377: $i,SV650: $i > $o,SV137: $i,SV708: $i > $o] :
( ( ( SV708 @ ( sK65_SY1340 @ SV137 @ SV650 @ SV708 @ SV377 ) )
= $true )
| ( ( SV650 @ ( sK47_SY1295 @ SV708 @ SV650 @ SV377 @ SV137 ) )
= $true )
| ( ( ( dsetconstr @ SV137
@ ^ [SY1246: $i] : ( SV650 @ SY1246 ) )
= ( dsetconstr @ SV377
@ ^ [SY1298: $i] : ( SV708 @ SY1298 ) ) )
= $true )
| ( ( SV137 = SV377 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4003]) ).
thf(4066,plain,
! [SV181: $i,SV413: $i,SV758: $o,SV661: $i,SV770: $i] :
( ( ( in @ SV770 @ SV661 )
= $true )
| ( SV758 = $true )
| ( ( in @ SV770 @ SV413 )
= $true )
| ( ( in @ SV770 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV770 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4006]) ).
thf(4067,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV771: $i] :
( ( ( in @ SV771 @ SV661 )
= $true )
| ( $true = $true )
| ( ( in @ SV771 @ SV413 )
= $true )
| ( ( in @ SV771 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV771 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4009]) ).
thf(4068,plain,
! [SV181: $i,SV413: $i,SV661: $i,SV772: $i] :
( ( ( in @ SV772 @ SV661 )
= $true )
| ( $false = $true )
| ( ( in @ SV772 @ SV413 )
= $true )
| ( ( in @ SV772 @ ( binunion @ SV413 @ SV661 ) )
= $false )
| ( ( in @ SV772 @ SV181 )
= $false )
| ( ( in @ SV661 @ ( powerset @ SV181 ) )
= $false )
| ( ( in @ SV413 @ ( powerset @ SV181 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4012]) ).
thf(4069,plain,
! [SV812: $i,SV196: $i,SV823: $i] :
( ( ( in @ SV823 @ SV196 )
= $false )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) )
| ( SV812 = SV823 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4015]) ).
thf(4070,plain,
! [SV196: $i,SV791: $i,SV784: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ SV784 ) )
= $true )
| ( ( in @ SV849 @ SV791 )
= $true )
| ( ( ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4016]) ).
thf(4071,plain,
! [SV840: $i,SV759: $i,SV196: $i] :
( ( ( ! [SY1329: $i] :
~ ~ ! [SY1330: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1329 @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1330 @ SV759 ) )
| ~ ~ ~ ! [SY1331: $i] :
~ ~ ( ~ ( in @ SY1331 @ SY1329 )
| ~ ( in @ SY1331 @ SV759 ) ) )
| ~ ! [SY1159: $i] :
( ~ ( in @ SY1159 @ ( sK5_SY484 @ SV196 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1159 )
| ( in @ SX6 @ SY1329 ) )
| ( in @ SY1330 @ SY1159 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4017]) ).
thf(4072,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ! [SY1402: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1402 @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1404: $i] :
( ~ ( in @ SY1404 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1404 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ SY1402 @ SY1404 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4018]) ).
thf(4073,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( ~ ( SV227 @ SV829 ) )
= $true )
| ( ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4019]) ).
thf(4074,plain,
! [SV227: $i > $o,SV671: $i,SV829: $i] :
( ( ( SV829
!= ( sK91_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV829 )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4075,plain,
! [SV671: $i,SV826: $i,SV227: $i > $o] :
( ( ( SV227 @ SV826 )
= $false )
| ( ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4021]) ).
thf(4076,plain,
! [SV227: $i > $o,SV671: $i,SV826: $i] :
( ( ( SV826
= ( sK85_SY579 @ SV671 @ SV227 ) )
= $false )
| ( ( SV227 @ SV826 )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV671
= ( sK72_SY1265 @ SV671 @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4077,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4023]) ).
thf(4078,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4079,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV841 )
| ~ ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4025]) ).
thf(4080,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV833 ) )
= $true )
| ( ( ~ ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4081,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV834 ) )
= $true )
| ( ( ~ ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4027]) ).
thf(4082,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4028]) ).
thf(4083,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( in @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4030]) ).
thf(4084,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4031]) ).
thf(4085,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4031]) ).
thf(4086,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( ~ ( in @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4087,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
| ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4088,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( in @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4034]) ).
thf(4089,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4035]) ).
thf(4090,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4035]) ).
thf(4091,plain,
! [SV628: $i,SV856: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV856 )
| ( ( sK98_SY39 @ SV628 @ SV12 )
= SV856 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4037]) ).
thf(4092,plain,
! [SV628: $i,SV850: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV850 ) )
= $true )
| ( ( ( sK95_SY39 @ SV628 @ SV12 )
= SV850 )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4038]) ).
thf(4093,plain,
! [SV628: $i,SV851: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV851 ) )
= $true )
| ( ( ( sK96_SY39 @ SV628 @ SV12 )
= SV851 )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4039]) ).
thf(4094,plain,
! [SV628: $i,SV842: $i,SV12: $i > $o] :
( ( ( SV12 @ SV842 )
= $false )
| ( ( ( sK86_SY39 @ SV628 @ SV12 )
= SV842 )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4040]) ).
thf(4095,plain,
! [SV629: $i,SV843: $i,SV13: $i > $o] :
( ( ( SV13 @ SV843 )
= $false )
| ( ( ( sK87_SY44 @ SV629 @ SV13 )
= SV843 )
= $true )
| ( ( SV13 @ ( sK51_SY1335 @ SV629 @ SV13 ) )
= $true )
| ( ( SV13 @ SV629 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4042]) ).
thf(4096,plain,
! [SV817: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4044]) ).
thf(4097,plain,
! [SV15: $i > $o,SV270: $i > $o,SV817: $i] :
( ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4044]) ).
thf(4098,plain,
! [SV818: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4045]) ).
thf(4099,plain,
! [SV270: $i > $o,SV15: $i > $o,SV818: $i] :
( ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4045]) ).
thf(4100,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ SV857 )
| ~ ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4046]) ).
thf(4101,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ SV858 )
| ~ ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4047]) ).
thf(4102,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ SV852 )
| ~ ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4103,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ SV853 )
| ~ ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4104,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ SV854 )
| ~ ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4105,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ SV855 )
| ~ ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4051]) ).
thf(4106,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV844 )
| ~ ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4052]) ).
thf(4107,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV845 )
| ~ ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4053]) ).
thf(4108,plain,
! [SV630: $i,SV846: $i,SV19: $i > $o] :
( ( ( SV19 @ SV846 )
= $false )
| ( ( ( sK88_SY64 @ SV630 @ SV19 )
= SV846 )
= $true )
| ( ( SV19 @ SV630 )
= $false )
| ( ( SV19 @ ( sK61_SY1222 @ SV630 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4054]) ).
thf(4109,plain,
! [SV298: $i,SV46: $i > $i > $o,SV778: $i] :
( ( ( in @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV298 )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4056]) ).
thf(4110,plain,
! [SV298: $i,SV778: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ ( sK103_SY1344 @ SV778 @ SV46 @ SV298 ) @ SV778 )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $false )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4057]) ).
thf(4111,plain,
! [SV778: $i,SV46: $i > $i > $o,SV298: $i,SV831: $i] :
( ( ( in @ SV831 @ SV298 )
= $false )
| ( ( ~ ( SV46 @ SV831 @ SV778 ) )
= $true )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4112,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( ~ ( ~ ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4059]) ).
thf(4113,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ( ~ ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) )
| ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4059]) ).
thf(4114,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4060]) ).
thf(4115,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) )
| ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4061]) ).
thf(4116,plain,
! [SV639: $i,SV848: $i,SV89: $i > $o] :
( ( ( SV89 @ SV848 )
= $false )
| ( ( ( sK89_SY225 @ SV639 @ SV89 )
= SV848 )
= $true )
| ( ( SV89 @ SV639 )
= $false )
| ( ( SV89 @ ( sK62_SY1234 @ SV639 @ SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4117,plain,
! [SV823: $i,SV812: $i,SV196: $i] :
( ( ( ~ ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4069]) ).
thf(4118,plain,
! [SV196: $i,SV791: $i,SV784: $i,SV849: $i] :
( ( ( in @ SV849 @ SV784 )
= $false )
| ( ( in @ SV849 @ SV791 )
= $true )
| ( ( ! [SY1351: $i] :
( ~ ( in @ SY1351 @ SV791 )
| ( in @ SY1351 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4070]) ).
thf(4119,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ! [SY1408: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1408 @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1410: $i] :
( ~ ( in @ SY1410 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1410 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ SY1408 @ SY1410 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4071]) ).
thf(4120,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ! [SY1402: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1402 @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1404: $i] :
( ~ ( in @ SY1404 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1404 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ SY1402 @ SY1404 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4072]) ).
thf(4121,plain,
! [SV671: $i,SV829: $i,SV227: $i > $o] :
( ( ( SV227 @ SV829 )
= $false )
| ( ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4073]) ).
thf(4122,plain,
! [SV227: $i > $o,SV671: $i,SV829: $i] :
( ( ( SV829
= ( sK91_SY579 @ SV671 @ SV227 ) )
= $false )
| ( ( SV227 @ SV829 )
= $true )
| ( ( SV227 @ SV671 )
= $false )
| ( ( SV227 @ ( sK72_SY1265 @ SV671 @ SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4123,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4077]) ).
thf(4124,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4078]) ).
thf(4125,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( ~ ( SV237 @ SV841 ) )
= $true )
| ( ( ~ ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4079]) ).
thf(4126,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4127,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4081]) ).
thf(4128,plain,
! [SV461: $i > $o,SV830: $i,SV237: $i > $o] :
( ( ( ! [SY1382: $i] :
( ~ ( SV237 @ SY1382 )
| ( SV830 = SY1382 ) ) )
= $false )
| ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4129,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK101_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK107_SY1383 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) @ SV265 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4084]) ).
thf(4130,plain,
! [SV265: $i,SV486: $i,SV680: $i,SV5: $i] :
( ( ( in @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) @ SV265 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4086]) ).
thf(4131,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 ) )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4132,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV486 )
= $false )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4133,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK102_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK108_SY1384 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV680 )
= $false )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4089]) ).
thf(4134,plain,
! [SV628: $i,SV856: $i,SV12: $i > $o] :
( ( ( ~ ( SV12 @ SV856 ) )
= $true )
| ( ( ( sK98_SY39 @ SV628 @ SV12 )
= SV856 )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4091]) ).
thf(4135,plain,
! [SV628: $i,SV850: $i,SV12: $i > $o] :
( ( ( SV12 @ SV850 )
= $false )
| ( ( ( sK95_SY39 @ SV628 @ SV12 )
= SV850 )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4136,plain,
! [SV628: $i,SV851: $i,SV12: $i > $o] :
( ( ( SV12 @ SV851 )
= $false )
| ( ( ( sK96_SY39 @ SV628 @ SV12 )
= SV851 )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $false )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4137,plain,
! [SV817: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4096]) ).
thf(4138,plain,
! [SV817: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4097]) ).
thf(4139,plain,
! [SV818: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4098]) ).
thf(4140,plain,
! [SV818: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4099]) ).
thf(4141,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ SV857 )
| ~ ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) ) )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4142,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ SV858 )
| ~ ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) ) )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4143,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV852 )
| ~ ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4102]) ).
thf(4144,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV853 )
| ~ ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4103]) ).
thf(4145,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV854 )
| ~ ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4104]) ).
thf(4146,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV855 )
| ~ ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4105]) ).
thf(4147,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV844 ) )
= $true )
| ( ( ~ ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4106]) ).
thf(4148,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV845 ) )
= $true )
| ( ( ~ ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4107]) ).
