%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU814^1 : 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 : n009.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 10:48:48 AM UTC 2026
% Result : Theorem 215.31s 36.34s
% Output : CNFRefutation 35.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 334
% Syntax : Number of formulae : 6246 (2204 unt; 0 typ; 333 def)
% Number of atoms : 54979 (20364 equ; 0 cnn)
% Maximal formula atoms : 334 ( 8 avg)
% Number of connectives : 112832 (20257 ~;20759 |; 60 &;70344 @)
% ( 17 <=>;1395 =>; 0 <=; 0 <~>)
% Maximal formula depth : 339 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2844 (2844 >; 0 *; 0 +; 0 <<)
% Number of symbols : 589 ( 586 usr; 337 con; 0-6 aty)
% Number of variables : 22886 (1329 ^;21513 !; 44 ?;22886 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_antisymmetric,type,
antisymmetric: $i > $i > $o ).
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_binintTransitive,type,
binintTransitive: $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_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1Set,type,
breln1Set: $i > $i ).
thf(tp_breln1SetBreln1,type,
breln1SetBreln1: $o ).
thf(tp_breln1all1,type,
breln1all1: $o ).
thf(tp_breln1all2,type,
breln1all2: $o ).
thf(tp_breln1compE,type,
breln1compE: $o ).
thf(tp_breln1compEex,type,
breln1compEex: $o ).
thf(tp_breln1compI,type,
breln1compI: $o ).
thf(tp_breln1compprop,type,
breln1compprop: $o ).
thf(tp_breln1compset,type,
breln1compset: $i > $i > $i > $i ).
thf(tp_breln1invE,type,
breln1invE: $o ).
thf(tp_breln1invI,type,
breln1invI: $o ).
thf(tp_breln1invprop,type,
breln1invprop: $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_breln1unionCommutes,type,
breln1unionCommutes: $o ).
thf(tp_breln1unionE,type,
breln1unionE: $o ).
thf(tp_breln1unionEcases,type,
breln1unionEcases: $o ).
thf(tp_breln1unionI,type,
breln1unionI: $o ).
thf(tp_breln1unionIL,type,
breln1unionIL: $o ).
thf(tp_breln1unionIR,type,
breln1unionIR: $o ).
thf(tp_breln1unionprop,type,
breln1unionprop: $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_choice2fnsingleton,type,
choice2fnsingleton: $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_complementUnionInPowersetComplement,type,
complementUnionInPowersetComplement: $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_demorgan1,type,
demorgan1: $o ).
thf(tp_demorgan1a,type,
demorgan1a: $o ).
thf(tp_demorgan1b,type,
demorgan1b: $o ).
thf(tp_demorgan2,type,
demorgan2: $o ).
thf(tp_demorgan2a,type,
demorgan2a: $o ).
thf(tp_demorgan2a1,type,
demorgan2a1: $o ).
thf(tp_demorgan2a2,type,
demorgan2a2: $o ).
thf(tp_demorgan2b,type,
demorgan2b: $o ).
thf(tp_demorgan2b2,type,
demorgan2b2: $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_eqbreln1,type,
eqbreln1: $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_foundation2,type,
foundation2: $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_image1,type,
image1: $i > ( $i > $i ) > $i ).
thf(tp_image1E,type,
image1E: $o ).
thf(tp_image1Equiv,type,
image1Equiv: $o ).
thf(tp_image1Ex,type,
image1Ex: $o ).
thf(tp_image1Ex1,type,
image1Ex1: $o ).
thf(tp_image1I,type,
image1I: $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_injFuncInInjFuncSet,type,
injFuncInInjFuncSet: $o ).
thf(tp_injFuncSet,type,
injFuncSet: $i > $i > $i ).
thf(tp_injFuncSetFuncIn,type,
injFuncSetFuncIn: $o ).
thf(tp_injFuncSetFuncInj,type,
injFuncSetFuncInj: $o ).
thf(tp_injective,type,
injective: $i > $i > $i > $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_leftInvIsSurj,type,
leftInvIsSurj: $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_notinself,type,
notinself: $o ).
thf(tp_notinself2,type,
notinself2: $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_omegaS,type,
omegaS: $i > $i ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omegaSclos,type,
omegaSclos: $o ).
thf(tp_omegaSp,type,
omegaSp: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_peano,type,
peano: $i > $i > $i > $o ).
thf(tp_peano0notS,type,
peano0notS: $o ).
thf(tp_peano3,type,
peano3: $i > $i > $i > $o ).
thf(tp_peano4,type,
peano4: $i > $i > $i > $o ).
thf(tp_peano5,type,
peano5: $i > $i > $i > $o ).
thf(tp_peanoSinj,type,
peanoSinj: $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_reflexive,type,
reflexive: $i > $i > $o ).
thf(tp_refllinearorder,type,
refllinearorder: $i > $i > $o ).
thf(tp_refltransitive,type,
refltransitive: $i > $i > $o ).
thf(tp_reflwellordering,type,
reflwellordering: $i > $i > $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK100_SY432,type,
sK100_SY432: $i > ( $i > $o ) > $i ).
thf(tp_sK101_SY436,type,
sK101_SY436: $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY1751,type,
sK102_SY1751: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK103_SY1783,type,
sK103_SY1783: ( $i > $i ) > $i > $i > $i > $i ).
thf(tp_sK104_SY1754,type,
sK104_SY1754: $i > $i > $i ).
thf(tp_sK105_SY1285,type,
sK105_SY1285: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK106_SY752,type,
sK106_SY752: $i > ( $i > $o ) > $i ).
thf(tp_sK107_SY796,type,
sK107_SY796: $i > ( $i > $o ) > $i ).
thf(tp_sK108_SY1619,type,
sK108_SY1619: $i > $i > $i > $i ).
thf(tp_sK109_SY1619,type,
sK109_SY1619: $i > $i > $i > $i ).
thf(tp_sK10_SY725,type,
sK10_SY725: $i > $i ).
thf(tp_sK110_SY401,type,
sK110_SY401: $i > ( $i > $o ) > $i ).
thf(tp_sK111_SY432,type,
sK111_SY432: $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY436,type,
sK112_SY436: $i > ( $i > $o ) > $i ).
thf(tp_sK113_SY462,type,
sK113_SY462: $i > ( $i > $o ) > $i ).
thf(tp_sK114_SY1656,type,
sK114_SY1656: $i > $i > $i > $i ).
thf(tp_sK115_SY752,type,
sK115_SY752: $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY796,type,
sK116_SY796: $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1772,type,
sK117_SY1772: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK118_SY1619,type,
sK118_SY1619: $i > $i > $i > $i ).
thf(tp_sK119_SY1713,type,
sK119_SY1713: $i > $i > $i > $i > $i ).
thf(tp_sK11_SY901,type,
sK11_SY901: ( $i > $o ) > $i > $i ).
thf(tp_sK120_SY462,type,
sK120_SY462: $i > ( $i > $o ) > $i ).
thf(tp_sK121_SY462,type,
sK121_SY462: $i > ( $i > $o ) > $i ).
thf(tp_sK122_SY1790,type,
sK122_SY1790: $i > $i > $i > $i > $i > $i ).
thf(tp_sK123_SY462,type,
sK123_SY462: $i > ( $i > $o ) > $i ).
thf(tp_sK124_SY1167,type,
sK124_SY1167: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK125_SY1833,type,
sK125_SY1833: $i > $i > $i > $i ).
thf(tp_sK126_SY1656,type,
sK126_SY1656: $i > $i > $i > $i ).
thf(tp_sK127_SY1656,type,
sK127_SY1656: $i > $i > $i > $i ).
thf(tp_sK128_SY1836,type,
sK128_SY1836: $i > $i > $i > $i > $i ).
thf(tp_sK129_SY1713,type,
sK129_SY1713: $i > $i > $i > $i > $i ).
thf(tp_sK12_SY994,type,
sK12_SY994: $i > $i > $i ).
thf(tp_sK130_SY1713,type,
sK130_SY1713: $i > $i > $i > $i > $i ).
thf(tp_sK131_SY1794,type,
sK131_SY1794: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK132_SY1167,type,
sK132_SY1167: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK133_SY1806,type,
sK133_SY1806: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK134_SY1656,type,
sK134_SY1656: $i > $i > $i > $i ).
thf(tp_sK135_SY1835,type,
sK135_SY1835: $o > $i > $i > $i > $i > $i > $i ).
thf(tp_sK136_SX0,type,
sK136_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK137_SX0,type,
sK137_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK138_SY1713,type,
sK138_SY1713: $i > $i > $i > $i > $i ).
thf(tp_sK139_SY1844,type,
sK139_SY1844: $i > $i > $i > $i ).
thf(tp_sK13_SY1008,type,
sK13_SY1008: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK140_SY1845,type,
sK140_SY1845: $i > $i > $i > $i ).
thf(tp_sK141_SY1846,type,
sK141_SY1846: $i > $i > $i > $i > $i ).
thf(tp_sK142_SY1847,type,
sK142_SY1847: $i > $i > $i > $i > $i ).
thf(tp_sK143_SY1853,type,
sK143_SY1853: $i > $i > $i > $i ).
thf(tp_sK144_SY1823,type,
sK144_SY1823: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK145_SY1824,type,
sK145_SY1824: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK146_SY1854,type,
sK146_SY1854: $i > $i > $i > $i > $i ).
thf(tp_sK147_SY1756,type,
sK147_SY1756: $i > $i > $i > $i ).
thf(tp_sK148_SY1803,type,
sK148_SY1803: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK149_SY1756,type,
sK149_SY1756: $i > $i > $i > $i ).
thf(tp_sK14_SY1032,type,
sK14_SY1032: ( $i > $o ) > $i > $i ).