thf(4149,plain,
! [SV298: $i,SV778: $i,SV831: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ SV831 @ SV778 )
= $false )
| ( ( in @ SV831 @ SV298 )
= $false )
| ( ( in @ SV778 @ ( sK46_SY736 @ SV46 @ SV298 ) )
= $true )
| ( ( in @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV298 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4111]) ).
thf(4150,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
| ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4112]) ).
thf(4151,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) )
| ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4113]) ).
thf(4152,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) ) )
= $true )
| ( ( ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4114]) ).
thf(4153,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4115]) ).
thf(4154,plain,
! [SV823: $i,SV812: $i,SV196: $i] :
( ( ( ! [SY1373: $i] :
( ~ ( in @ SY1373 @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ SY1373 )
| ( in @ SV823 @ SY1373 ) )
| ~ ( ~ ( in @ SV823 @ SY1373 )
| ( in @ SV812 @ SY1373 ) ) ) ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4117]) ).
thf(4155,plain,
! [SV196: $i,SV849: $i,SV784: $i,SV791: $i,SV859: $i] :
( ( ( ~ ( in @ SV859 @ SV791 )
| ( in @ SV859 @ SV784 ) )
= $true )
| ( ( in @ SV849 @ SV791 )
= $true )
| ( ( in @ SV849 @ SV784 )
= $false )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4118]) ).
thf(4156,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ! [SY1408: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1408 @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1410: $i] :
( ~ ( in @ SY1410 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1410 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ SY1408 @ SY1410 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4119]) ).
thf(4157,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ! [SY1402: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1402 @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1404: $i] :
( ~ ( in @ SY1404 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1404 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ SY1402 @ SY1404 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4120]) ).
thf(4158,plain,
! [SV792: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4123]) ).
thf(4159,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV860 )
| ~ ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4124]) ).
thf(4160,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) )
= $true )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4125]) ).
thf(4161,plain,
! [SV461: $i > $o,SV833: $i,SV237: $i > $o] :
( ( ( ! [SY1388: $i] :
( ~ ( SV237 @ SY1388 )
| ( SV833 = SY1388 ) ) )
= $false )
| ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4126]) ).
thf(4162,plain,
! [SV461: $i > $o,SV834: $i,SV237: $i > $o] :
( ( ( ! [SY1389: $i] :
( ~ ( SV237 @ SY1389 )
| ( SV834 = SY1389 ) ) )
= $false )
| ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4163,plain,
! [SV830: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
| ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4128]) ).
thf(4164,plain,
! [SV5: $i,SV265: $i,SV680: $i,SV486: $i] :
( ( ( in @ ( kpair @ ( sK106_SY1279 @ SV486 @ SV680 @ SV265 @ SV5 ) @ ( sK109_SY1390 @ SV5 @ SV680 @ SV486 @ SV265 ) ) @ SV680 )
= $true )
| ( ( SV486 = SV680 )
= $true )
| ( ( in @ ( kpair @ ( sK60_SY1277 @ SV680 @ SV486 @ SV265 @ SV5 ) @ ( sK74_SY1343 @ SV5 @ SV486 @ SV680 @ SV265 ) ) @ SV486 )
= $true )
| ( ( subset @ SV680 @ ( cartprod @ SV5 @ SV265 ) )
= $false )
| ( ( subset @ SV486 @ ( cartprod @ SV5 @ SV265 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4131]) ).
thf(4165,plain,
! [SV628: $i,SV856: $i,SV12: $i > $o] :
( ( ( SV12 @ SV856 )
= $false )
| ( ( ( sK98_SY39 @ SV628 @ SV12 )
= SV856 )
= $true )
| ( ( SV12 @ ( sK31_SY1220 @ SV628 @ SV12 ) )
= $true )
| ( ( ( sK31_SY1220 @ SV628 @ SV12 )
= SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4166,plain,
! [SV817: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4167,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK115_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1413: $i] :
( ~ ( SV270 @ SY1413 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SY1413 ) ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4138]) ).
thf(4168,plain,
! [SV818: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4139]) ).
thf(4169,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK116_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1414: $i] :
( ~ ( SV15 @ SY1414 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SY1414 ) ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4140]) ).
thf(4170,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV857 )
| ~ ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4141]) ).
thf(4171,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV858 )
| ~ ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4142]) ).
thf(4172,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV852 ) )
= $true )
| ( ( ~ ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4143]) ).
thf(4173,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV853 ) )
= $true )
| ( ( ~ ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4144]) ).
thf(4174,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV854 ) )
= $true )
| ( ( ~ ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4145]) ).
thf(4175,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV855 ) )
= $true )
| ( ( ~ ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4146]) ).
thf(4176,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4177,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4178,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) ) )
= $true )
| ( ( ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4179,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4151]) ).
thf(4180,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV838: $i] :
( ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( ~ ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4181,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4182,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( ~ ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
| ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4154]) ).
thf(4183,plain,
! [SV196: $i,SV849: $i,SV784: $i,SV791: $i,SV859: $i] :
( ( ( ~ ( in @ SV859 @ SV791 ) )
= $true )
| ( ( in @ SV859 @ SV784 )
= $true )
| ( ( in @ SV849 @ SV791 )
= $true )
| ( ( in @ SV849 @ SV784 )
= $false )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4184,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ! [SY1408: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ SY1408 @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1410: $i] :
( ~ ( in @ SY1410 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1410 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ SY1408 @ SY1410 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4185,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1416: $i] :
( ~ ( in @ SY1416 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1416 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SY1416 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4157]) ).
thf(4186,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV861 )
| ~ ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4158]) ).
thf(4187,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV860 )
| ~ ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4159]) ).
thf(4188,plain,
! [SV461: $i > $o,SV841: $i,SV237: $i > $o] :
( ( ( ! [SY1393: $i] :
( ~ ( SV237 @ SY1393 )
| ( SV841 = SY1393 ) ) )
= $false )
| ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4160]) ).
thf(4189,plain,
! [SV833: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
| ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4161]) ).
thf(4190,plain,
! [SV834: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
| ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4162]) ).
thf(4191,plain,
! [SV830: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4163]) ).
thf(4192,plain,
! [SV237: $i > $o,SV461: $i > $o,SV830: $i] :
( ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4163]) ).
thf(4193,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK121_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1419: $i] :
( ~ ( SV270 @ SY1419 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SY1419 ) ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4166]) ).
thf(4194,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK115_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1413: $i] :
( ~ ( SV270 @ SY1413 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SY1413 ) ) ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4167]) ).
thf(4195,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK122_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1420: $i] :
( ~ ( SV15 @ SY1420 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SY1420 ) ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4168]) ).
thf(4196,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK116_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1414: $i] :
( ~ ( SV15 @ SY1414 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SY1414 ) ) ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4169]) ).
thf(4197,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV857 ) )
= $true )
| ( ( ~ ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4170]) ).
thf(4198,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV858 ) )
= $true )
| ( ( ~ ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4199,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4172]) ).
thf(4200,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4173]) ).
thf(4201,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4174]) ).
thf(4202,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4203,plain,
! [SV270: $i > $o,SV844: $i,SV15: $i > $o] :
( ( ( ! [SY1394: $i] :
( ~ ( SV15 @ SY1394 )
| ( SV844 = SY1394 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4204,plain,
! [SV15: $i > $o,SV845: $i,SV270: $i > $o] :
( ( ( ! [SY1395: $i] :
( ~ ( SV270 @ SY1395 )
| ( SV845 = SY1395 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4205,plain,
! [SV298: $i,SV46: $i > $i > $o,SV746: $i,SV847: $i] :
( ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( ~ ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4206,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ~ ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4179]) ).
thf(4207,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1391: $i] :
~ ~ ( ~ ( in @ SY1391 @ SV298 )
| ~ ( SV46 @ SY1391 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4180]) ).
thf(4208,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1392: $i] :
~ ~ ( ~ ( in @ SY1392 @ SV298 )
| ~ ( SV46 @ SY1392 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4181]) ).
thf(4209,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) @ ( sK5_SY484 @ SV196 ) ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4182]) ).
thf(4210,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
| ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4182]) ).
thf(4211,plain,
! [SV196: $i,SV849: $i,SV784: $i,SV791: $i,SV859: $i] :
( ( ( in @ SV859 @ SV791 )
= $false )
| ( ( in @ SV859 @ SV784 )
= $true )
| ( ( in @ SV849 @ SV791 )
= $true )
| ( ( in @ SV849 @ SV784 )
= $false )
| ( ( in @ SV784 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ SV791 @ ( sK5_SY484 @ SV196 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4212,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1422 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SY1422 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4184]) ).
thf(4213,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1416: $i] :
( ~ ( in @ SY1416 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1416 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SY1416 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4185]) ).
thf(4214,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV861 )
| ~ ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4186]) ).
thf(4215,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV860 )
| ~ ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4187]) ).
thf(4216,plain,
! [SV841: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
| ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4188]) ).
thf(4217,plain,
! [SV833: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4218,plain,
! [SV237: $i > $o,SV461: $i > $o,SV833: $i] :
( ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4189]) ).
thf(4219,plain,
! [SV834: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4220,plain,
! [SV237: $i > $o,SV461: $i > $o,SV834: $i] :
( ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4221,plain,
! [SV830: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4191]) ).
thf(4222,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4192]) ).
thf(4223,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK121_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1419: $i] :
( ~ ( SV270 @ SY1419 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SY1419 ) ) ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4193]) ).
thf(4224,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK115_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1413: $i] :
( ~ ( SV270 @ SY1413 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SY1413 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4225,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK122_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1420: $i] :
( ~ ( SV15 @ SY1420 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SY1420 ) ) ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4195]) ).
thf(4226,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK116_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1414: $i] :
( ~ ( SV15 @ SY1414 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SY1414 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4227,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) )
= $true )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4197]) ).
thf(4228,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) )
= $true )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4198]) ).
thf(4229,plain,
! [SV270: $i > $o,SV852: $i,SV15: $i > $o] :
( ( ( ! [SY1398: $i] :
( ~ ( SV15 @ SY1398 )
| ( SV852 = SY1398 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4199]) ).
thf(4230,plain,
! [SV15: $i > $o,SV853: $i,SV270: $i > $o] :
( ( ( ! [SY1399: $i] :
( ~ ( SV270 @ SY1399 )
| ( SV853 = SY1399 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4200]) ).
thf(4231,plain,
! [SV270: $i > $o,SV854: $i,SV15: $i > $o] :
( ( ( ! [SY1400: $i] :
( ~ ( SV15 @ SY1400 )
| ( SV854 = SY1400 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4201]) ).
thf(4232,plain,
! [SV15: $i > $o,SV855: $i,SV270: $i > $o] :
( ( ( ! [SY1401: $i] :
( ~ ( SV270 @ SY1401 )
| ( SV855 = SY1401 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4233,plain,
! [SV844: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
| ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4203]) ).
thf(4234,plain,
! [SV845: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
| ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4204]) ).
thf(4235,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1396: $i] :
~ ~ ( ~ ( in @ SY1396 @ SV298 )
| ~ ( SV46 @ SY1396 @ SV847 ) ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4205]) ).
thf(4236,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i] :
( ( ( ! [SY1397: $i] :
~ ~ ( ~ ( in @ SY1397 @ SV298 )
| ~ ( SV46 @ SY1397 @ SV847 ) ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4206]) ).
thf(4237,plain,
! [SV298: $i,SV46: $i > $i > $o,SV838: $i,SV746: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4207]) ).
thf(4238,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i,SV862: $i] :
( ( ( ~ ~ ( ~ ( in @ SV862 @ SV298 )
| ~ ( SV46 @ SV862 @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4208]) ).
thf(4239,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( in @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4209]) ).
thf(4240,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( ~ ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
| ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4210]) ).
thf(4241,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1422 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SY1422 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4212]) ).
thf(4242,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
| ~ ! [SY1416: $i] :
( ~ ( in @ SY1416 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1416 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SY1416 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4243,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV861 )
| ~ ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4214]) ).
thf(4244,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV860 ) )
= $true )
| ( ( ~ ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4215]) ).
thf(4245,plain,
! [SV841: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( ~ ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) ) )
= $false )
| ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4216]) ).
thf(4246,plain,
! [SV237: $i > $o,SV461: $i > $o,SV841: $i] :
( ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4216]) ).
thf(4247,plain,
! [SV833: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4217]) ).
thf(4248,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4218]) ).
thf(4249,plain,
! [SV834: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4219]) ).
thf(4250,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4220]) ).
thf(4251,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4221]) ).
thf(4252,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4253,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK121_SY689 @ SV817 @ SV15 @ SV270 ) )
| ~ ! [SY1419: $i] :
( ~ ( SV270 @ SY1419 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SY1419 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4223]) ).
thf(4254,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK115_SY689 @ SV817 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4224]) ).
thf(4255,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1413: $i] :
( ~ ( SV270 @ SY1413 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SY1413 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4224]) ).
thf(4256,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK122_SY58 @ SV818 @ SV270 @ SV15 ) )
| ~ ! [SY1420: $i] :
( ~ ( SV15 @ SY1420 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SY1420 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4257,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK116_SY58 @ SV818 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4226]) ).
thf(4258,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1414: $i] :
( ~ ( SV15 @ SY1414 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SY1414 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4226]) ).
thf(4259,plain,
! [SV270: $i > $o,SV857: $i,SV15: $i > $o] :
( ( ( ! [SY1406: $i] :
( ~ ( SV15 @ SY1406 )
| ( SV857 = SY1406 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4260,plain,
! [SV15: $i > $o,SV858: $i,SV270: $i > $o] :
( ( ( ! [SY1407: $i] :
( ~ ( SV270 @ SY1407 )
| ( SV858 = SY1407 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4228]) ).
thf(4261,plain,
! [SV852: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
| ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4229]) ).
thf(4262,plain,
! [SV853: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
| ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4230]) ).
thf(4263,plain,
! [SV854: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
| ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4231]) ).
thf(4264,plain,
! [SV855: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
| ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4232]) ).
thf(4265,plain,
! [SV844: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4233]) ).
thf(4266,plain,
! [SV15: $i > $o,SV270: $i > $o,SV844: $i] :
( ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4233]) ).
thf(4267,plain,
! [SV845: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4234]) ).
thf(4268,plain,
! [SV270: $i > $o,SV15: $i > $o,SV845: $i] :
( ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4234]) ).
thf(4269,plain,
! [SV298: $i,SV46: $i > $i > $o,SV847: $i,SV746: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV847 ) ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4235]) ).
thf(4270,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i,SV863: $i] :
( ( ( ~ ~ ( ~ ( in @ SV863 @ SV298 )
| ~ ( SV46 @ SV863 @ SV847 ) ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4236]) ).
thf(4271,plain,
! [SV298: $i,SV46: $i > $i > $o,SV838: $i,SV746: $i] :
( ( ( ~ ( ~ ( in @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV838 ) ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4237]) ).
thf(4272,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i,SV862: $i] :
( ( ( ~ ( ~ ( in @ SV862 @ SV298 )
| ~ ( SV46 @ SV862 @ SV838 ) ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4273,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( ~ ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4240]) ).
thf(4274,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
| ~ ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1422 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SY1422 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4241]) ).
thf(4275,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4242]) ).
thf(4276,plain,
! [SV759: $i,SV832: $i,SV196: $i] :
( ( ( ~ ! [SY1416: $i] :
( ~ ( in @ SY1416 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1416 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SY1416 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4242]) ).
thf(4277,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV861 ) )
= $true )
| ( ( ~ ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4243]) ).
thf(4278,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( SV461 @ SV860 )
= $false )
| ( ( ~ ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4244]) ).
thf(4279,plain,
! [SV841: $i,SV461: $i > $o,SV237: $i > $o] :
( ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) )
| ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4245]) ).
thf(4280,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4246]) ).
thf(4281,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4247]) ).
thf(4282,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4283,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4249]) ).
thf(4284,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4250]) ).
thf(4285,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4251]) ).
thf(4286,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4252]) ).
thf(4287,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK121_SY689 @ SV817 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4288,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1419: $i] :
( ~ ( SV270 @ SY1419 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SY1419 ) ) )
= $false )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4253]) ).
thf(4289,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK115_SY689 @ SV817 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4254]) ).
thf(4290,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ! [SY1413: $i] :
( ~ ( SV270 @ SY1413 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SY1413 ) ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4255]) ).
thf(4291,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK122_SY58 @ SV818 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4292,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1420: $i] :
( ~ ( SV15 @ SY1420 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SY1420 ) ) )
= $false )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4256]) ).
thf(4293,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK116_SY58 @ SV818 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4257]) ).
thf(4294,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ! [SY1414: $i] :
( ~ ( SV15 @ SY1414 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SY1414 ) ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4258]) ).
thf(4295,plain,
! [SV857: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
| ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4259]) ).
thf(4296,plain,
! [SV858: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
| ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4260]) ).
thf(4297,plain,
! [SV852: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4261]) ).
thf(4298,plain,
! [SV15: $i > $o,SV270: $i > $o,SV852: $i] :
( ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4261]) ).
thf(4299,plain,
! [SV853: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4262]) ).
thf(4300,plain,
! [SV270: $i > $o,SV15: $i > $o,SV853: $i] :
( ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4262]) ).
thf(4301,plain,
! [SV854: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4263]) ).
thf(4302,plain,
! [SV15: $i > $o,SV270: $i > $o,SV854: $i] :
( ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4263]) ).
thf(4303,plain,
! [SV855: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4264]) ).
thf(4304,plain,
! [SV270: $i > $o,SV15: $i > $o,SV855: $i] :
( ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4264]) ).
thf(4305,plain,
! [SV844: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4265]) ).
thf(4306,plain,
! [SV844: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4266]) ).
thf(4307,plain,
! [SV845: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4267]) ).
thf(4308,plain,
! [SV845: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4309,plain,
! [SV298: $i,SV46: $i > $i > $o,SV847: $i,SV746: $i] :
( ( ( ~ ( ~ ( in @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV847 ) ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4269]) ).
thf(4310,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i,SV863: $i] :
( ( ( ~ ( ~ ( in @ SV863 @ SV298 )
| ~ ( SV46 @ SV863 @ SV847 ) ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4311,plain,
! [SV298: $i,SV46: $i > $i > $o,SV838: $i,SV746: $i] :
( ( ( ~ ( in @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV838 ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4312,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV298 )
| ~ ( SV46 @ SV862 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4272]) ).
thf(4313,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4273]) ).
thf(4314,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4274]) ).
thf(4315,plain,
! [SV759: $i,SV840: $i,SV196: $i] :
( ( ( ~ ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1422 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SY1422 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4274]) ).
thf(4316,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4275]) ).
thf(4317,plain,
! [SV759: $i,SV832: $i,SV196: $i] :
( ( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1405: $i] :
( ~ ( in @ SY1405 @ SY1416 )
| ( in @ SY1405 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SY1416 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4276]) ).
thf(4318,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( SV461 @ SV861 )
= $false )
| ( ( ~ ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4277]) ).
thf(4319,plain,
! [SV792: $i,SV237: $i > $o,SV860: $i,SV461: $i > $o] :
( ( ( ! [SY1412: $i] :
( ~ ( SV461 @ SY1412 )
| ( SV860 = SY1412 ) ) )
= $false )
| ( ( SV461 @ SV860 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4278]) ).
thf(4320,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4279]) ).
thf(4321,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4280]) ).
thf(4322,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4281]) ).
thf(4323,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4282]) ).
thf(4324,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4283]) ).
thf(4325,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4284]) ).
thf(4326,plain,
! [SV830: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4285]) ).
thf(4327,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV864 )
| ~ ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4286]) ).
thf(4328,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK121_SY689 @ SV817 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4287]) ).
thf(4329,plain,
! [SV15: $i > $o,SV817: $i,SV270: $i > $o] :
( ( ( ! [SY1419: $i] :
( ~ ( SV270 @ SY1419 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SY1419 ) ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4288]) ).
thf(4330,plain,
! [SV15: $i > $o,SV817: $i,SV865: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV865 )
| ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SV865 ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4290]) ).
thf(4331,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK122_SY58 @ SV818 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4291]) ).
thf(4332,plain,
! [SV270: $i > $o,SV818: $i,SV15: $i > $o] :
( ( ( ! [SY1420: $i] :
( ~ ( SV15 @ SY1420 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SY1420 ) ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4292]) ).
thf(4333,plain,
! [SV270: $i > $o,SV818: $i,SV866: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV866 )
| ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SV866 ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4294]) ).
thf(4334,plain,
! [SV857: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4295]) ).
thf(4335,plain,
! [SV15: $i > $o,SV270: $i > $o,SV857: $i] :
( ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4295]) ).
thf(4336,plain,
! [SV858: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4296]) ).
thf(4337,plain,
! [SV270: $i > $o,SV15: $i > $o,SV858: $i] :
( ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4296]) ).
thf(4338,plain,
! [SV852: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4297]) ).
thf(4339,plain,
! [SV852: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4298]) ).
thf(4340,plain,
! [SV853: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4299]) ).
thf(4341,plain,
! [SV853: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4300]) ).
thf(4342,plain,
! [SV854: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4301]) ).
thf(4343,plain,
! [SV854: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4302]) ).
thf(4344,plain,
! [SV855: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4303]) ).
thf(4345,plain,
! [SV855: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4346,plain,
! [SV844: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4305]) ).
thf(4347,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK135_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1425: $i] :
( ~ ( SV270 @ SY1425 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SY1425 ) ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4306]) ).
thf(4348,plain,
! [SV845: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4349,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK136_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1426: $i] :
( ~ ( SV15 @ SY1426 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SY1426 ) ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4308]) ).
thf(4350,plain,
! [SV298: $i,SV46: $i > $i > $o,SV847: $i,SV746: $i] :
( ( ( ~ ( in @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV298 )
| ~ ( SV46 @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV847 ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4309]) ).
thf(4351,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ SV298 )
| ~ ( SV46 @ SV863 @ SV847 ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4310]) ).
thf(4352,plain,
! [SV298: $i,SV46: $i > $i > $o,SV838: $i,SV746: $i] :
( ( ( ~ ( in @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV298 ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4311]) ).
thf(4353,plain,
! [SV298: $i,SV838: $i,SV746: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV838 ) )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4311]) ).
thf(4354,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV298 ) )
= $true )
| ( ( ~ ( SV46 @ SV862 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4355,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4313]) ).
thf(4356,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4313]) ).
thf(4357,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4314]) ).
thf(4358,plain,
! [SV759: $i,SV840: $i,SV196: $i] :
( ( ( ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SY1422 )
| ( in @ SY1411 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SY1422 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4315]) ).
thf(4359,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
| ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4360,plain,
! [SV759: $i,SV832: $i,SV196: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SV867 )
| ( in @ SY1427 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4317]) ).
thf(4361,plain,
! [SV792: $i,SV237: $i > $o,SV861: $i,SV461: $i > $o] :
( ( ( ! [SY1418: $i] :
( ~ ( SV461 @ SY1418 )
| ( SV861 = SY1418 ) ) )
= $false )
| ( ( SV461 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4362,plain,
! [SV860: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK137_SY1412 @ SV792 @ SV237 @ SV860 @ SV461 ) )
| ( SV860
= ( sK137_SY1412 @ SV792 @ SV237 @ SV860 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV860 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4319]) ).
thf(4363,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ~ ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4364,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4321]) ).
thf(4365,plain,
! [SV833: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4322]) ).
thf(4366,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV868 )
| ~ ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4323]) ).
thf(4367,plain,
! [SV834: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4324]) ).
thf(4368,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV869 )
| ~ ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4369,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV870 )
| ~ ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4326]) ).
thf(4370,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV864 )
| ~ ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4327]) ).