thf(tp_sK150_SY1843,type,
sK150_SY1843: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK151_SY1012,type,
sK151_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY259,type,
sK152_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK153_SY1829,type,
sK153_SY1829: $i > $i > $i > $i ).
thf(tp_sK154_SY1868,type,
sK154_SY1868: $i > $i > $i > $i ).
thf(tp_sK155_SY1851,type,
sK155_SY1851: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK156_SY1852,type,
sK156_SY1852: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK157_SY1012,type,
sK157_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK158_SY259,type,
sK158_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK159_SY1874,type,
sK159_SY1874: $i > $i > $i > $i ).
thf(tp_sK15_SY1043,type,
sK15_SY1043: $i > $i > $i ).
thf(tp_sK160_SY1857,type,
sK160_SY1857: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK161_SY1858,type,
sK161_SY1858: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK162_SY1859,type,
sK162_SY1859: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK163_SY1855,type,
sK163_SY1855: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK164_SY1864,type,
sK164_SY1864: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK165_SY1865,type,
sK165_SY1865: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK166_SY1866,type,
sK166_SY1866: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK167_SY1867,type,
sK167_SY1867: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK168_SY1860,type,
sK168_SY1860: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK169_SY1872,type,
sK169_SY1872: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY1044,type,
sK16_SY1044: $i > $i > $i ).
thf(tp_sK170_SY1873,type,
sK170_SY1873: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK171_SY1803,type,
sK171_SY1803: $i > $i > ( $i > $i ) > $i > $i ).
thf(tp_sK172_SY1012,type,
sK172_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK173_SY259,type,
sK173_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK174_SY1878,type,
sK174_SY1878: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK175_SY1012,type,
sK175_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK176_SY259,type,
sK176_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK177_SY1012,type,
sK177_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK178_SY259,type,
sK178_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK179_SY1012,type,
sK179_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK17_SY1086,type,
sK17_SY1086: $i > $i > $i ).
thf(tp_sK180_SY259,type,
sK180_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK181_SY1884,type,
sK181_SY1884: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK182_SY1012,type,
sK182_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK183_SY259,type,
sK183_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK184_SY1012,type,
sK184_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK185_SY259,type,
sK185_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK186_SY1012,type,
sK186_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK187_SY259,type,
sK187_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK188_SY1012,type,
sK188_SY1012: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK189_SY259,type,
sK189_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK18_SY1164,type,
sK18_SY1164: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK190_SY1890,type,
sK190_SY1890: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK191_SY1894,type,
sK191_SY1894: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK192_SY1895,type,
sK192_SY1895: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK193_SY1896,type,
sK193_SY1896: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK194_SY1904,type,
sK194_SY1904: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK195_SY1905,type,
sK195_SY1905: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK196_SY1906,type,
sK196_SY1906: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK197_SY1913,type,
sK197_SY1913: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK19_SY1212,type,
sK19_SY1212: $i > $i > $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK20_SY1240,type,
sK20_SY1240: ( $i > $o ) > $i > $i ).
thf(tp_sK21_SY1266,type,
sK21_SY1266: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK22_SY1366,type,
sK22_SY1366: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK23_SY1378,type,
sK23_SY1378: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK24_SY1390,type,
sK24_SY1390: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK25_SY1408,type,
sK25_SY1408: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK26_SY1601,type,
sK26_SY1601: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK27_SY275,type,
sK27_SY275: $i > $i ).
thf(tp_sK28_SY1428,type,
sK28_SY1428: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK29_SY1085,type,
sK29_SY1085: ( $i > $o ) > $i > $i ).
thf(tp_sK2_SY0,type,
sK2_SY0: $i ).
thf(tp_sK30_SY1463,type,
sK30_SY1463: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK31_SY1142,type,
sK31_SY1142: $i > $i > $i ).
thf(tp_sK32_SY1481,type,
sK32_SY1481: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK33_SY1510,type,
sK33_SY1510: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK34_SY1652,type,
sK34_SY1652: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK35_SY742,type,
sK35_SY742: $i > $i ).
thf(tp_sK36_SY804,type,
sK36_SY804: $i > $i ).
thf(tp_sK37_SY899,type,
sK37_SY899: ( $i > $o ) > $i > $i ).
thf(tp_sK38_SY940,type,
sK38_SY940: ( $i > $o ) > $i > $i ).
thf(tp_sK39_SY1424,type,
sK39_SY1424: $i > $i > $i > $i ).
thf(tp_sK3_SY2,type,
sK3_SY2: $i ).
thf(tp_sK40_SY1605,type,
sK40_SY1605: ( $i > $o ) > $i > $i ).
thf(tp_sK41_SY1445,type,
sK41_SY1445: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK42_SY1627,type,
sK42_SY1627: $i > ( $i > $o ) > $i ).
thf(tp_sK43_SY1221,type,
sK43_SY1221: $i > $i > $i ).
thf(tp_sK44_SY1645,type,
sK44_SY1645: ( $i > $o ) > $i > $i ).
thf(tp_sK45_SY168,type,
sK45_SY168: $i > $i > $i ).
thf(tp_sK46_SY1606,type,
sK46_SY1606: $o > $i > $i > $i ).
thf(tp_sK47_SX0,type,
sK47_SX0: $i > $i > $i ).
thf(tp_sK48_SX0,type,
sK48_SX0: $i > $i > $i ).
thf(tp_sK49_SY1615,type,
sK49_SY1615: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK4_SY557,type,
sK4_SY557: $i > $i ).
thf(tp_sK50_SY1622,type,
sK50_SY1622: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK51_SY601,type,
sK51_SY601: $i > $i ).
thf(tp_sK52_SY1247,type,
sK52_SY1247: $i > $i > $i ).
thf(tp_sK53_SY1685,type,
sK53_SY1685: $i > $i > $i ).
thf(tp_sK54_SY1690,type,
sK54_SY1690: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK55_SY928,type,
sK55_SY928: $i > $i > $i ).
thf(tp_sK56_SY430,type,
sK56_SY430: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY1715,type,
sK57_SY1715: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK58_SY1167,type,
sK58_SY1167: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK59_SY1213,type,
sK59_SY1213: $i > $i > $i ).
thf(tp_sK5_SY5,type,
sK5_SY5: $i > $i ).
thf(tp_sK60_SY1724,type,
sK60_SY1724: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK61_SY1730,type,
sK61_SY1730: $i > $i > $i ).
thf(tp_sK62_SY1370,type,
sK62_SY1370: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK63_SY945,type,
sK63_SY945: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK64_SY1747,type,
sK64_SY1747: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK65_SY1618,type,
sK65_SY1618: $i > $i > $i > $i ).
thf(tp_sK66_SY1748,type,
sK66_SY1748: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK67_SY1777,type,
sK67_SY1777: $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY1460,type,
sK68_SY1460: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK69_SY1638,type,
sK69_SY1638: $i > $i > $i > $i ).
thf(tp_sK6_SY13,type,
sK6_SY13: $i > $i ).
thf(tp_sK70_SY1213,type,
sK70_SY1213: $i > $i > $i ).
thf(tp_sK71_SY1215,type,
sK71_SY1215: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK72_SY1654,type,
sK72_SY1654: $i > $i > $i > $i ).
thf(tp_sK73_SY1670,type,
sK73_SY1670: $i > $i > $i > $i ).
thf(tp_sK74_SY1678,type,
sK74_SY1678: $i > $i > $i > $i ).
thf(tp_sK75_SY1687,type,
sK75_SY1687: $i > $i > $i > $i > $i ).
thf(tp_sK76_SY1770,type,
sK76_SY1770: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK77_SY1700,type,
sK77_SY1700: $i > $i > $i > $i > $i ).
thf(tp_sK78_SY1610,type,
sK78_SY1610: $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY1611,type,
sK79_SY1611: $i > ( $i > $o ) > $i ).
thf(tp_sK7_SY1036,type,
sK7_SY1036: ( $i > $i ) > $i > $i ).
thf(tp_sK80_SY1707,type,
sK80_SY1707: $i > $i > $i > $i > $i ).
thf(tp_sK81_SY1621,type,
sK81_SY1621: $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY1625,type,
sK82_SY1625: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY1711,type,
sK83_SY1711: $i > $i > $i > $i > $i ).
thf(tp_sK84_SY1779,type,
sK84_SY1779: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK85_SY1787,type,
sK85_SY1787: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK86_SY1666,type,
sK86_SY1666: $i > ( $i > $o ) > $i ).
thf(tp_sK87_SY1728,type,
sK87_SY1728: $i > $i > $i > $i > $i ).
thf(tp_sK88_SY1674,type,
sK88_SY1674: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY1684,type,
sK89_SY1684: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY1067,type,
sK8_SY1067: ( $i > $i ) > $i > $i ).
thf(tp_sK90_SY1774,type,
sK90_SY1774: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK91_SY1788,type,
sK91_SY1788: $i > $i > $i > $i ).
thf(tp_sK92_SY1789,type,
sK92_SY1789: $i > $i > $i > $i ).
thf(tp_sK93_SY1732,type,
sK93_SY1732: $i > $i > $i > $i ).
thf(tp_sK94_SY1701,type,
sK94_SY1701: ( $i > $i ) > $i > $i > $i ).
thf(tp_sK95_SY1793,type,
sK95_SY1793: $i > $i > $i > $i > $i ).
thf(tp_sK96_SY1752,type,
sK96_SY1752: ( $i > $i ) > $i > $i > $i > $i ).
thf(tp_sK97_SY1801,type,
sK97_SY1801: $i > $i > $i > $i > $i ).
thf(tp_sK98_SY401,type,
sK98_SY401: $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY432,type,
sK99_SY432: $i > ( $i > $o ) > $i ).