thf(4371,plain,
! [SV15: $i > $o,SV817: $i,SV871: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV871 )
| ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SV871 ) )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4329]) ).
thf(4372,plain,
! [SV15: $i > $o,SV817: $i,SV865: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV865 ) )
= $true )
| ( ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SV865 )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4330]) ).
thf(4373,plain,
! [SV270: $i > $o,SV818: $i,SV872: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV872 )
| ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SV872 ) )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4332]) ).
thf(4374,plain,
! [SV270: $i > $o,SV818: $i,SV866: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV866 ) )
= $true )
| ( ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SV866 )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4333]) ).
thf(4375,plain,
! [SV857: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( ~ ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4334]) ).
thf(4376,plain,
! [SV857: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4335]) ).
thf(4377,plain,
! [SV858: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( ~ ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4336]) ).
thf(4378,plain,
! [SV858: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4337]) ).
thf(4379,plain,
! [SV852: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4338]) ).
thf(4380,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK138_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1431: $i] :
( ~ ( SV270 @ SY1431 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SY1431 ) ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4339]) ).
thf(4381,plain,
! [SV853: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4340]) ).
thf(4382,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK139_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1432: $i] :
( ~ ( SV15 @ SY1432 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SY1432 ) ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4341]) ).
thf(4383,plain,
! [SV854: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4384,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK140_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1433: $i] :
( ~ ( SV270 @ SY1433 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SY1433 ) ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4343]) ).
thf(4385,plain,
! [SV855: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4386,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK141_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1434: $i] :
( ~ ( SV15 @ SY1434 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SY1434 ) ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4345]) ).
thf(4387,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK142_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1435: $i] :
( ~ ( SV270 @ SY1435 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SY1435 ) ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4346]) ).
thf(4388,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK135_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1425: $i] :
( ~ ( SV270 @ SY1425 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SY1425 ) ) ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4347]) ).
thf(4389,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK143_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1436: $i] :
( ~ ( SV15 @ SY1436 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SY1436 ) ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4348]) ).
thf(4390,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK136_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1426: $i] :
( ~ ( SV15 @ SY1426 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SY1426 ) ) ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4349]) ).
thf(4391,plain,
! [SV298: $i,SV46: $i > $i > $o,SV847: $i,SV746: $i] :
( ( ( ~ ( in @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV298 ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4350]) ).
thf(4392,plain,
! [SV298: $i,SV847: $i,SV746: $i,SV46: $i > $i > $o] :
( ( ( ~ ( SV46 @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV847 ) )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4350]) ).
thf(4393,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ SV298 ) )
= $true )
| ( ( ~ ( SV46 @ SV863 @ SV847 ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4351]) ).
thf(4394,plain,
! [SV298: $i,SV46: $i > $i > $o,SV838: $i,SV746: $i] :
( ( ( in @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV298 )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4352]) ).
thf(4395,plain,
! [SV298: $i,SV838: $i,SV746: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ ( sK127_SY1391 @ SV746 @ SV838 @ SV46 @ SV298 ) @ SV838 )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4353]) ).
thf(4396,plain,
! [SV746: $i,SV838: $i,SV46: $i > $i > $o,SV298: $i,SV862: $i] :
( ( ( in @ SV862 @ SV298 )
= $false )
| ( ( ~ ( SV46 @ SV862 @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4354]) ).
thf(4397,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4355]) ).
thf(4398,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4399,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
| ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4357]) ).
thf(4400,plain,
! [SV759: $i,SV840: $i,SV196: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
| ! [SY1437: $i] :
( ~ ( in @ SY1437 @ SV873 )
| ( in @ SY1437 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4401,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4359]) ).
thf(4402,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4359]) ).
thf(4403,plain,
! [SV759: $i,SV832: $i,SV196: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SV867 )
| ( in @ SY1427 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4360]) ).
thf(4404,plain,
! [SV861: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK144_SY1418 @ SV792 @ SV237 @ SV861 @ SV461 ) )
| ( SV861
= ( sK144_SY1418 @ SV792 @ SV237 @ SV861 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4361]) ).
thf(4405,plain,
! [SV860: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK137_SY1412 @ SV792 @ SV237 @ SV860 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV860 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4406,plain,
! [SV461: $i > $o,SV237: $i > $o,SV792: $i,SV860: $i] :
( ( ( SV860
= ( sK137_SY1412 @ SV792 @ SV237 @ SV860 @ SV461 ) )
= $false )
| ( ( SV461 @ SV860 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4407,plain,
! [SV841: $i,SV237: $i > $o,SV461: $i > $o] :
( ( ( ! [SY999: $i] :
~ ~ ( ~ ( SV461 @ SY999 )
| ~ ! [SY1000: $i] :
( ~ ( SV461 @ SY1000 )
| ( SY999 = SY1000 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4363]) ).
thf(4408,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV874 )
| ~ ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4364]) ).
thf(4409,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV875 )
| ~ ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4365]) ).
thf(4410,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV868 )
| ~ ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4411,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV876 )
| ~ ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4367]) ).
thf(4412,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV869 )
| ~ ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4413,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV870 )
| ~ ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4369]) ).
thf(4414,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV864 )
| ~ ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4370]) ).
thf(4415,plain,
! [SV15: $i > $o,SV817: $i,SV871: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV871 ) )
= $true )
| ( ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SV871 )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4371]) ).
thf(4416,plain,
! [SV15: $i > $o,SV817: $i,SV865: $i,SV270: $i > $o] :
( ( ( SV270 @ SV865 )
= $false )
| ( ( ( sK115_SY689 @ SV817 @ SV15 @ SV270 )
= SV865 )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV817
= ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4372]) ).
thf(4417,plain,
! [SV270: $i > $o,SV818: $i,SV872: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV872 ) )
= $true )
| ( ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SV872 )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4373]) ).
thf(4418,plain,
! [SV270: $i > $o,SV818: $i,SV866: $i,SV15: $i > $o] :
( ( ( SV15 @ SV866 )
= $false )
| ( ( ( sK116_SY58 @ SV818 @ SV270 @ SV15 )
= SV866 )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV818
= ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $false )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4374]) ).
thf(4419,plain,
! [SV857: $i,SV15: $i > $o,SV270: $i > $o] :
( ( ( ! [SY689: $i] :
~ ~ ( ~ ( SV270 @ SY689 )
| ~ ! [SY690: $i] :
( ~ ( SV270 @ SY690 )
| ( SY689 = SY690 ) ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4375]) ).
thf(4420,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK145_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1441: $i] :
( ~ ( SV270 @ SY1441 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SY1441 ) ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4376]) ).
thf(4421,plain,
! [SV858: $i,SV270: $i > $o,SV15: $i > $o] :
( ( ( ! [SY58: $i] :
~ ~ ( ~ ( SV15 @ SY58 )
| ~ ! [SY59: $i] :
( ~ ( SV15 @ SY59 )
| ( SY58 = SY59 ) ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4377]) ).
thf(4422,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK146_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1442: $i] :
( ~ ( SV15 @ SY1442 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SY1442 ) ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4378]) ).
thf(4423,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK147_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1443: $i] :
( ~ ( SV270 @ SY1443 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SY1443 ) ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4379]) ).
thf(4424,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK138_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1431: $i] :
( ~ ( SV270 @ SY1431 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SY1431 ) ) ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4380]) ).
thf(4425,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK148_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1444: $i] :
( ~ ( SV15 @ SY1444 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SY1444 ) ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4381]) ).
thf(4426,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK139_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1432: $i] :
( ~ ( SV15 @ SY1432 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SY1432 ) ) ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4382]) ).
thf(4427,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK149_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1445: $i] :
( ~ ( SV270 @ SY1445 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SY1445 ) ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4383]) ).
thf(4428,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK140_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1433: $i] :
( ~ ( SV270 @ SY1433 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SY1433 ) ) ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4384]) ).
thf(4429,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK150_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1446: $i] :
( ~ ( SV15 @ SY1446 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SY1446 ) ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4385]) ).
thf(4430,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK141_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1434: $i] :
( ~ ( SV15 @ SY1434 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SY1434 ) ) ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4386]) ).
thf(4431,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK142_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1435: $i] :
( ~ ( SV270 @ SY1435 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SY1435 ) ) ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4387]) ).
thf(4432,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK135_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1425: $i] :
( ~ ( SV270 @ SY1425 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SY1425 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4388]) ).
thf(4433,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK143_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1436: $i] :
( ~ ( SV15 @ SY1436 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SY1436 ) ) ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4389]) ).
thf(4434,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK136_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1426: $i] :
( ~ ( SV15 @ SY1426 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SY1426 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4390]) ).
thf(4435,plain,
! [SV298: $i,SV46: $i > $i > $o,SV847: $i,SV746: $i] :
( ( ( in @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV298 )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4391]) ).
thf(4436,plain,
! [SV298: $i,SV847: $i,SV746: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ ( sK132_SY1396 @ SV746 @ SV847 @ SV46 @ SV298 ) @ SV847 )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4392]) ).
thf(4437,plain,
! [SV746: $i,SV847: $i,SV46: $i > $i > $o,SV298: $i,SV863: $i] :
( ( ( in @ SV863 @ SV298 )
= $false )
| ( ( ~ ( SV46 @ SV863 @ SV847 ) )
= $true )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4393]) ).
thf(4438,plain,
! [SV746: $i,SV298: $i,SV838: $i,SV862: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ SV862 @ SV838 )
= $false )
| ( ( in @ SV862 @ SV298 )
= $false )
| ( ( in @ SV838 @ ( sK99_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV746
= ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4439,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
| ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4440,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4441,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4398]) ).
thf(4442,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4399]) ).
thf(4443,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4399]) ).
thf(4444,plain,
! [SV759: $i,SV840: $i,SV196: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ ( sK5_SY484 @ SV196 ) ) )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( in @ SY1437 @ SV873 )
| ( in @ SY1437 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4445,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4401]) ).
thf(4446,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4402]) ).
thf(4447,plain,
! [SV759: $i,SV832: $i,SV196: $i,SV867: $i] :
( ( ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SV867 )
| ( in @ SY1427 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
| ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4448,plain,
! [SV861: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK144_SY1418 @ SV792 @ SV237 @ SV861 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4449,plain,
! [SV461: $i > $o,SV237: $i > $o,SV792: $i,SV861: $i] :
( ( ( SV861
= ( sK144_SY1418 @ SV792 @ SV237 @ SV861 @ SV461 ) )
= $false )
| ( ( SV461 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4404]) ).
thf(4450,plain,
! [SV860: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK137_SY1412 @ SV792 @ SV237 @ SV860 @ SV461 ) )
= $true )
| ( ( SV461 @ SV860 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV792
= ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $false )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4405]) ).
thf(4451,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( ~ ~ ( ~ ( SV461 @ SV877 )
| ~ ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4407]) ).
thf(4452,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV874 )
| ~ ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4453,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV875 )
| ~ ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4409]) ).
thf(4454,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV868 )
| ~ ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4410]) ).
thf(4455,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV876 )
| ~ ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4456,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV869 )
| ~ ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4457,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV870 )
| ~ ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4413]) ).
thf(4458,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV864 ) )
= $true )
| ( ( ~ ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(4459,plain,
! [SV15: $i > $o,SV817: $i,SV871: $i,SV270: $i > $o] :
( ( ( SV270 @ SV871 )
= $false )
| ( ( ( sK121_SY689 @ SV817 @ SV15 @ SV270 )
= SV871 )
= $true )
| ( ( SV15 @ SV817 )
= $false )
| ( ( SV15 @ ( sK110_SY1369 @ SV270 @ SV817 @ SV15 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4415]) ).
thf(4460,plain,
! [SV270: $i > $o,SV818: $i,SV872: $i,SV15: $i > $o] :
( ( ( SV15 @ SV872 )
= $false )
| ( ( ( sK122_SY58 @ SV818 @ SV270 @ SV15 )
= SV872 )
= $true )
| ( ( SV270 @ SV818 )
= $false )
| ( ( SV270 @ ( sK111_SY1370 @ SV15 @ SV818 @ SV270 ) )
= $true )
| ( ( ( sK9_SY685 @ SV270 @ SV15 )
= ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4417]) ).
thf(4461,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ~ ( ~ ( SV270 @ ( sK151_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1448: $i] :
( ~ ( SV270 @ SY1448 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SY1448 ) ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4419]) ).
thf(4462,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK145_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1441: $i] :
( ~ ( SV270 @ SY1441 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SY1441 ) ) ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4420]) ).
thf(4463,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ~ ( ~ ( SV15 @ ( sK152_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1449: $i] :
( ~ ( SV15 @ SY1449 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SY1449 ) ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4421]) ).
thf(4464,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK146_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1442: $i] :
( ~ ( SV15 @ SY1442 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SY1442 ) ) ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4422]) ).
thf(4465,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK147_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1443: $i] :
( ~ ( SV270 @ SY1443 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SY1443 ) ) ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4423]) ).
thf(4466,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK138_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1431: $i] :
( ~ ( SV270 @ SY1431 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SY1431 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4424]) ).
thf(4467,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK148_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1444: $i] :
( ~ ( SV15 @ SY1444 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SY1444 ) ) ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4425]) ).
thf(4468,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK139_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1432: $i] :
( ~ ( SV15 @ SY1432 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SY1432 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4426]) ).
thf(4469,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK149_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1445: $i] :
( ~ ( SV270 @ SY1445 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SY1445 ) ) ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4427]) ).
thf(4470,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK140_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1433: $i] :
( ~ ( SV270 @ SY1433 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SY1433 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4428]) ).
thf(4471,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK150_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1446: $i] :
( ~ ( SV15 @ SY1446 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SY1446 ) ) ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4429]) ).
thf(4472,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK141_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1434: $i] :
( ~ ( SV15 @ SY1434 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SY1434 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4430]) ).
thf(4473,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK142_SY689 @ SV844 @ SV15 @ SV270 ) )
| ~ ! [SY1435: $i] :
( ~ ( SV270 @ SY1435 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SY1435 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4431]) ).
thf(4474,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK135_SY689 @ SV844 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4475,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1425: $i] :
( ~ ( SV270 @ SY1425 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SY1425 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4476,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK143_SY58 @ SV845 @ SV270 @ SV15 ) )
| ~ ! [SY1436: $i] :
( ~ ( SV15 @ SY1436 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SY1436 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4433]) ).
thf(4477,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK136_SY58 @ SV845 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4478,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1426: $i] :
( ~ ( SV15 @ SY1426 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SY1426 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4434]) ).
thf(4479,plain,
! [SV746: $i,SV298: $i,SV847: $i,SV863: $i,SV46: $i > $i > $o] :
( ( ( SV46 @ SV863 @ SV847 )
= $false )
| ( ( in @ SV863 @ SV298 )
= $false )
| ( ( in @ SV847 @ ( sK104_SY736 @ SV746 @ SV46 @ SV298 ) )
= $true )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ SV746 )
= $false )
| ( ( SV46 @ ( sK10_SY733 @ SV46 @ SV298 ) @ ( sK80_SY1321 @ SV746 @ SV298 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(4480,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) ) )
= $false )
| ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4439]) ).
thf(4481,plain,
! [SV196: $i,SV823: $i,SV812: $i] :
( ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4439]) ).
thf(4482,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $false )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4440]) ).
thf(4483,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4442]) ).
thf(4484,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4443]) ).
thf(4485,plain,
! [SV759: $i,SV840: $i,SV196: $i,SV873: $i] :
( ( ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( ! [SY1437: $i] :
( ~ ( in @ SY1437 @ SV873 )
| ( in @ SY1437 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
| ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4486,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4487,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4446]) ).
thf(4488,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV867: $i] :
( ( ( ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SV867 )
| ( in @ SY1427 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) ) )
= $true )
| ( ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 )
= $true )
| ( ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4489,plain,
! [SV861: $i,SV237: $i > $o,SV792: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK144_SY1418 @ SV792 @ SV237 @ SV861 @ SV461 ) )
= $true )
| ( ( SV461 @ SV861 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV792 )
= $false )
| ( ( SV237 @ ( sK105_SY1352 @ SV461 @ SV792 @ SV237 ) )
= $true )
| ( ( ( sK18_SY995 @ SV461 @ SV237 )
= ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4448]) ).
thf(4490,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( ~ ( ~ ( SV461 @ SV877 )
| ~ ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4491,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV874 )
| ~ ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4452]) ).
thf(4492,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV875 )
| ~ ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4453]) ).
thf(4493,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV868 ) )
= $true )
| ( ( ~ ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4454]) ).
thf(4494,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV876 )
| ~ ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4455]) ).
thf(4495,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV869 ) )
= $true )
| ( ( ~ ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4456]) ).
thf(4496,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV870 ) )
= $true )
| ( ( ~ ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4457]) ).
thf(4497,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( SV461 @ SV864 )
= $false )
| ( ( ~ ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4458]) ).
thf(4498,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( ~ ( SV270 @ ( sK151_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1448: $i] :
( ~ ( SV270 @ SY1448 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SY1448 ) ) ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4461]) ).
thf(4499,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK145_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1441: $i] :
( ~ ( SV270 @ SY1441 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SY1441 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4462]) ).
thf(4500,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( ~ ( SV15 @ ( sK152_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1449: $i] :
( ~ ( SV15 @ SY1449 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SY1449 ) ) ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4463]) ).
thf(4501,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK146_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1442: $i] :
( ~ ( SV15 @ SY1442 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SY1442 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4464]) ).
thf(4502,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK147_SY689 @ SV852 @ SV15 @ SV270 ) )
| ~ ! [SY1443: $i] :
( ~ ( SV270 @ SY1443 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SY1443 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4465]) ).
thf(4503,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK138_SY689 @ SV852 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4466]) ).
thf(4504,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1431: $i] :
( ~ ( SV270 @ SY1431 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SY1431 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4466]) ).
thf(4505,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK148_SY58 @ SV853 @ SV270 @ SV15 ) )
| ~ ! [SY1444: $i] :
( ~ ( SV15 @ SY1444 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SY1444 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4467]) ).
thf(4506,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK139_SY58 @ SV853 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4507,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1432: $i] :
( ~ ( SV15 @ SY1432 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SY1432 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4468]) ).
thf(4508,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK149_SY689 @ SV854 @ SV15 @ SV270 ) )
| ~ ! [SY1445: $i] :
( ~ ( SV270 @ SY1445 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SY1445 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4509,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK140_SY689 @ SV854 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4510,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1433: $i] :
( ~ ( SV270 @ SY1433 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SY1433 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4470]) ).
thf(4511,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK150_SY58 @ SV855 @ SV270 @ SV15 ) )
| ~ ! [SY1446: $i] :
( ~ ( SV15 @ SY1446 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SY1446 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4471]) ).
thf(4512,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK141_SY58 @ SV855 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4472]) ).
thf(4513,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1434: $i] :
( ~ ( SV15 @ SY1434 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SY1434 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4472]) ).
thf(4514,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK142_SY689 @ SV844 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4473]) ).
thf(4515,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1435: $i] :
( ~ ( SV270 @ SY1435 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SY1435 ) ) )
= $false )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4473]) ).
thf(4516,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK135_SY689 @ SV844 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4474]) ).
thf(4517,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ! [SY1425: $i] :
( ~ ( SV270 @ SY1425 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SY1425 ) ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4475]) ).
thf(4518,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK143_SY58 @ SV845 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4476]) ).
thf(4519,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1436: $i] :
( ~ ( SV15 @ SY1436 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SY1436 ) ) )
= $false )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4476]) ).
thf(4520,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK136_SY58 @ SV845 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4477]) ).
thf(4521,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ! [SY1426: $i] :
( ~ ( SV15 @ SY1426 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SY1426 ) ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4478]) ).
thf(4522,plain,
! [SV196: $i,SV812: $i,SV823: $i] :
( ( ( in @ SV823 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( in @ SV812 @ ( sK117_SY1373 @ SV823 @ SV812 @ SV196 ) )
= $true )
| ( ( SV812 = SV823 )
= $true )
| ( ( in @ SV812 @ SV196 )
= $false )
| ( ( in @ SV823 @ SV196 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4480]) ).
thf(4523,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
| ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4483]) ).
thf(4524,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4484]) ).
thf(4525,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV873: $i] :
( ( ( ! [SY1437: $i] :
( ~ ( in @ SY1437 @ SV873 )
| ( in @ SY1437 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) ) )
= $true )
| ( ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 )
= $true )
| ( ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4485]) ).
thf(4526,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ~ ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4527,plain,
! [SV832: $i,SV759: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4486]) ).
thf(4528,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( ! [SY1403: $i] :
~ ~ ( ~ ( in @ SY1403 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SY1403 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4487]) ).
thf(4529,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV867: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV867 )
| ( in @ SV878 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
= $true )
| ( ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 )
= $true )
| ( ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4488]) ).
thf(4530,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV877 )
| ~ ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4490]) ).
thf(4531,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV874 ) )
= $true )
| ( ( ~ ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4491]) ).
thf(4532,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV875 ) )
= $true )
| ( ( ~ ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4492]) ).
thf(4533,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( SV461 @ SV868 )
= $false )
| ( ( ~ ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4493]) ).
thf(4534,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV876 ) )
= $true )
| ( ( ~ ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4494]) ).
thf(4535,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( SV461 @ SV869 )
= $false )
| ( ( ~ ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4495]) ).
thf(4536,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( SV461 @ SV870 )
= $false )
| ( ( ~ ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4537,plain,
! [SV830: $i,SV237: $i > $o,SV864: $i,SV461: $i > $o] :
( ( ( ! [SY1424: $i] :
( ~ ( SV461 @ SY1424 )
| ( SV864 = SY1424 ) ) )
= $false )
| ( ( SV461 @ SV864 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4497]) ).
thf(4538,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK151_SY689 @ SV857 @ SV15 @ SV270 ) )
| ~ ! [SY1448: $i] :
( ~ ( SV270 @ SY1448 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SY1448 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4539,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK145_SY689 @ SV857 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4540,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1441: $i] :
( ~ ( SV270 @ SY1441 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SY1441 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4541,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK152_SY58 @ SV858 @ SV270 @ SV15 ) )
| ~ ! [SY1449: $i] :
( ~ ( SV15 @ SY1449 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SY1449 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4500]) ).
thf(4542,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK146_SY58 @ SV858 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4501]) ).
thf(4543,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1442: $i] :
( ~ ( SV15 @ SY1442 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SY1442 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4501]) ).
thf(4544,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK147_SY689 @ SV852 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4502]) ).
thf(4545,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1443: $i] :
( ~ ( SV270 @ SY1443 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SY1443 ) ) )
= $false )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4502]) ).
thf(4546,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK138_SY689 @ SV852 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4503]) ).
thf(4547,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ! [SY1431: $i] :
( ~ ( SV270 @ SY1431 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SY1431 ) ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4504]) ).
thf(4548,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK148_SY58 @ SV853 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4549,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1444: $i] :
( ~ ( SV15 @ SY1444 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SY1444 ) ) )
= $false )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4550,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK139_SY58 @ SV853 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4506]) ).
thf(4551,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ! [SY1432: $i] :
( ~ ( SV15 @ SY1432 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SY1432 ) ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4507]) ).
thf(4552,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK149_SY689 @ SV854 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4508]) ).
thf(4553,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1445: $i] :
( ~ ( SV270 @ SY1445 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SY1445 ) ) )
= $false )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4508]) ).
thf(4554,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK140_SY689 @ SV854 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4509]) ).
thf(4555,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ! [SY1433: $i] :
( ~ ( SV270 @ SY1433 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SY1433 ) ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4510]) ).