thf(tp_sK9_SY527,type,
sK9_SY527: $i > $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_setOfPairsIsBReln1,type,
setOfPairsIsBReln1: $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_subbreln1,type,
subbreln1: $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_surjCantorThm,type,
surjCantorThm: $o ).
thf(tp_surjFuncSet,type,
surjFuncSet: $i > $i > $i ).
thf(tp_surjFuncSetFuncIn,type,
surjFuncSetFuncIn: $o ).
thf(tp_surjFuncSetFuncSurj,type,
surjFuncSetFuncSurj: $o ).
thf(tp_surjective,type,
surjective: $i > $i > $i > $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_transitive,type,
transitive: $i > $i > $o ).
thf(tp_transitiveset,type,
transitiveset: $i > $o ).
thf(tp_transitivesetOp1,type,
transitivesetOp1: $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(tp_woz13rule0,type,
woz13rule0: $o ).
thf(tp_woz13rule1,type,
woz13rule1: $o ).
thf(tp_woz13rule2,type,
woz13rule2: $o ).
thf(tp_woz13rule3,type,
woz13rule3: $o ).
thf(tp_woz13rule4,type,
woz13rule4: $o ).
thf(tp_woz1_1,type,
woz1_1: $o ).
thf(tp_woz1_2,type,
woz1_2: $o ).
thf(tp_woz1_3,type,
woz1_3: $o ).
thf(tp_woz1_4,type,
woz1_4: $o ).
thf(tp_woz1_5,type,
woz1_5: $o ).
thf(tp_woz2A,type,
woz2A: $o ).
thf(tp_woz2B,type,
woz2B: $o ).
thf(tp_woz2Ex,type,
woz2Ex: $o ).
thf(tp_woz2W,type,
woz2W: $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(binintTransitive,definition,
( binintTransitive
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [Y: $i] :
( ( transitiveset @ Y )
=> ( transitiveset @ ( binintersect @ X @ Y ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintTransitive) ).
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(breln1SetBreln1,definition,
( breln1SetBreln1
= ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1SetBreln1) ).
thf(breln1all1,definition,
( breln1all1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1all1) ).
thf(breln1all2,definition,
( breln1all2
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1all2) ).
thf(breln1compE,definition,
( breln1compE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ? [Xz: $i] :
( ( in @ Xz @ A )
& ( in @ ( kpair @ Xx @ Xz ) @ R )
& ( in @ ( kpair @ Xz @ Xy ) @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE) ).
thf(breln1compEex,definition,
( breln1compEex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) )
=> ! [Xphi: $o] :
( ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> Xphi ) ) )
=> Xphi ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compEex) ).
thf(breln1compI,definition,
( breln1compI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ! [Xz: $i] :
( ( in @ Xz @ A )
=> ( ( in @ ( kpair @ Xx @ Xz ) @ R )
=> ( ( in @ ( kpair @ Xz @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( breln1compset @ A @ R @ S ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compI) ).
thf(breln1compprop,definition,
( breln1compprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compprop) ).
thf(breln1invE,definition,
( breln1invE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invE) ).
thf(breln1invI,definition,
( breln1invI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invI) ).
thf(breln1invprop,definition,
( breln1invprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invprop) ).
thf(breln1unionCommutes,definition,
( breln1unionCommutes
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( binunion @ R @ S )
= ( binunion @ S @ R ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionCommutes) ).
thf(breln1unionE,definition,
( breln1unionE
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionE) ).
thf(breln1unionEcases,definition,
( breln1unionEcases
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) )
=> ! [Xphi: $o] :
( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> Xphi )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionEcases) ).
thf(breln1unionI,definition,
( breln1unionI
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( ( in @ ( kpair @ Xx @ Xy ) @ R )
| ( in @ ( kpair @ Xx @ Xy ) @ S ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionI) ).
thf(breln1unionIL,definition,
( breln1unionIL
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIL) ).
thf(breln1unionIR,definition,
( breln1unionIR
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( binunion @ R @ S ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionIR) ).
thf(breln1unionprop,definition,
( breln1unionprop
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1unionprop) ).
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(choice2fnsingleton,definition,
( choice2fnsingleton
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy ) ) )
=> ! [R: $i] :
( ( in @ R @ ( breln1Set @ B ) )
=> ( ( reflwellordering @ B @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] :
( ( Xphi @ Xx @ Xy )
& ! [Xz: $i] :
( ( in @ Xz @ B )
=> ( ( Xphi @ Xx @ Xz )
=> ( in @ ( kpair @ Xy @ Xz ) @ R ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2fnsingleton) ).
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(complementUnionInPowersetComplement,definition,
( complementUnionInPowersetComplement
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementUnionInPowersetComplement) ).
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(demorgan1,definition,
( demorgan1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ X @ Y ) )
= ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1) ).
thf(demorgan1a,definition,
( demorgan1a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
=> ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a) ).
thf(demorgan1b,definition,
( demorgan1b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1b) ).
thf(demorgan2,definition,
( demorgan2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binunion @ X @ Y ) )
= ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2) ).
thf(demorgan2a,definition,
( demorgan2a
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a) ).
thf(demorgan2a1,definition,
( demorgan2a1
= ( ! [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(demorgan2a2,definition,
( demorgan2a2
= ( ! [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 @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a2) ).
thf(demorgan2b,definition,
( demorgan2b
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b) ).
thf(demorgan2b2,definition,
( demorgan2b2
= ( ! [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 @ Y ) )
=> ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2b2) ).
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(eqbreln1,definition,
( eqbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln1) ).
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(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(foundation2,definition,
( foundation2
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [X: $i] :
( ( in @ X @ A )
& ( ( binintersect @ X @ A )
= emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundation2) ).
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(image1E,definition,
( image1E
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1E) ).
thf(image1Equiv,definition,
( image1Equiv
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv) ).
thf(image1Ex,definition,
( image1Ex
= ( ! [A: $i,Xf: $i > $i] :
? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex) ).
thf(image1Ex1,definition,
( image1Ex1
= ( ! [A: $i,Xf: $i > $i] :
( exu
@ ^ [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex1) ).
thf(image1I,definition,
( image1I
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1I) ).
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(injFuncInInjFuncSet,definition,
( injFuncInInjFuncSet
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( injective @ A @ B @ Xf )
=> ( in @ Xf @ ( injFuncSet @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncInInjFuncSet) ).
thf(injFuncSetFuncIn,definition,
( injFuncSetFuncIn
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSetFuncIn) ).
thf(injFuncSetFuncInj,definition,
( injFuncSetFuncInj
= ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( injFuncSet @ Xx @ Xy ) )
=> ( injective @ Xx @ Xy @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',injFuncSetFuncInj) ).
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(leftInvIsSurj,definition,
( leftInvIsSurj
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ B @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ B @ A @ Xg @ ( Xf @ Xx ) )
= Xx ) )
=> ( surjective @ B @ A @ Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leftInvIsSurj) ).
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(notinself,definition,
( notinself
= ( ! [A: $i] :
~ ( in @ A @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself) ).
thf(notinself2,definition,
( notinself2
= ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2) ).
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(omegaSclos,definition,
( omegaSclos
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSclos) ).
thf(omegaSp,definition,
( omegaSp
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( omegaS @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSp) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(peano0notS,definition,
( peano0notS
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( ( omegaS @ Xx )
!= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peano0notS) ).
thf(peanoSinj,definition,
( peanoSinj
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ! [Xy: $i] :
( ( in @ Xy @ omega )
=> ( ( ( omegaS @ Xx )
= ( omegaS @ Xy ) )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',peanoSinj) ).
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(setOfPairsIsBReln1,definition,
( setOfPairsIsBReln1
= ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln1) ).
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(subbreln1,definition,
( subbreln1
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln1) ).
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(surjCantorThm,definition,
( surjCantorThm
= ( ! [A: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ ( powerset @ A ) ) )
=> ~ ( surjective @ A @ ( powerset @ A ) @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjCantorThm) ).
thf(surjFuncSetFuncIn,definition,
( surjFuncSetFuncIn
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ A @ B ) )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjFuncSetFuncIn) ).
thf(surjFuncSetFuncSurj,definition,
( surjFuncSetFuncSurj
= ( ! [Xx: $i,Xy: $i,Xf: $i] :
( ( in @ Xf @ ( surjFuncSet @ Xx @ Xy ) )
=> ( surjective @ Xx @ Xy @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',surjFuncSetFuncSurj) ).
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(transitiveset,definition,
( transitiveset
= ( ^ [A: $i] :
! [X: $i] :
( ( in @ X @ A )
=> ( subset @ X @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitiveset) ).
thf(transitivesetOp1,definition,
( transitivesetOp1
= ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i] :
( ( in @ A @ X )
=> ( subset @ A @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp1) ).