thf(4556,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK150_SY58 @ SV855 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4511]) ).
thf(4557,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1446: $i] :
( ~ ( SV15 @ SY1446 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SY1446 ) ) )
= $false )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4511]) ).
thf(4558,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK141_SY58 @ SV855 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4512]) ).
thf(4559,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ! [SY1434: $i] :
( ~ ( SV15 @ SY1434 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SY1434 ) ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4513]) ).
thf(4560,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK142_SY689 @ SV844 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4514]) ).
thf(4561,plain,
! [SV15: $i > $o,SV844: $i,SV270: $i > $o] :
( ( ( ! [SY1435: $i] :
( ~ ( SV270 @ SY1435 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SY1435 ) ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4515]) ).
thf(4562,plain,
! [SV15: $i > $o,SV844: $i,SV879: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV879 )
| ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SV879 ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4517]) ).
thf(4563,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK143_SY58 @ SV845 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4518]) ).
thf(4564,plain,
! [SV270: $i > $o,SV845: $i,SV15: $i > $o] :
( ( ( ! [SY1436: $i] :
( ~ ( SV15 @ SY1436 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SY1436 ) ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4519]) ).
thf(4565,plain,
! [SV270: $i > $o,SV845: $i,SV880: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV880 )
| ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SV880 ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4521]) ).
thf(4566,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ~ ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4523]) ).
thf(4567,plain,
! [SV840: $i,SV759: $i,SV196: $i] :
( ( ( ~ ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4523]) ).
thf(4568,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( ! [SY1409: $i] :
~ ~ ( ~ ( in @ SY1409 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SY1409 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4524]) ).
thf(4569,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV873: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ SV873 )
| ( in @ SV881 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
= $true )
| ( ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 )
= $true )
| ( ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4525]) ).
thf(4570,plain,
! [SV196: $i,SV759: $i,SV832: $i] :
( ( ( in @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4526]) ).
thf(4571,plain,
! [SV832: $i,SV759: $i,SV196: $i] :
( ( ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV759 )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4527]) ).
thf(4572,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV882: $i] :
( ( ( ~ ~ ( ~ ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SV882 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4528]) ).
thf(4573,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV867: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV867 ) )
= $true )
| ( ( in @ SV878 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
= $true )
| ( ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 )
= $true )
| ( ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4529]) ).
thf(4574,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ SV877 ) )
= $true )
| ( ( ~ ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4530]) ).
thf(4575,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( SV461 @ SV874 )
= $false )
| ( ( ~ ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4531]) ).
thf(4576,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( SV461 @ SV875 )
= $false )
| ( ( ~ ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4532]) ).
thf(4577,plain,
! [SV833: $i,SV237: $i > $o,SV868: $i,SV461: $i > $o] :
( ( ( ! [SY1428: $i] :
( ~ ( SV461 @ SY1428 )
| ( SV868 = SY1428 ) ) )
= $false )
| ( ( SV461 @ SV868 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4533]) ).
thf(4578,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( SV461 @ SV876 )
= $false )
| ( ( ~ ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4579,plain,
! [SV834: $i,SV237: $i > $o,SV869: $i,SV461: $i > $o] :
( ( ( ! [SY1429: $i] :
( ~ ( SV461 @ SY1429 )
| ( SV869 = SY1429 ) ) )
= $false )
| ( ( SV461 @ SV869 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4535]) ).
thf(4580,plain,
! [SV830: $i,SV237: $i > $o,SV870: $i,SV461: $i > $o] :
( ( ( ! [SY1430: $i] :
( ~ ( SV461 @ SY1430 )
| ( SV870 = SY1430 ) ) )
= $false )
| ( ( SV461 @ SV870 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4536]) ).
thf(4581,plain,
! [SV864: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK153_SY1424 @ SV830 @ SV237 @ SV864 @ SV461 ) )
| ( SV864
= ( sK153_SY1424 @ SV830 @ SV237 @ SV864 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV864 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4537]) ).
thf(4582,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ ( sK151_SY689 @ SV857 @ SV15 @ SV270 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4583,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ~ ! [SY1448: $i] :
( ~ ( SV270 @ SY1448 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SY1448 ) ) )
= $false )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4584,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK145_SY689 @ SV857 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4539]) ).
thf(4585,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ! [SY1441: $i] :
( ~ ( SV270 @ SY1441 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SY1441 ) ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4540]) ).
thf(4586,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ ( sK152_SY58 @ SV858 @ SV270 @ SV15 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4587,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ~ ! [SY1449: $i] :
( ~ ( SV15 @ SY1449 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SY1449 ) ) )
= $false )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4541]) ).
thf(4588,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK146_SY58 @ SV858 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4542]) ).
thf(4589,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ! [SY1442: $i] :
( ~ ( SV15 @ SY1442 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SY1442 ) ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4543]) ).
thf(4590,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK147_SY689 @ SV852 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4544]) ).
thf(4591,plain,
! [SV15: $i > $o,SV852: $i,SV270: $i > $o] :
( ( ( ! [SY1443: $i] :
( ~ ( SV270 @ SY1443 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SY1443 ) ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4545]) ).
thf(4592,plain,
! [SV15: $i > $o,SV852: $i,SV883: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV883 )
| ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SV883 ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4547]) ).
thf(4593,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK148_SY58 @ SV853 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4548]) ).
thf(4594,plain,
! [SV270: $i > $o,SV853: $i,SV15: $i > $o] :
( ( ( ! [SY1444: $i] :
( ~ ( SV15 @ SY1444 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SY1444 ) ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4549]) ).
thf(4595,plain,
! [SV270: $i > $o,SV853: $i,SV884: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV884 )
| ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SV884 ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4551]) ).
thf(4596,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK149_SY689 @ SV854 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4552]) ).
thf(4597,plain,
! [SV15: $i > $o,SV854: $i,SV270: $i > $o] :
( ( ( ! [SY1445: $i] :
( ~ ( SV270 @ SY1445 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SY1445 ) ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4553]) ).
thf(4598,plain,
! [SV15: $i > $o,SV854: $i,SV885: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV885 )
| ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SV885 ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4555]) ).
thf(4599,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK150_SY58 @ SV855 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4556]) ).
thf(4600,plain,
! [SV270: $i > $o,SV855: $i,SV15: $i > $o] :
( ( ( ! [SY1446: $i] :
( ~ ( SV15 @ SY1446 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SY1446 ) ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4557]) ).
thf(4601,plain,
! [SV270: $i > $o,SV855: $i,SV886: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV886 )
| ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SV886 ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4559]) ).
thf(4602,plain,
! [SV15: $i > $o,SV844: $i,SV887: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV887 )
| ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SV887 ) )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4561]) ).
thf(4603,plain,
! [SV15: $i > $o,SV844: $i,SV879: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV879 ) )
= $true )
| ( ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SV879 )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4562]) ).
thf(4604,plain,
! [SV270: $i > $o,SV845: $i,SV888: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV888 )
| ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SV888 ) )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4564]) ).
thf(4605,plain,
! [SV270: $i > $o,SV845: $i,SV880: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV880 ) )
= $true )
| ( ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SV880 )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(4606,plain,
! [SV196: $i,SV759: $i,SV840: $i] :
( ( ( in @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) @ ( sK5_SY484 @ SV196 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4566]) ).
thf(4607,plain,
! [SV840: $i,SV759: $i,SV196: $i] :
( ( ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV759 )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4567]) ).
thf(4608,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV889: $i] :
( ( ( ~ ~ ( ~ ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SV889 @ SV759 ) ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4568]) ).
thf(4609,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV873: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ SV873 ) )
= $true )
| ( ( in @ SV881 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
= $true )
| ( ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 )
= $true )
| ( ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4569]) ).
thf(4610,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV882: $i] :
( ( ( ~ ( ~ ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SV882 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4572]) ).
thf(4611,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV867: $i,SV878: $i] :
( ( ( in @ SV878 @ SV867 )
= $false )
| ( ( in @ SV878 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
= $true )
| ( ( in @ ( sK118_SY1402 @ SV196 @ SV759 @ SV832 ) @ SV867 )
= $true )
| ( ( in @ SV867 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4573]) ).
thf(4612,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( SV461 @ SV877 )
= $false )
| ( ( ~ ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4574]) ).
thf(4613,plain,
! [SV841: $i,SV237: $i > $o,SV874: $i,SV461: $i > $o] :
( ( ( ! [SY1438: $i] :
( ~ ( SV461 @ SY1438 )
| ( SV874 = SY1438 ) ) )
= $false )
| ( ( SV461 @ SV874 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4614,plain,
! [SV833: $i,SV237: $i > $o,SV875: $i,SV461: $i > $o] :
( ( ( ! [SY1439: $i] :
( ~ ( SV461 @ SY1439 )
| ( SV875 = SY1439 ) ) )
= $false )
| ( ( SV461 @ SV875 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(4615,plain,
! [SV868: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK154_SY1428 @ SV833 @ SV237 @ SV868 @ SV461 ) )
| ( SV868
= ( sK154_SY1428 @ SV833 @ SV237 @ SV868 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV868 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4577]) ).
thf(4616,plain,
! [SV834: $i,SV237: $i > $o,SV876: $i,SV461: $i > $o] :
( ( ( ! [SY1440: $i] :
( ~ ( SV461 @ SY1440 )
| ( SV876 = SY1440 ) ) )
= $false )
| ( ( SV461 @ SV876 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(4617,plain,
! [SV869: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK155_SY1429 @ SV834 @ SV237 @ SV869 @ SV461 ) )
| ( SV869
= ( sK155_SY1429 @ SV834 @ SV237 @ SV869 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV869 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4579]) ).
thf(4618,plain,
! [SV870: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK156_SY1430 @ SV830 @ SV237 @ SV870 @ SV461 ) )
| ( SV870
= ( sK156_SY1430 @ SV830 @ SV237 @ SV870 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV870 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4580]) ).
thf(4619,plain,
! [SV864: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK153_SY1424 @ SV830 @ SV237 @ SV864 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV864 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4581]) ).
thf(4620,plain,
! [SV461: $i > $o,SV237: $i > $o,SV830: $i,SV864: $i] :
( ( ( SV864
= ( sK153_SY1424 @ SV830 @ SV237 @ SV864 @ SV461 ) )
= $false )
| ( ( SV461 @ SV864 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4581]) ).
thf(4621,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( SV270 @ ( sK151_SY689 @ SV857 @ SV15 @ SV270 ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4582]) ).
thf(4622,plain,
! [SV15: $i > $o,SV857: $i,SV270: $i > $o] :
( ( ( ! [SY1448: $i] :
( ~ ( SV270 @ SY1448 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SY1448 ) ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4583]) ).
thf(4623,plain,
! [SV15: $i > $o,SV857: $i,SV890: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV890 )
| ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SV890 ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4585]) ).
thf(4624,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( SV15 @ ( sK152_SY58 @ SV858 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4586]) ).
thf(4625,plain,
! [SV270: $i > $o,SV858: $i,SV15: $i > $o] :
( ( ( ! [SY1449: $i] :
( ~ ( SV15 @ SY1449 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SY1449 ) ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4587]) ).
thf(4626,plain,
! [SV270: $i > $o,SV858: $i,SV891: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV891 )
| ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SV891 ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4589]) ).
thf(4627,plain,
! [SV15: $i > $o,SV852: $i,SV892: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV892 )
| ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SV892 ) )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4591]) ).
thf(4628,plain,
! [SV15: $i > $o,SV852: $i,SV883: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV883 ) )
= $true )
| ( ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SV883 )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4592]) ).
thf(4629,plain,
! [SV270: $i > $o,SV853: $i,SV893: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV893 )
| ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SV893 ) )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4594]) ).
thf(4630,plain,
! [SV270: $i > $o,SV853: $i,SV884: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV884 ) )
= $true )
| ( ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SV884 )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4595]) ).