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(woz13rule0,definition,
( woz13rule0
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule0) ).
thf(woz13rule1,definition,
( woz13rule1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule1) ).
thf(woz13rule2,definition,
( woz13rule2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ Y @ Z )
=> ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule2) ).
thf(woz13rule3,definition,
( woz13rule3
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( ( subset @ X @ Z )
=> ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule3) ).
thf(woz13rule4,definition,
( woz13rule4
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( subset @ X @ Z )
=> ( ( subset @ Y @ W )
=> ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz13rule4) ).
thf(woz1_1,definition,
( woz1_1
= ( ! [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',woz1_1) ).
thf(woz1_2,definition,
( woz1_2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [W: $i] :
( ( in @ W @ ( powerset @ A ) )
=> ( ( setminus @ A @ ( binintersect @ ( binunion @ X @ Y ) @ ( binunion @ Z @ W ) ) )
= ( binunion @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) @ ( binintersect @ ( setminus @ A @ Z ) @ ( setminus @ A @ W ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_2) ).
thf(woz1_3,definition,
( woz1_3
= ( ! [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',woz1_3) ).
thf(woz1_4,definition,
( woz1_4
= ( ! [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',woz1_4) ).
thf(woz1_5,definition,
( woz1_5
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz1_5) ).
thf(woz2A,definition,
( woz2A
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1compset @ A @ R @ T ) @ ( breln1compset @ A @ S @ T ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2A) ).
thf(woz2B,definition,
( woz2B
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ! [T: $i] :
( ( breln1 @ A @ T )
=> ( ( breln1compset @ A @ ( binunion @ R @ S ) @ T )
= ( binunion @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ S ) ) ) @ ( breln1invset @ A @ ( breln1compset @ A @ ( breln1invset @ A @ T ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2B) ).
thf(woz2Ex,definition,
( woz2Ex
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( R
= ( breln1invset @ A @ ( breln1invset @ A @ R ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2Ex) ).
thf(woz2W,definition,
( woz2W
= ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( ( breln1invset @ A @ ( breln1compset @ A @ R @ S ) )
= ( breln1compset @ A @ ( breln1invset @ A @ S ) @ ( breln1invset @ A @ R ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',woz2W) ).
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
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i,Xx: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivesetOp2) ).
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
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ( woz13rule4
=> ( woz1_1
=> ( woz1_2
=> ( woz1_3
=> ( woz1_4
=> ( woz1_5
=> ( breln1all2
=> ( breln1SetBreln1
=> ( choice2fnsingleton
=> ( setOfPairsIsBReln1
=> ( breln1all1
=> ( subbreln1
=> ( eqbreln1
=> ( breln1invprop
=> ( breln1invI
=> ( breln1invE
=> ( breln1compprop
=> ( breln1compI
=> ( breln1compE
=> ( breln1compEex
=> ( breln1unionprop
=> ( breln1unionIL
=> ( breln1unionIR
=> ( breln1unionI
=> ( breln1unionE
=> ( breln1unionEcases
=> ( breln1unionCommutes
=> ( woz2Ex
=> ( woz2W
=> ( woz2A
=> ( woz2B
=> ( image1Ex
=> ( image1Ex1
=> ( image1Equiv
=> ( image1E
=> ( image1I
=> ( injFuncInInjFuncSet
=> ( injFuncSetFuncIn
=> ( injFuncSetFuncInj
=> ( surjFuncSetFuncIn
=> ( surjFuncSetFuncSurj
=> ( leftInvIsSurj
=> ( surjCantorThm
=> ( foundation2
=> ( notinself
=> ( notinself2
=> ( omegaSp
=> ( omegaSclos
=> ( peano0notS
=> ( peanoSinj
=> ( transitivesetOp1
=> ( binintTransitive
=> ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i,Xx: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ 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,
demorgan2a1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(268,plain,
complementUnionInPowersetComplement = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(269,plain,
demorgan2a2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(270,plain,
demorgan1a = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(271,plain,
demorgan1b = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(272,plain,
demorgan1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(273,plain,
demorgan2a = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(274,plain,
demorgan2b2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(275,plain,
demorgan2b = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(276,plain,
demorgan2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(277,plain,
woz13rule0 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(278,plain,
woz13rule1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(279,plain,
woz13rule2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(280,plain,
woz13rule3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(281,plain,
woz13rule4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(282,plain,
woz1_1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(283,plain,
woz1_2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(284,plain,
woz1_3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(285,plain,
woz1_4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(286,plain,
woz1_5 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(287,plain,
breln1all2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(288,plain,
breln1SetBreln1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(289,plain,
choice2fnsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(290,plain,
setOfPairsIsBReln1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(291,plain,
breln1all1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(292,plain,
subbreln1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(293,plain,
eqbreln1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(294,plain,
breln1invprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(295,plain,
breln1invI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(296,plain,
breln1invE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(297,plain,
breln1compprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(298,plain,
breln1compI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(299,plain,
breln1compE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(300,plain,
breln1compEex = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(301,plain,
breln1unionprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(302,plain,
breln1unionIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(303,plain,
breln1unionIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(304,plain,
breln1unionI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(305,plain,
breln1unionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(306,plain,
breln1unionEcases = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(307,plain,
breln1unionCommutes = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(308,plain,
woz2Ex = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(309,plain,
woz2W = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(310,plain,
woz2A = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(311,plain,
woz2B = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(312,plain,
image1Ex = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(313,plain,
image1Ex1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(314,plain,
image1Equiv = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(315,plain,
image1E = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(316,plain,
image1I = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(317,plain,
injFuncInInjFuncSet = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(318,plain,
injFuncSetFuncIn = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(319,plain,
injFuncSetFuncInj = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(320,plain,
surjFuncSetFuncIn = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(321,plain,
surjFuncSetFuncSurj = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(322,plain,
leftInvIsSurj = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(323,plain,
surjCantorThm = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(324,plain,
foundation2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(325,plain,
notinself = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(326,plain,
notinself2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(327,plain,
omegaSp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(328,plain,
omegaSclos = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(329,plain,
peano0notS = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(330,plain,
peanoSinj = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(331,plain,
transitivesetOp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(332,plain,
binintTransitive = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(333,plain,
( ( ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i,Xx: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(334,plain,
( ( ~ ! [X: $i] :
( ( transitiveset @ X )
=> ! [A: $i,Xx: $i] :
( ( in @ A @ X )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[333]) ).
thf(335,plain,
( ( ( transitiveset @ sK1_X )
& ( in @ sK2_SY0 @ sK1_X )
& ( in @ sK3_SY2 @ sK2_SY0 )
& ~ ( in @ sK3_SY2 @ sK1_X ) )
= $true ),
inference(extcnf_combined,[status(esa)],[334]) ).
thf(336,plain,
binintTransitive = $true,
inference(copy,[status(thm)],[332]) ).
thf(337,plain,
transitivesetOp1 = $true,
inference(copy,[status(thm)],[331]) ).
thf(338,plain,
peanoSinj = $true,
inference(copy,[status(thm)],[330]) ).
thf(339,plain,
peano0notS = $true,
inference(copy,[status(thm)],[329]) ).
thf(340,plain,
omegaSclos = $true,
inference(copy,[status(thm)],[328]) ).
thf(341,plain,
omegaSp = $true,
inference(copy,[status(thm)],[327]) ).
thf(342,plain,
notinself2 = $true,
inference(copy,[status(thm)],[326]) ).
thf(343,plain,
notinself = $true,
inference(copy,[status(thm)],[325]) ).
thf(344,plain,
foundation2 = $true,
inference(copy,[status(thm)],[324]) ).
thf(345,plain,
surjCantorThm = $true,
inference(copy,[status(thm)],[323]) ).
thf(346,plain,
leftInvIsSurj = $true,
inference(copy,[status(thm)],[322]) ).
thf(347,plain,
surjFuncSetFuncSurj = $true,
inference(copy,[status(thm)],[321]) ).
thf(348,plain,
surjFuncSetFuncIn = $true,
inference(copy,[status(thm)],[320]) ).
thf(349,plain,
injFuncSetFuncInj = $true,
inference(copy,[status(thm)],[319]) ).
thf(350,plain,
injFuncSetFuncIn = $true,
inference(copy,[status(thm)],[318]) ).
thf(351,plain,
injFuncInInjFuncSet = $true,
inference(copy,[status(thm)],[317]) ).
thf(352,plain,
image1I = $true,
inference(copy,[status(thm)],[316]) ).
thf(353,plain,
image1E = $true,
inference(copy,[status(thm)],[315]) ).
thf(354,plain,
image1Equiv = $true,
inference(copy,[status(thm)],[314]) ).
thf(355,plain,
image1Ex1 = $true,
inference(copy,[status(thm)],[313]) ).
thf(356,plain,
image1Ex = $true,
inference(copy,[status(thm)],[312]) ).
thf(357,plain,
woz2B = $true,
inference(copy,[status(thm)],[311]) ).
thf(358,plain,
woz2A = $true,
inference(copy,[status(thm)],[310]) ).
thf(359,plain,
woz2W = $true,
inference(copy,[status(thm)],[309]) ).
thf(360,plain,
woz2Ex = $true,
inference(copy,[status(thm)],[308]) ).
thf(361,plain,
breln1unionCommutes = $true,
inference(copy,[status(thm)],[307]) ).
thf(362,plain,
breln1unionEcases = $true,
inference(copy,[status(thm)],[306]) ).
thf(363,plain,
breln1unionE = $true,
inference(copy,[status(thm)],[305]) ).
thf(364,plain,
breln1unionI = $true,
inference(copy,[status(thm)],[304]) ).
thf(365,plain,
breln1unionIR = $true,
inference(copy,[status(thm)],[303]) ).
thf(366,plain,
breln1unionIL = $true,
inference(copy,[status(thm)],[302]) ).
thf(367,plain,
breln1unionprop = $true,
inference(copy,[status(thm)],[301]) ).
thf(368,plain,
breln1compEex = $true,
inference(copy,[status(thm)],[300]) ).
thf(369,plain,
breln1compE = $true,
inference(copy,[status(thm)],[299]) ).
thf(370,plain,
breln1compI = $true,
inference(copy,[status(thm)],[298]) ).
thf(371,plain,
breln1compprop = $true,
inference(copy,[status(thm)],[297]) ).
thf(372,plain,
breln1invE = $true,
inference(copy,[status(thm)],[296]) ).
thf(373,plain,
breln1invI = $true,
inference(copy,[status(thm)],[295]) ).
thf(374,plain,
breln1invprop = $true,
inference(copy,[status(thm)],[294]) ).
thf(375,plain,
eqbreln1 = $true,
inference(copy,[status(thm)],[293]) ).
thf(376,plain,
subbreln1 = $true,
inference(copy,[status(thm)],[292]) ).
thf(377,plain,
breln1all1 = $true,
inference(copy,[status(thm)],[291]) ).
thf(378,plain,
setOfPairsIsBReln1 = $true,
inference(copy,[status(thm)],[290]) ).
thf(379,plain,
choice2fnsingleton = $true,
inference(copy,[status(thm)],[289]) ).
thf(380,plain,
breln1SetBreln1 = $true,
inference(copy,[status(thm)],[288]) ).
thf(381,plain,
breln1all2 = $true,
inference(copy,[status(thm)],[287]) ).
thf(382,plain,
woz1_5 = $true,
inference(copy,[status(thm)],[286]) ).
thf(383,plain,
woz1_4 = $true,
inference(copy,[status(thm)],[285]) ).
thf(384,plain,
woz1_3 = $true,
inference(copy,[status(thm)],[284]) ).
thf(385,plain,
woz1_2 = $true,
inference(copy,[status(thm)],[283]) ).
thf(386,plain,
woz1_1 = $true,
inference(copy,[status(thm)],[282]) ).
thf(387,plain,
woz13rule4 = $true,
inference(copy,[status(thm)],[281]) ).
thf(388,plain,
woz13rule3 = $true,
inference(copy,[status(thm)],[280]) ).
thf(389,plain,
woz13rule2 = $true,
inference(copy,[status(thm)],[279]) ).
thf(390,plain,
woz13rule1 = $true,
inference(copy,[status(thm)],[278]) ).
thf(391,plain,
woz13rule0 = $true,
inference(copy,[status(thm)],[277]) ).
thf(392,plain,
demorgan2 = $true,
inference(copy,[status(thm)],[276]) ).
thf(393,plain,
demorgan2b = $true,
inference(copy,[status(thm)],[275]) ).
thf(394,plain,
demorgan2b2 = $true,
inference(copy,[status(thm)],[274]) ).
thf(395,plain,
demorgan2a = $true,
inference(copy,[status(thm)],[273]) ).
thf(396,plain,
demorgan1 = $true,
inference(copy,[status(thm)],[272]) ).
thf(397,plain,
demorgan1b = $true,
inference(copy,[status(thm)],[271]) ).
thf(398,plain,
demorgan1a = $true,
inference(copy,[status(thm)],[270]) ).
thf(399,plain,
demorgan2a2 = $true,
inference(copy,[status(thm)],[269]) ).
thf(400,plain,
complementUnionInPowersetComplement = $true,
inference(copy,[status(thm)],[268]) ).
thf(401,plain,
demorgan2a1 = $true,
inference(copy,[status(thm)],[267]) ).
thf(402,plain,
binunionTEcontra = $true,
inference(copy,[status(thm)],[266]) ).
thf(403,plain,
binunionTE = $true,
inference(copy,[status(thm)],[265]) ).
thf(404,plain,
inComplementUnionImpInComplement1 = $true,
inference(copy,[status(thm)],[264]) ).
thf(405,plain,
inComplementUnionImpNotIn1 = $true,
inference(copy,[status(thm)],[263]) ).
thf(406,plain,
intersectInPowersetIntersectUnions = $true,
inference(copy,[status(thm)],[262]) ).
thf(407,plain,
inIntersectImpInIntersectUnions = $true,
inference(copy,[status(thm)],[261]) ).
thf(408,plain,
inIntersectImpInUnion2 = $true,
inference(copy,[status(thm)],[260]) ).
thf(409,plain,
inIntersectImpInUnion = $true,
inference(copy,[status(thm)],[259]) ).
thf(410,plain,
binunionTIRcontra = $true,
inference(copy,[status(thm)],[258]) ).
thf(411,plain,
binunionTILcontra = $true,
inference(copy,[status(thm)],[257]) ).
thf(412,plain,
complementTcontraSubset = $true,
inference(copy,[status(thm)],[256]) ).
thf(413,plain,
contraSubsetComplement = $true,
inference(copy,[status(thm)],[255]) ).
thf(414,plain,
complementInPowersetComplementIntersect = $true,
inference(copy,[status(thm)],[254]) ).
thf(415,plain,
complementSubsetComplementIntersect = $true,
inference(copy,[status(thm)],[253]) ).
thf(416,plain,
complementImpComplementIntersect = $true,
inference(copy,[status(thm)],[252]) ).
thf(417,plain,
complementTnotintersectT = $true,
inference(copy,[status(thm)],[251]) ).
thf(418,plain,
doubleComplementEq = $true,
inference(copy,[status(thm)],[250]) ).
thf(419,plain,
doubleComplementSub2 = $true,
inference(copy,[status(thm)],[249]) ).
thf(420,plain,
doubleComplementSub1 = $true,
inference(copy,[status(thm)],[248]) ).
thf(421,plain,
doubleComplementE1 = $true,
inference(copy,[status(thm)],[247]) ).
thf(422,plain,
doubleComplementI1 = $true,
inference(copy,[status(thm)],[246]) ).
thf(423,plain,
contrasubsetT3 = $true,
inference(copy,[status(thm)],[245]) ).
thf(424,plain,
contrasubsetT2 = $true,
inference(copy,[status(thm)],[244]) ).
thf(425,plain,
contrasubsetT1 = $true,
inference(copy,[status(thm)],[243]) ).
thf(426,plain,
contrasubsetT = $true,
inference(copy,[status(thm)],[242]) ).
thf(427,plain,
binintersectTERcontra = $true,
inference(copy,[status(thm)],[241]) ).
thf(428,plain,
binintersectTELcontra = $true,
inference(copy,[status(thm)],[240]) ).
thf(429,plain,
complementTE1 = $true,
inference(copy,[status(thm)],[239]) ).
thf(430,plain,
complementTI1 = $true,
inference(copy,[status(thm)],[238]) ).
thf(431,plain,
powersetTE1 = $true,
inference(copy,[status(thm)],[237]) ).
thf(432,plain,
powersetTI1 = $true,
inference(copy,[status(thm)],[236]) ).
thf(433,plain,
subsetTI = $true,
inference(copy,[status(thm)],[235]) ).
thf(434,plain,
setextT = $true,
inference(copy,[status(thm)],[234]) ).
thf(435,plain,
complementT_lem = $true,
inference(copy,[status(thm)],[233]) ).
thf(436,plain,
setminusT_lem = $true,
inference(copy,[status(thm)],[232]) ).
thf(437,plain,
powersetT_lem = $true,
inference(copy,[status(thm)],[231]) ).
thf(438,plain,
binunionT_lem = $true,
inference(copy,[status(thm)],[230]) ).
thf(439,plain,
binintersectT_lem = $true,
inference(copy,[status(thm)],[229]) ).
thf(440,plain,
iftrueorfalse = $true,
inference(copy,[status(thm)],[228]) ).
thf(441,plain,
iffalse = $true,
inference(copy,[status(thm)],[227]) ).
thf(442,plain,
iftrue = $true,
inference(copy,[status(thm)],[226]) ).
thf(443,plain,
theeq = $true,
inference(copy,[status(thm)],[225]) ).
thf(444,plain,
ifp = $true,
inference(copy,[status(thm)],[224]) ).
thf(445,plain,
ifSingleton = $true,
inference(copy,[status(thm)],[223]) ).
thf(446,plain,
iftrueProp2 = $true,
inference(copy,[status(thm)],[222]) ).
thf(447,plain,
iftrueProp1 = $true,
inference(copy,[status(thm)],[221]) ).
thf(448,plain,
iffalseProp2 = $true,
inference(copy,[status(thm)],[220]) ).
thf(449,plain,
iffalseProp1 = $true,
inference(copy,[status(thm)],[219]) ).
thf(450,plain,
eta2 = $true,
inference(copy,[status(thm)],[218]) ).
thf(451,plain,
beta2 = $true,
inference(copy,[status(thm)],[217]) ).
thf(452,plain,
lam2lamEq = $true,
inference(copy,[status(thm)],[216]) ).
thf(453,plain,
eta1 = $true,
inference(copy,[status(thm)],[215]) ).
thf(454,plain,
beta1 = $true,
inference(copy,[status(thm)],[214]) ).
thf(455,plain,
ap2apEq2 = $true,
inference(copy,[status(thm)],[213]) ).
thf(456,plain,
ap2apEq1 = $true,
inference(copy,[status(thm)],[212]) ).
thf(457,plain,
funcext2 = $true,
inference(copy,[status(thm)],[211]) ).
thf(458,plain,
funcext = $true,
inference(copy,[status(thm)],[210]) ).
thf(459,plain,
eqbreln = $true,
inference(copy,[status(thm)],[209]) ).
thf(460,plain,
subbreln = $true,
inference(copy,[status(thm)],[208]) ).
thf(461,plain,
funcGraphProp4 = $true,
inference(copy,[status(thm)],[207]) ).
thf(462,plain,
funcextLem = $true,
inference(copy,[status(thm)],[206]) ).
thf(463,plain,
funcGraphProp2 = $true,
inference(copy,[status(thm)],[205]) ).
thf(464,plain,
funcGraphProp3 = $true,
inference(copy,[status(thm)],[204]) ).
thf(465,plain,
funcGraphProp1 = $true,
inference(copy,[status(thm)],[203]) ).
thf(466,plain,
ex1E2 = $true,
inference(copy,[status(thm)],[202]) ).
thf(467,plain,
brelnall2 = $true,
inference(copy,[status(thm)],[201]) ).
thf(468,plain,
brelnall1 = $true,
inference(copy,[status(thm)],[200]) ).
thf(469,plain,
lam2p = $true,
inference(copy,[status(thm)],[199]) ).
thf(470,plain,
lamp = $true,
inference(copy,[status(thm)],[198]) ).