thf(4631,plain,
! [SV15: $i > $o,SV854: $i,SV894: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV894 )
| ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SV894 ) )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4597]) ).
thf(4632,plain,
! [SV15: $i > $o,SV854: $i,SV885: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV885 ) )
= $true )
| ( ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SV885 )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4598]) ).
thf(4633,plain,
! [SV270: $i > $o,SV855: $i,SV895: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV895 )
| ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SV895 ) )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4600]) ).
thf(4634,plain,
! [SV270: $i > $o,SV855: $i,SV886: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV886 ) )
= $true )
| ( ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SV886 )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4601]) ).
thf(4635,plain,
! [SV15: $i > $o,SV844: $i,SV887: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV887 ) )
= $true )
| ( ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SV887 )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4602]) ).
thf(4636,plain,
! [SV15: $i > $o,SV844: $i,SV879: $i,SV270: $i > $o] :
( ( ( SV270 @ SV879 )
= $false )
| ( ( ( sK135_SY689 @ SV844 @ SV15 @ SV270 )
= SV879 )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV844
= ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4603]) ).
thf(4637,plain,
! [SV270: $i > $o,SV845: $i,SV888: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV888 ) )
= $true )
| ( ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SV888 )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4604]) ).
thf(4638,plain,
! [SV270: $i > $o,SV845: $i,SV880: $i,SV15: $i > $o] :
( ( ( SV15 @ SV880 )
= $false )
| ( ( ( sK136_SY58 @ SV845 @ SV270 @ SV15 )
= SV880 )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV845
= ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4605]) ).
thf(4639,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV889: $i] :
( ( ( ~ ( ~ ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SV889 @ SV759 ) ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4608]) ).
thf(4640,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV873: $i,SV881: $i] :
( ( ( in @ SV881 @ SV873 )
= $false )
| ( ( in @ SV881 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
= $true )
| ( ( in @ ( sK123_SY1408 @ SV196 @ SV759 @ SV840 ) @ SV873 )
= $true )
| ( ( in @ SV873 @ ( sK5_SY484 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4609]) ).
thf(4641,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
| ~ ( in @ SV882 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4610]) ).
thf(4642,plain,
! [SV841: $i,SV237: $i > $o,SV877: $i,SV461: $i > $o] :
( ( ( ! [SY1447: $i] :
( ~ ( SV461 @ SY1447 )
| ( SV877 = SY1447 ) ) )
= $false )
| ( ( SV461 @ SV877 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4612]) ).
thf(4643,plain,
! [SV874: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK157_SY1438 @ SV841 @ SV237 @ SV874 @ SV461 ) )
| ( SV874
= ( sK157_SY1438 @ SV841 @ SV237 @ SV874 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV874 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4613]) ).
thf(4644,plain,
! [SV875: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK158_SY1439 @ SV833 @ SV237 @ SV875 @ SV461 ) )
| ( SV875
= ( sK158_SY1439 @ SV833 @ SV237 @ SV875 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV875 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4614]) ).
thf(4645,plain,
! [SV868: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK154_SY1428 @ SV833 @ SV237 @ SV868 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV868 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4615]) ).
thf(4646,plain,
! [SV461: $i > $o,SV237: $i > $o,SV833: $i,SV868: $i] :
( ( ( SV868
= ( sK154_SY1428 @ SV833 @ SV237 @ SV868 @ SV461 ) )
= $false )
| ( ( SV461 @ SV868 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4615]) ).
thf(4647,plain,
! [SV876: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK159_SY1440 @ SV834 @ SV237 @ SV876 @ SV461 ) )
| ( SV876
= ( sK159_SY1440 @ SV834 @ SV237 @ SV876 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV876 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4616]) ).
thf(4648,plain,
! [SV869: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK155_SY1429 @ SV834 @ SV237 @ SV869 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV869 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4617]) ).
thf(4649,plain,
! [SV461: $i > $o,SV237: $i > $o,SV834: $i,SV869: $i] :
( ( ( SV869
= ( sK155_SY1429 @ SV834 @ SV237 @ SV869 @ SV461 ) )
= $false )
| ( ( SV461 @ SV869 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4617]) ).
thf(4650,plain,
! [SV870: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK156_SY1430 @ SV830 @ SV237 @ SV870 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV870 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4618]) ).
thf(4651,plain,
! [SV461: $i > $o,SV237: $i > $o,SV830: $i,SV870: $i] :
( ( ( SV870
= ( sK156_SY1430 @ SV830 @ SV237 @ SV870 @ SV461 ) )
= $false )
| ( ( SV461 @ SV870 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4618]) ).
thf(4652,plain,
! [SV864: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK153_SY1424 @ SV830 @ SV237 @ SV864 @ SV461 ) )
= $true )
| ( ( SV461 @ SV864 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV830
= ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4619]) ).
thf(4653,plain,
! [SV15: $i > $o,SV857: $i,SV896: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV896 )
| ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SV896 ) )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4622]) ).
thf(4654,plain,
! [SV15: $i > $o,SV857: $i,SV890: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV890 ) )
= $true )
| ( ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SV890 )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(4655,plain,
! [SV270: $i > $o,SV858: $i,SV897: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV897 )
| ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SV897 ) )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4625]) ).
thf(4656,plain,
! [SV270: $i > $o,SV858: $i,SV891: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV891 ) )
= $true )
| ( ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SV891 )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4626]) ).
thf(4657,plain,
! [SV15: $i > $o,SV852: $i,SV892: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV892 ) )
= $true )
| ( ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SV892 )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4627]) ).
thf(4658,plain,
! [SV15: $i > $o,SV852: $i,SV883: $i,SV270: $i > $o] :
( ( ( SV270 @ SV883 )
= $false )
| ( ( ( sK138_SY689 @ SV852 @ SV15 @ SV270 )
= SV883 )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV852
= ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4628]) ).
thf(4659,plain,
! [SV270: $i > $o,SV853: $i,SV893: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV893 ) )
= $true )
| ( ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SV893 )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4629]) ).
thf(4660,plain,
! [SV270: $i > $o,SV853: $i,SV884: $i,SV15: $i > $o] :
( ( ( SV15 @ SV884 )
= $false )
| ( ( ( sK139_SY58 @ SV853 @ SV270 @ SV15 )
= SV884 )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV853
= ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4630]) ).
thf(4661,plain,
! [SV15: $i > $o,SV854: $i,SV894: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV894 ) )
= $true )
| ( ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SV894 )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4631]) ).
thf(4662,plain,
! [SV15: $i > $o,SV854: $i,SV885: $i,SV270: $i > $o] :
( ( ( SV270 @ SV885 )
= $false )
| ( ( ( sK140_SY689 @ SV854 @ SV15 @ SV270 )
= SV885 )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV854
= ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4632]) ).
thf(4663,plain,
! [SV270: $i > $o,SV855: $i,SV895: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV895 ) )
= $true )
| ( ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SV895 )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(4664,plain,
! [SV270: $i > $o,SV855: $i,SV886: $i,SV15: $i > $o] :
( ( ( SV15 @ SV886 )
= $false )
| ( ( ( sK141_SY58 @ SV855 @ SV270 @ SV15 )
= SV886 )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV855
= ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4634]) ).
thf(4665,plain,
! [SV15: $i > $o,SV844: $i,SV887: $i,SV270: $i > $o] :
( ( ( SV270 @ SV887 )
= $false )
| ( ( ( sK142_SY689 @ SV844 @ SV15 @ SV270 )
= SV887 )
= $true )
| ( ( SV15 @ SV844 )
= $false )
| ( ( SV15 @ ( sK125_SY1394 @ SV270 @ SV844 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4635]) ).
thf(4666,plain,
! [SV270: $i > $o,SV845: $i,SV888: $i,SV15: $i > $o] :
( ( ( SV15 @ SV888 )
= $false )
| ( ( ( sK143_SY58 @ SV845 @ SV270 @ SV15 )
= SV888 )
= $true )
| ( ( SV270 @ SV845 )
= $false )
| ( ( SV270 @ ( sK126_SY1395 @ SV15 @ SV845 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4667,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
| ~ ( in @ SV889 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4639]) ).
thf(4668,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ SV882 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4641]) ).
thf(4669,plain,
! [SV877: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK160_SY1447 @ SV841 @ SV237 @ SV877 @ SV461 ) )
| ( SV877
= ( sK160_SY1447 @ SV841 @ SV237 @ SV877 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV877 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4642]) ).
thf(4670,plain,
! [SV874: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK157_SY1438 @ SV841 @ SV237 @ SV874 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV874 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4643]) ).
thf(4671,plain,
! [SV461: $i > $o,SV237: $i > $o,SV841: $i,SV874: $i] :
( ( ( SV874
= ( sK157_SY1438 @ SV841 @ SV237 @ SV874 @ SV461 ) )
= $false )
| ( ( SV461 @ SV874 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4643]) ).
thf(4672,plain,
! [SV875: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK158_SY1439 @ SV833 @ SV237 @ SV875 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV875 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4644]) ).
thf(4673,plain,
! [SV461: $i > $o,SV237: $i > $o,SV833: $i,SV875: $i] :
( ( ( SV875
= ( sK158_SY1439 @ SV833 @ SV237 @ SV875 @ SV461 ) )
= $false )
| ( ( SV461 @ SV875 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4644]) ).
thf(4674,plain,
! [SV868: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK154_SY1428 @ SV833 @ SV237 @ SV868 @ SV461 ) )
= $true )
| ( ( SV461 @ SV868 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV833
= ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4645]) ).
thf(4675,plain,
! [SV876: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK159_SY1440 @ SV834 @ SV237 @ SV876 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV876 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4647]) ).
thf(4676,plain,
! [SV461: $i > $o,SV237: $i > $o,SV834: $i,SV876: $i] :
( ( ( SV876
= ( sK159_SY1440 @ SV834 @ SV237 @ SV876 @ SV461 ) )
= $false )
| ( ( SV461 @ SV876 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4647]) ).
thf(4677,plain,
! [SV869: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK155_SY1429 @ SV834 @ SV237 @ SV869 @ SV461 ) )
= $true )
| ( ( SV461 @ SV869 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV834
= ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4648]) ).
thf(4678,plain,
! [SV870: $i,SV237: $i > $o,SV830: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK156_SY1430 @ SV830 @ SV237 @ SV870 @ SV461 ) )
= $true )
| ( ( SV461 @ SV870 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV830 )
= $false )
| ( ( SV237 @ ( sK114_SY1382 @ SV461 @ SV830 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4650]) ).
thf(4679,plain,
! [SV15: $i > $o,SV857: $i,SV896: $i,SV270: $i > $o] :
( ( ( ~ ( SV270 @ SV896 ) )
= $true )
| ( ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SV896 )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4653]) ).
thf(4680,plain,
! [SV15: $i > $o,SV857: $i,SV890: $i,SV270: $i > $o] :
( ( ( SV270 @ SV890 )
= $false )
| ( ( ( sK145_SY689 @ SV857 @ SV15 @ SV270 )
= SV890 )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV857
= ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4681,plain,
! [SV270: $i > $o,SV858: $i,SV897: $i,SV15: $i > $o] :
( ( ( ~ ( SV15 @ SV897 ) )
= $true )
| ( ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SV897 )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4655]) ).
thf(4682,plain,
! [SV270: $i > $o,SV858: $i,SV891: $i,SV15: $i > $o] :
( ( ( SV15 @ SV891 )
= $false )
| ( ( ( sK146_SY58 @ SV858 @ SV270 @ SV15 )
= SV891 )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV858
= ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $false )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4656]) ).