thf(471,plain,
lamProp = $true,
inference(copy,[status(thm)],[197]) ).
thf(472,plain,
funcinfuncset = $true,
inference(copy,[status(thm)],[196]) ).
thf(473,plain,
ap2p = $true,
inference(copy,[status(thm)],[195]) ).
thf(474,plain,
infuncsetfunc = $true,
inference(copy,[status(thm)],[194]) ).
thf(475,plain,
app = $true,
inference(copy,[status(thm)],[193]) ).
thf(476,plain,
apProp = $true,
inference(copy,[status(thm)],[192]) ).
thf(477,plain,
funcImageSingleton = $true,
inference(copy,[status(thm)],[191]) ).
thf(478,plain,
dpsetconstrER = $true,
inference(copy,[status(thm)],[190]) ).
thf(479,plain,
dpsetconstrEL2 = $true,
inference(copy,[status(thm)],[189]) ).
thf(480,plain,
dpsetconstrEL1 = $true,
inference(copy,[status(thm)],[188]) ).
thf(481,plain,
dpsetconstrERa = $true,
inference(copy,[status(thm)],[187]) ).
thf(482,plain,
setOfPairsIsBReln = $true,
inference(copy,[status(thm)],[186]) ).
thf(483,plain,
dpsetconstrSub = $true,
inference(copy,[status(thm)],[185]) ).
thf(484,plain,
dpsetconstrI = $true,
inference(copy,[status(thm)],[184]) ).
thf(485,plain,
cartprodpairsurjEq = $true,
inference(copy,[status(thm)],[183]) ).
thf(486,plain,
cartprodsndpairEq = $true,
inference(copy,[status(thm)],[182]) ).
thf(487,plain,
cartprodfstpairEq = $true,
inference(copy,[status(thm)],[181]) ).
thf(488,plain,
cartprodmempaircEq = $true,
inference(copy,[status(thm)],[180]) ).
thf(489,plain,
cartprodpairmemER = $true,
inference(copy,[status(thm)],[179]) ).
thf(490,plain,
cartprodpairmemEL = $true,
inference(copy,[status(thm)],[178]) ).
thf(491,plain,
cartprodsndin = $true,
inference(copy,[status(thm)],[177]) ).
thf(492,plain,
kpairsurjEq = $true,
inference(copy,[status(thm)],[176]) ).
thf(493,plain,
ksndpairEq = $true,
inference(copy,[status(thm)],[175]) ).
thf(494,plain,
ksndsingleton = $true,
inference(copy,[status(thm)],[174]) ).
thf(495,plain,
setukpairinjR = $true,
inference(copy,[status(thm)],[173]) ).
thf(496,plain,
setukpairinjR2 = $true,
inference(copy,[status(thm)],[172]) ).
thf(497,plain,
upairequniteq = $true,
inference(copy,[status(thm)],[171]) ).
thf(498,plain,
setukpairinjR1 = $true,
inference(copy,[status(thm)],[170]) ).
thf(499,plain,
setukpairinjR12 = $true,
inference(copy,[status(thm)],[169]) ).
thf(500,plain,
setukpairinjR11 = $true,
inference(copy,[status(thm)],[168]) ).
thf(501,plain,
setukpairinjL = $true,
inference(copy,[status(thm)],[167]) ).
thf(502,plain,
setukpairinjL2 = $true,
inference(copy,[status(thm)],[166]) ).
thf(503,plain,
cartprodfstin = $true,
inference(copy,[status(thm)],[165]) ).
thf(504,plain,
kfstpairEq = $true,
inference(copy,[status(thm)],[164]) ).
thf(505,plain,
theprop = $true,
inference(copy,[status(thm)],[163]) ).
thf(506,plain,
kfstsingleton = $true,
inference(copy,[status(thm)],[162]) ).
thf(507,plain,
setukpairinjL1 = $true,
inference(copy,[status(thm)],[161]) ).
thf(508,plain,
singletonsuniq = $true,
inference(copy,[status(thm)],[160]) ).
thf(509,plain,
ex1I2 = $true,
inference(copy,[status(thm)],[159]) ).
thf(510,plain,
ex1I = $true,
inference(copy,[status(thm)],[158]) ).
thf(511,plain,
ex1E1 = $true,
inference(copy,[status(thm)],[157]) ).
thf(512,plain,
singletonprop = $true,
inference(copy,[status(thm)],[156]) ).
thf(513,plain,
setunionsingleton = $true,
inference(copy,[status(thm)],[155]) ).
thf(514,plain,
setunionsingleton2 = $true,
inference(copy,[status(thm)],[154]) ).
thf(515,plain,
setunionsingleton1 = $true,
inference(copy,[status(thm)],[153]) ).
thf(516,plain,
setunionE2 = $true,
inference(copy,[status(thm)],[152]) ).
thf(517,plain,
cartprodmempair = $true,
inference(copy,[status(thm)],[151]) ).
thf(518,plain,
cartprodmempair1 = $true,
inference(copy,[status(thm)],[150]) ).
thf(519,plain,
cartprodpairin = $true,
inference(copy,[status(thm)],[149]) ).
thf(520,plain,
ubforcartprodlem3 = $true,
inference(copy,[status(thm)],[148]) ).
thf(521,plain,
ubforcartprodlem2 = $true,
inference(copy,[status(thm)],[147]) ).
thf(522,plain,
ubforcartprodlem1 = $true,
inference(copy,[status(thm)],[146]) ).
thf(523,plain,
upairinpowunion = $true,
inference(copy,[status(thm)],[145]) ).
thf(524,plain,
upairsubunion = $true,
inference(copy,[status(thm)],[144]) ).
thf(525,plain,
upairset2E = $true,
inference(copy,[status(thm)],[143]) ).
thf(526,plain,
singletoninpowunion = $true,
inference(copy,[status(thm)],[142]) ).
thf(527,plain,
singletoninpowerset = $true,
inference(copy,[status(thm)],[141]) ).
thf(528,plain,
singletonsubset = $true,
inference(copy,[status(thm)],[140]) ).
thf(529,plain,
kpairp = $true,
inference(copy,[status(thm)],[139]) ).
thf(530,plain,
kpairiskpair = $true,
inference(copy,[status(thm)],[138]) ).
thf(531,plain,
setukpairIR = $true,
inference(copy,[status(thm)],[137]) ).
thf(532,plain,
setukpairIL = $true,
inference(copy,[status(thm)],[136]) ).
thf(533,plain,
secondinupair = $true,
inference(copy,[status(thm)],[135]) ).
thf(534,plain,
symdiffIneg2 = $true,
inference(copy,[status(thm)],[134]) ).
thf(535,plain,
symdiffIneg1 = $true,
inference(copy,[status(thm)],[133]) ).
thf(536,plain,
symdiffI2 = $true,
inference(copy,[status(thm)],[132]) ).
thf(537,plain,
symdiffI1 = $true,
inference(copy,[status(thm)],[131]) ).
thf(538,plain,
symdiffE = $true,
inference(copy,[status(thm)],[130]) ).
thf(539,plain,
setminusSubset1 = $true,
inference(copy,[status(thm)],[129]) ).
thf(540,plain,
setminusLsub = $true,
inference(copy,[status(thm)],[128]) ).
thf(541,plain,
setminusIRneg = $true,
inference(copy,[status(thm)],[127]) ).
thf(542,plain,
setminusILneg = $true,
inference(copy,[status(thm)],[126]) ).
thf(543,plain,
setminusELneg = $true,
inference(copy,[status(thm)],[125]) ).
thf(544,plain,
setminusERneg = $true,
inference(copy,[status(thm)],[124]) ).
thf(545,plain,
setminusSubset2 = $true,
inference(copy,[status(thm)],[123]) ).
thf(546,plain,
setminusER = $true,
inference(copy,[status(thm)],[122]) ).
thf(547,plain,
setminusEL = $true,
inference(copy,[status(thm)],[121]) ).
thf(548,plain,
setminusI = $true,
inference(copy,[status(thm)],[120]) ).
thf(549,plain,
bs114d = $true,
inference(copy,[status(thm)],[119]) ).
thf(550,plain,
binintersectSubset1 = $true,
inference(copy,[status(thm)],[118]) ).
thf(551,plain,
binintersectSubset4 = $true,
inference(copy,[status(thm)],[117]) ).
thf(552,plain,
binintersectRsub = $true,
inference(copy,[status(thm)],[116]) ).
thf(553,plain,
disjointsetsI1 = $true,
inference(copy,[status(thm)],[115]) ).
thf(554,plain,
binintersectER = $true,
inference(copy,[status(thm)],[114]) ).
thf(555,plain,
binintersectSubset3 = $true,
inference(copy,[status(thm)],[113]) ).
thf(556,plain,
binintersectSubset2 = $true,
inference(copy,[status(thm)],[112]) ).
thf(557,plain,
binintersectLsub = $true,
inference(copy,[status(thm)],[111]) ).
thf(558,plain,
binintersectEL = $true,
inference(copy,[status(thm)],[110]) ).
thf(559,plain,
binintersectSubset5 = $true,
inference(copy,[status(thm)],[109]) ).
thf(560,plain,
binintersectI = $true,
inference(copy,[status(thm)],[108]) ).
thf(561,plain,
binunionRsub = $true,
inference(copy,[status(thm)],[107]) ).
thf(562,plain,
binunionLsub = $true,
inference(copy,[status(thm)],[106]) ).
thf(563,plain,
binunionE = $true,
inference(copy,[status(thm)],[105]) ).
thf(564,plain,
binunionEcases = $true,
inference(copy,[status(thm)],[104]) ).
thf(565,plain,
binunionIR = $true,
inference(copy,[status(thm)],[103]) ).
thf(566,plain,
upairset2IR = $true,
inference(copy,[status(thm)],[102]) ).
thf(567,plain,
binunionIL = $true,
inference(copy,[status(thm)],[101]) ).
thf(568,plain,
sepSubset = $true,
inference(copy,[status(thm)],[100]) ).
thf(569,plain,
sepInPowerset = $true,
inference(copy,[status(thm)],[99]) ).
thf(570,plain,
powersetsubset = $true,
inference(copy,[status(thm)],[98]) ).
thf(571,plain,
inPowerset = $true,
inference(copy,[status(thm)],[97]) ).
thf(572,plain,
powersetE1 = $true,
inference(copy,[status(thm)],[96]) ).
thf(573,plain,
powersetI1 = $true,
inference(copy,[status(thm)],[95]) ).
thf(574,plain,
subsetemptysetimpeq = $true,
inference(copy,[status(thm)],[94]) ).
thf(575,plain,
setextsub = $true,
inference(copy,[status(thm)],[93]) ).
thf(576,plain,
subset2powerset = $true,
inference(copy,[status(thm)],[92]) ).
thf(577,plain,
setadjoinSub2 = $true,
inference(copy,[status(thm)],[91]) ).
thf(578,plain,
setadjoinSub = $true,
inference(copy,[status(thm)],[90]) ).
thf(579,plain,
subsetTrans = $true,
inference(copy,[status(thm)],[89]) ).
thf(580,plain,
subsetRefl = $true,
inference(copy,[status(thm)],[88]) ).
thf(581,plain,
notequalI2 = $true,
inference(copy,[status(thm)],[87]) ).
thf(582,plain,
notequalI1 = $true,
inference(copy,[status(thm)],[86]) ).
thf(583,plain,
notsubsetI = $true,
inference(copy,[status(thm)],[85]) ).
thf(584,plain,
subsetE2 = $true,
inference(copy,[status(thm)],[84]) ).
thf(585,plain,
subsetE = $true,
inference(copy,[status(thm)],[83]) ).
thf(586,plain,
emptysetsubset = $true,
inference(copy,[status(thm)],[82]) ).
thf(587,plain,
subsetI2 = $true,
inference(copy,[status(thm)],[81]) ).
thf(588,plain,
eqimpsubset1 = $true,
inference(copy,[status(thm)],[80]) ).
thf(589,plain,
eqimpsubset2 = $true,
inference(copy,[status(thm)],[79]) ).
thf(590,plain,
subsetI1 = $true,
inference(copy,[status(thm)],[78]) ).
thf(591,plain,
dsetconstr__Cong = $true,
inference(copy,[status(thm)],[77]) ).
thf(592,plain,
descr__Cong = $true,
inference(copy,[status(thm)],[76]) ).
thf(593,plain,
exuEu = $true,
inference(copy,[status(thm)],[75]) ).
thf(594,plain,
omega__Cong = $true,
inference(copy,[status(thm)],[74]) ).
thf(595,plain,
setunion__Cong = $true,
inference(copy,[status(thm)],[73]) ).
thf(596,plain,
powerset__Cong = $true,
inference(copy,[status(thm)],[72]) ).
thf(597,plain,
setadjoin__Cong = $true,
inference(copy,[status(thm)],[71]) ).
thf(598,plain,
emptyset__Cong = $true,
inference(copy,[status(thm)],[70]) ).
thf(599,plain,
exu__Cong = $true,
inference(copy,[status(thm)],[69]) ).
thf(600,plain,
exuE3u = $true,
inference(copy,[status(thm)],[68]) ).
thf(601,plain,
in__Cong = $true,
inference(copy,[status(thm)],[67]) ).
thf(602,plain,
inCongP = $true,
inference(copy,[status(thm)],[66]) ).
thf(603,plain,
exuI2 = $true,
inference(copy,[status(thm)],[65]) ).
thf(604,plain,
exuI3 = $true,
inference(copy,[status(thm)],[64]) ).
thf(605,plain,
exuI1 = $true,
inference(copy,[status(thm)],[63]) ).
thf(606,plain,
notdallE = $true,
inference(copy,[status(thm)],[62]) ).
thf(607,plain,
notdexE = $true,
inference(copy,[status(thm)],[61]) ).
thf(608,plain,
prop2set2propI = $true,
inference(copy,[status(thm)],[60]) ).
thf(609,plain,
prop2setI = $true,
inference(copy,[status(thm)],[59]) ).
thf(610,plain,
quantDeMorgan4 = $true,
inference(copy,[status(thm)],[58]) ).
thf(611,plain,
quantDeMorgan3 = $true,
inference(copy,[status(thm)],[57]) ).
thf(612,plain,
quantDeMorgan2 = $true,
inference(copy,[status(thm)],[56]) ).
thf(613,plain,
quantDeMorgan1 = $true,
inference(copy,[status(thm)],[55]) ).
thf(614,plain,
vacuousDall = $true,
inference(copy,[status(thm)],[54]) ).
thf(615,plain,
emptyE1 = $true,
inference(copy,[status(thm)],[53]) ).
thf(616,plain,
upairsetIR = $true,
inference(copy,[status(thm)],[52]) ).
thf(617,plain,
upairsetIL = $true,
inference(copy,[status(thm)],[51]) ).
thf(618,plain,
upairsetE = $true,
inference(copy,[status(thm)],[50]) ).
thf(619,plain,
singletonsswitch = $true,
inference(copy,[status(thm)],[49]) ).
thf(620,plain,
eqinunit = $true,
inference(copy,[status(thm)],[48]) ).
thf(621,plain,
notinsingleton = $true,
inference(copy,[status(thm)],[47]) ).
thf(622,plain,
uniqinunit = $true,
inference(copy,[status(thm)],[46]) ).
thf(623,plain,
nonemptyImpWitness = $true,
inference(copy,[status(thm)],[45]) ).
thf(624,plain,
exuE2 = $true,
inference(copy,[status(thm)],[44]) ).
thf(625,plain,
subPowSU = $true,
inference(copy,[status(thm)],[43]) ).
thf(626,plain,
setunionE = $true,
inference(copy,[status(thm)],[42]) ).
thf(627,plain,
setunionI = $true,
inference(copy,[status(thm)],[41]) ).
thf(628,plain,
powersetE = $true,
inference(copy,[status(thm)],[40]) ).
thf(629,plain,
emptyInPowerset = $true,
inference(copy,[status(thm)],[39]) ).
thf(630,plain,
emptyinPowerset = $true,
inference(copy,[status(thm)],[38]) ).
thf(631,plain,
powersetI = $true,
inference(copy,[status(thm)],[37]) ).
thf(632,plain,
setoftrueEq = $true,
inference(copy,[status(thm)],[36]) ).
thf(633,plain,
setadjoinOr = $true,
inference(copy,[status(thm)],[35]) ).
thf(634,plain,
setadjoinE = $true,
inference(copy,[status(thm)],[34]) ).
thf(635,plain,
setadjoinIR = $true,
inference(copy,[status(thm)],[33]) ).
thf(636,plain,
emptyinunitempty = $true,
inference(copy,[status(thm)],[32]) ).
thf(637,plain,
setadjoinIL = $true,
inference(copy,[status(thm)],[31]) ).
thf(638,plain,
nonemptyI1 = $true,
inference(copy,[status(thm)],[30]) ).
thf(639,plain,
nonemptyI = $true,
inference(copy,[status(thm)],[29]) ).
thf(640,plain,
nonemptyE1 = $true,
inference(copy,[status(thm)],[28]) ).
thf(641,plain,
setbeta = $true,
inference(copy,[status(thm)],[27]) ).
thf(642,plain,
noeltsimpempty = $true,
inference(copy,[status(thm)],[26]) ).
thf(643,plain,
emptyI = $true,
inference(copy,[status(thm)],[25]) ).
thf(644,plain,
setext = $true,
inference(copy,[status(thm)],[24]) ).
thf(645,plain,
exuE3e = $true,
inference(copy,[status(thm)],[23]) ).
thf(646,plain,
notinemptyset = $true,
inference(copy,[status(thm)],[22]) ).
thf(647,plain,
emptysetimpfalse = $true,
inference(copy,[status(thm)],[21]) ).
thf(648,plain,
emptysetE = $true,
inference(copy,[status(thm)],[20]) ).
thf(649,plain,
prop2setE = $true,
inference(copy,[status(thm)],[19]) ).
thf(650,plain,
exuE1 = $true,
inference(copy,[status(thm)],[18]) ).
thf(651,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[17]) ).
thf(652,plain,
dsetconstrEL = $true,
inference(copy,[status(thm)],[16]) ).
thf(653,plain,
dsetconstrI = $true,
inference(copy,[status(thm)],[15]) ).
thf(654,plain,
descrp = $true,
inference(copy,[status(thm)],[14]) ).
thf(655,plain,
wellorderingAx = $true,
inference(copy,[status(thm)],[13]) ).
thf(656,plain,
foundationAx = $true,
inference(copy,[status(thm)],[12]) ).
thf(657,plain,
replAx = $true,
inference(copy,[status(thm)],[11]) ).
thf(658,plain,
omegaIndAx = $true,
inference(copy,[status(thm)],[10]) ).
thf(659,plain,
omegaSAx = $true,
inference(copy,[status(thm)],[9]) ).
thf(660,plain,
omega0Ax = $true,
inference(copy,[status(thm)],[8]) ).
thf(661,plain,
setunionAx = $true,
inference(copy,[status(thm)],[7]) ).
thf(662,plain,
powersetAx = $true,
inference(copy,[status(thm)],[6]) ).
thf(663,plain,
setadjoinAx = $true,
inference(copy,[status(thm)],[5]) ).
thf(664,plain,
emptysetAx = $true,
inference(copy,[status(thm)],[4]) ).