thf(4683,plain,
! [SV15: $i > $o,SV852: $i,SV892: $i,SV270: $i > $o] :
( ( ( SV270 @ SV892 )
= $false )
| ( ( ( sK147_SY689 @ SV852 @ SV15 @ SV270 )
= SV892 )
= $true )
| ( ( SV15 @ SV852 )
= $false )
| ( ( SV15 @ ( sK128_SY1398 @ SV270 @ SV852 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4684,plain,
! [SV270: $i > $o,SV853: $i,SV893: $i,SV15: $i > $o] :
( ( ( SV15 @ SV893 )
= $false )
| ( ( ( sK148_SY58 @ SV853 @ SV270 @ SV15 )
= SV893 )
= $true )
| ( ( SV270 @ SV853 )
= $false )
| ( ( SV270 @ ( sK129_SY1399 @ SV15 @ SV853 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4659]) ).
thf(4685,plain,
! [SV15: $i > $o,SV854: $i,SV894: $i,SV270: $i > $o] :
( ( ( SV270 @ SV894 )
= $false )
| ( ( ( sK149_SY689 @ SV854 @ SV15 @ SV270 )
= SV894 )
= $true )
| ( ( SV15 @ SV854 )
= $false )
| ( ( SV15 @ ( sK130_SY1400 @ SV270 @ SV854 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4686,plain,
! [SV270: $i > $o,SV855: $i,SV895: $i,SV15: $i > $o] :
( ( ( SV15 @ SV895 )
= $false )
| ( ( ( sK150_SY58 @ SV855 @ SV270 @ SV15 )
= SV895 )
= $true )
| ( ( SV270 @ SV855 )
= $false )
| ( ( SV270 @ ( sK131_SY1401 @ SV15 @ SV855 @ SV270 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $false )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4663]) ).
thf(4687,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) ) )
= $true )
| ( ( ~ ( in @ SV889 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4667]) ).
thf(4688,plain,
! [SV196: $i,SV759: $i,SV832: $i,SV882: $i] :
( ( ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
= $false )
| ( ( ~ ( in @ SV882 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4668]) ).
thf(4689,plain,
! [SV877: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( ~ ( SV461 @ ( sK160_SY1447 @ SV841 @ SV237 @ SV877 @ SV461 ) ) )
= $false )
| ( ( SV461 @ SV877 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4669]) ).
thf(4690,plain,
! [SV461: $i > $o,SV237: $i > $o,SV841: $i,SV877: $i] :
( ( ( SV877
= ( sK160_SY1447 @ SV841 @ SV237 @ SV877 @ SV461 ) )
= $false )
| ( ( SV461 @ SV877 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4669]) ).
thf(4691,plain,
! [SV874: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK157_SY1438 @ SV841 @ SV237 @ SV874 @ SV461 ) )
= $true )
| ( ( SV461 @ SV874 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV841
= ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $false )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4670]) ).
thf(4692,plain,
! [SV875: $i,SV237: $i > $o,SV833: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK158_SY1439 @ SV833 @ SV237 @ SV875 @ SV461 ) )
= $true )
| ( ( SV461 @ SV875 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV833 )
= $false )
| ( ( SV237 @ ( sK119_SY1388 @ SV461 @ SV833 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4672]) ).
thf(4693,plain,
! [SV876: $i,SV237: $i > $o,SV834: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK159_SY1440 @ SV834 @ SV237 @ SV876 @ SV461 ) )
= $true )
| ( ( SV461 @ SV876 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV834 )
= $false )
| ( ( SV237 @ ( sK120_SY1389 @ SV461 @ SV834 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $false )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4675]) ).
thf(4694,plain,
! [SV15: $i > $o,SV857: $i,SV896: $i,SV270: $i > $o] :
( ( ( SV270 @ SV896 )
= $false )
| ( ( ( sK151_SY689 @ SV857 @ SV15 @ SV270 )
= SV896 )
= $true )
| ( ( SV15 @ SV857 )
= $false )
| ( ( SV15 @ ( sK133_SY1406 @ SV270 @ SV857 @ SV15 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4679]) ).
thf(4695,plain,
! [SV270: $i > $o,SV858: $i,SV897: $i,SV15: $i > $o] :
( ( ( SV15 @ SV897 )
= $false )
| ( ( ( sK152_SY58 @ SV858 @ SV270 @ SV15 )
= SV897 )
= $true )
| ( ( SV270 @ SV858 )
= $false )
| ( ( SV270 @ ( sK134_SY1407 @ SV15 @ SV858 @ SV270 ) )
= $true )
| ( ( SV15 @ ( sK9_SY685 @ SV270 @ SV15 ) )
= $true )
| ( ( SV270 @ ( sK19_SY1221 @ SV15 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4681]) ).
thf(4696,plain,
! [SV196: $i,SV759: $i,SV840: $i,SV889: $i] :
( ( ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
= $false )
| ( ( ~ ( in @ SV889 @ SV759 ) )
= $true )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4687]) ).
thf(4697,plain,
! [SV196: $i,SV832: $i,SV759: $i,SV882: $i] :
( ( ( in @ SV882 @ SV759 )
= $false )
| ( ( in @ SV882 @ ( sK112_SY1329 @ SV832 @ SV759 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV196 )
= $false )
| ( ( in @ SV832 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4698,plain,
! [SV877: $i,SV237: $i > $o,SV841: $i,SV461: $i > $o] :
( ( ( SV461 @ ( sK160_SY1447 @ SV841 @ SV237 @ SV877 @ SV461 ) )
= $true )
| ( ( SV461 @ SV877 )
= $false )
| ( ( ( descr
@ ^ [SY609: $i] : ( SV237 @ SY609 ) )
= ( descr
@ ^ [SY1002: $i] : ( SV461 @ SY1002 ) ) )
= $true )
| ( ( SV237 @ SV841 )
= $false )
| ( ( SV237 @ ( sK124_SY1393 @ SV461 @ SV841 @ SV237 ) )
= $true )
| ( ( SV237 @ ( sK18_SY995 @ SV461 @ SV237 ) )
= $true )
| ( ( SV461 @ ( sK30_SY1267 @ SV237 @ SV461 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4689]) ).
thf(4699,plain,
! [SV196: $i,SV840: $i,SV759: $i,SV889: $i] :
( ( ( in @ SV889 @ SV759 )
= $false )
| ( ( in @ SV889 @ ( sK113_SY1329 @ SV840 @ SV759 @ SV196 ) )
= $false )
| ( ( in @ ( sK84_SY1327 @ SV196 @ SV759 ) @ SV759 )
= $true )
| ( ( in @ SV840 @ SV759 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4700,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[544,4699,4698,4697,4695,4694,4693,4692,4691,4690,4686,4685,4684,4683,4682,4680,4678,4677,4676,4674,4673,4671,4666,4665,4664,4662,4660,4658,4652,4651,4649,4646,4640,4638,4636,4624,4621,4620,4611,4607,4606,4599,4596,4593,4590,4588,4584,4571,4570,4563,4560,4558,4554,4550,4546,4522,4520,4516,4489,4482,4481,4479,4460,4459,4450,4449,4441,4438,4436,4435,4418,4416,4406,4395,4394,4331,4328,4293,4289,4239,4211,4165,4164,4149,4136,4135,4133,4132,4130,4129,4122,4121,4116,4110,4109,4108,4095,4094,4090,4088,4085,4083,4076,4075,4068,4067,4066,4065,4064,4063,4055,4043,4041,4036,4032,4029,4014,4013,4011,4010,4008,4007,4005,4004,4002,4001,3997,3975,3973,3970,3968,3964,3963,3961,3960,3949,3944,3943,3940,3937,3934,3933,3930,3928,3923,3922,3920,3913,3900,3897,3883,3882,3880,3879,3870,3857,3850,3846,3840,3834,3820,3816,3805,3804,3803,3802,3800,3797,3795,3787,3779,3738,3737,3736,3735,3734,3733,3717,3694,3692,3691,3684,3683,3675,3674,3669,3664,3663,3647,3644,3641,3626,3624,3614,3603,3599,3598,3593,3592,3581,3579,3576,3575,3574,3573,3564,3562,3561,3560,3546,3545,3542,3541,3540,3539,3536,3535,3534,3533,3530,3529,3509,3508,3507,3501,3500,3499,3494,3486,3485,3484,3483,3479,3477,3467,3463,3437,3433,3432,3423,3419,3416,3412,3409,3405,3388,3382,3375,3374,3372,3371,3369,3368,3363,3361,3359,3358,3357,3354,3347,3346,3344,3343,3341,3340,3327,3322,3316,3309,3302,3299,3298,3291,3290,3280,3247,3246,3236,3229,3226,3223,3216,3210,3206,3205,3203,3197,3194,3191,3179,3175,3174,3171,3169,3163,3138,3137,3135,3133,3101,3092,3070,3069,3064,3063,3036,3035,3034,3033,3027,3020,3015,3014,3013,3000,2988,2986,2985,2984,2982,2962,2961,2960,2937,2936,2935,2932,2931,2930,2922,2921,2918,2897,2895,2894,2885,2872,2862,2861,2859,2857,2856,2853,2852,2851,2849,2848,2834,2830,2828,2821,2804,2802,2801,2799,2798,2796,2766,2721,2720,2717,2709,2702,2701,2696,2685,2674,2644,2643,2642,2629,2628,2625,2624,2623,2622,2621,2619,2618,2600,2595,2594,2593,2592,2591,2590,2575,2574,2573,2568,2562,2560,2559,2558,2547,2537,2529,2525,2523,2519,2515,2514,2511,2499,2493,2488,2483,2477,2453,2420,2414,2410,2409,2406,2394,2392,2389,2382,2381,2375,2371,2365,2362,2352,2342,2317,2311,2308,2305,2302,2292,2281,2267,2246,2233,2203,2190,2187,2184,2160,2156,2145,2113,2106,2105,2104,2088,2085,2084,2080,2065,2063,2061,2055,2051,2035,2034,2017,2013,2004,1985,1978,1963,1951,1945,1943,1929,1920,1908,1900,1892,1890,1883,1877,1849,1842,1839,1824,1817,1816,1806,1780,1772,1767,1759,1758,1756,1753,1749,1735,1730,1729,1728,1709,1703,1690,1686,1681,1680,1679,1678,1665,1659,1637,1635,1634,1633,1626,1620,1602,1571,1560,1543,1542,1501,1499,1483,1443,1442,1441,1419,1405,1404,1403,1388,1370,1360,1339,1335,1329,1297,1294,1281,1271,1253,1223,1216,1208,1207,1200,1180,1176,1162,1145,1133,1099,1093,1090,1063,991,984,960,928,912,852,846,816,688,597,590]) ).
thf(4701,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[4700]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU748^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.23 % Computer : n010.cluster.edu
% 0.08/0.23 % Model : x86_64 x86_64
% 0.08/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.23 % Memory : 8046.5625MB
% 0.08/0.23 % OS : Linux 6.8.0-71-generic
% 0.08/0.23 % CPULimit : 300
% 0.08/0.23 % WCLimit : 300
% 0.08/0.23 % DateTime : Tue Oct 6 15:34:10 UTC 2026
% 0.08/0.24 % CPUTime :
% 0.08/0.24 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 92.69/15.79 .
% 92.69/15.79
% 92.69/15.79 No.of.Axioms: 0
% 92.69/15.79
% 92.69/15.79 Length.of.Defs: 62026
% 92.69/15.79
% 92.69/15.79 Contains.Choice.Funs: true
% 92.69/15.79 ...........................................................................................................................................................................
% 92.69/15.79
% 92.69/15.79 ********************************
% 92.69/15.79 * All subproblems solved! *
% 92.69/15.79 ********************************
% 92.69/15.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:264,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4700,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 92.69/15.79
% 92.69/15.79 %**** Beginning of derivation protocol ****
% 92.69/15.79 % SZS output start CNFRefutation
% See solution above
% 15.71/15.84
% 15.71/15.84 %**** End of derivation protocol ****
% 15.71/15.84 %**** no. of clauses in derivation: 4701 ****
% 15.71/15.84 %**** clause counter: 4700 ****
% 15.71/15.84
% 15.71/15.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:264,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:4700,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------