thf(665,plain,
setextAx = $true,
inference(copy,[status(thm)],[3]) ).
thf(666,plain,
( ( ( transitiveset @ sK1_X )
& ( in @ sK2_SY0 @ sK1_X )
& ( in @ sK3_SY2 @ sK2_SY0 )
& ~ ( in @ sK3_SY2 @ sK1_X ) )
= $true ),
inference(copy,[status(thm)],[335]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[620,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(668,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[621,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(669,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( subset @ SX2 @ SX1 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(670,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)],[469,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(671,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(672,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)],[486,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(673,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)],[652,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(674,plain,
( ( omega = omega )
= $true ),
inference(unfold_def,[status(thm)],[594,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(675,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX3 )
| ( SX3 = SX2 ) )
| ( ex1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(676,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)],[455,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(677,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)],[524,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(678,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)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(679,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(680,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)],[531,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(681,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)],[471,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[595,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[472,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(684,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)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(685,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)],[549,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [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)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(687,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)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(688,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)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(689,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[659,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(690,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(691,plain,
( ( emptyset = emptyset )
= $true ),
inference(unfold_def,[status(thm)],[598,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(692,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)],[601,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(693,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[648,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(694,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)],[611,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(695,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)],[612,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(696,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)],[473,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(697,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)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(698,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[630,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(699,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)],[663,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(700,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[646,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[572,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(702,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)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) )
= ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(704,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( omegaS @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(706,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)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(707,plain,
( ( ! [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : $true )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[632,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
| ~ ! [SX5: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX5 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX5 ) @ SX1 ) )
| ~ ( in @ ( kpair @ SX5 @ SX4 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln1 @ SX0 @ SX3 )
| ( ( breln1compset @ SX0 @ ( binunion @ SX1 @ SX2 ) @ SX3 )
= ( binunion @ ( breln1compset @ SX0 @ SX1 @ SX3 ) @ ( breln1compset @ SX0 @ SX2 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(711,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) )
| ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(712,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(713,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( breln1 @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(714,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[501,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(715,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)],[661,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[633,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(717,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( ( binunion @ SX1 @ SX2 )
= ( binunion @ SX2 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[361,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(718,plain,
( ( ! [SX0: $i] : ( in @ SX0 @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(719,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( ( omegaS @ SX0 )
!= ( omegaS @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(720,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 @ SX2 ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(721,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)],[424,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(722,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)],[423,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(723,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)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(724,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( SX1
= ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(725,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)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(726,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)],[607,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[546,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
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)],[606,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(730,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)],[454,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[542,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(732,plain,
( ( ! [SX0: $i] : ( subset @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[515,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(733,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(734,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)],[402,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(735,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)],[602,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(736,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[506,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[541,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(738,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)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(739,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(740,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(741,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)],[656,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( kfst @ ( kpair @ SX0 @ SX1 ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(743,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)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(744,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)],[431,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(745,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)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(746,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)],[489,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(747,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)],[520,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(748,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)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(750,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)],[428,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(751,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)],[478,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
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)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[544,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[508,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(755,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[537,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(756,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)],[532,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(757,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)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(758,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(759,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)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(760,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(761,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(762,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)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(763,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[631,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(764,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[533,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(765,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[636,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(766,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)],[538,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(767,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(unfold_def,[status(thm)],[660,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(768,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[547,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(769,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
| ! [SX5: $o] :
( ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX6 ) @ SX1 )
| ~ ( in @ ( kpair @ SX6 @ SX4 ) @ SX2 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( breln1Set @ SX0 ) )
| ( breln1 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(771,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(772,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(773,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ( breln1 @ SX0 @ ( breln1invset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(776,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)],[483,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(777,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)],[599,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(778,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX2 )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ SX1 @ ( binintersect @ SX2 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(779,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)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(780,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(781,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)],[518,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[552,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(783,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( ( binintersect @ SX1 @ SX0 )
!= emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[344,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(784,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(785,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)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(786,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)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(787,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)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(788,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 ) )
| ( ex1 @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[509,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(789,plain,
( ( ! [SX0: $i,SX1: $i > $i] :
~ ! [SX2: $i] :
~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(790,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)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(791,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)],[665,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(793,plain,
( ( ~ ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ( subset @ SX0 @ sK1_X ) )
| ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[666,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(794,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(795,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)],[470,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(796,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)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(797,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)],[626,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(799,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( breln1 @ SX0 @ ( breln1compset @ SX0 @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[371,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(800,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[577,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[637,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(803,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)],[498,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(804,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( setminus @ SX0 @ ( binintersect @ SX1 @ SX2 ) ) )
| ( in @ SX3 @ ( binunion @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(805,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 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 )
| ~ ( subset @ SX2 @ SX4 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ ( binintersect @ SX3 @ SX4 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(806,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( setminus @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[540,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(807,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)],[593,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(808,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[539,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(809,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)],[600,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(810,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)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(811,plain,
( ( ! [SX0: $i,SX1: $i > $i] :
~ ! [SX2: $i] :
~ ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) ) )
| ~ ( ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX0 )
| ( SX3
!= ( SX1 @ SX4 ) ) )
| ( in @ SX3 @ SX2 ) ) )
| ~ ! [SX3: $i] :
( ~ ! [SX4: $i] :
~ ( ~ ( ~ ( in @ SX4 @ SX3 )
| ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX0 )
| ( SX4
!= ( SX1 @ SX5 ) ) ) )
| ~ ( ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX0 )
| ( SX4
!= ( SX1 @ SX5 ) ) )
| ( in @ SX4 @ SX3 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[355,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(812,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)],[480,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(813,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)],[490,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(814,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX2 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(815,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ex1 @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[511,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(816,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(817,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( SX2 @ ( kpair @ SX3 @ SX4 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(818,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)],[499,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(819,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
( ~ ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(820,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)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(821,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) )
| ( injective @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[349,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(822,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( in
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[569,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(823,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[555,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(824,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)],[615,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(825,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln1 @ SX0 @ SX3 )
| ( ( breln1compset @ SX0 @ ( binunion @ SX1 @ SX2 ) @ SX3 )
= ( binunion @ ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX3 ) @ ( breln1invset @ SX0 @ SX2 ) ) ) @ ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX3 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(826,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)],[650,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(827,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( SX2 @ ( kpair @ SX3 @ SX4 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(828,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)],[519,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(829,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)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[628,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(831,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(832,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[579,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(833,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(834,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)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(835,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(836,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)],[639,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(837,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)],[604,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(838,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)],[624,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(839,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX3 )
| ~ ! [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)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(840,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[557,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(841,plain,
( ( ! [SX0: $i,SX1: $i > $i,SX2: $i] :
~ ( ~ ( ~ ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) ) )
| ~ ( ~ ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ( SX2
!= ( SX1 @ SX3 ) ) )
| ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(842,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)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(843,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)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(844,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[664,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(845,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)],[603,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(846,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)],[597,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(847,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)],[641,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(848,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(849,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(850,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)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(851,plain,
( ( ! [SX0: $i] : ( subset @ emptyset @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[586,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(852,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)],[442,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(853,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(854,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [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)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(855,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(856,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(857,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)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(858,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(859,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)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(860,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ex1 @ 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)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(861,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)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(862,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)],[657,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(863,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(864,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(865,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( surjFuncSet @ SX0 @ SX1 ) )
| ( surjective @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(866,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[566,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[526,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(868,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ( SX1
= ( breln1invset @ SX0 @ ( breln1invset @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(869,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ SX3 @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) )
| ( in @ SX3 @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(870,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ( injective @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( injFuncSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(871,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(872,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(873,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX1 @ SX0 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX1 @ SX0 @ SX3 @ ( SX2 @ SX4 ) )
= SX4 ) )
| ( surjective @ SX1 @ SX0 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(874,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[574,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(875,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(876,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)],[422,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(877,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ksnd @ ( kpair @ SX0 @ SX1 ) )
= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[493,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(878,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)],[653,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(879,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)],[479,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(880,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
| ( subset @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(881,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[625,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(882,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)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(883,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)],[655,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(884,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)],[456,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(885,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)],[440,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(886,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ~ ( SX2 @ SX3 @ SX4 ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( breln1Set @ SX1 ) )
| ~ ( reflwellordering @ SX1 @ SX3 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( singleton
@ ( dsetconstr @ SX1
@ ^ [SX5: $i] :
~ ( ~ ( SX2 @ SX4 @ SX5 )
| ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SX1 )
| ~ ( SX2 @ SX4 @ SX6 )
| ( in @ ( kpair @ SX5 @ SX6 ) @ SX3 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(887,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[576,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(888,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(889,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(890,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(891,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(892,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[545,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(893,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[497,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(894,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(895,plain,
( ( ! [SX0: $i] :
( ( setunion @ ( setadjoin @ SX0 @ emptyset ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[513,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(896,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)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(897,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)],[658,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(898,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)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(899,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(900,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) @ ( powerset @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(901,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)],[644,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(902,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[419,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(903,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)],[613,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(904,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(905,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX5 ) @ SX1 )
| ~ ( in @ ( kpair @ SX5 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( breln1compset @ SX0 @ SX1 @ SX2 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(906,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[553,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(907,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(908,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)],[502,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(909,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)],[481,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(910,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)],[523,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(911,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) ) @ ( powerset @ ( setminus @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(912,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)],[444,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(913,plain,
( ( ! [SX0: $i,SX1: $i > $i > $o] :
( breln1 @ SX0
@ ( dpsetconstr @ SX0 @ SX0
@ ^ [SX2: $i,SX3: $i] : ( SX1 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(914,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)],[453,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(915,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( subset
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[568,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(916,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)],[512,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(917,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)],[496,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(918,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(919,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)],[662,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(920,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[647,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(921,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)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(922,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(923,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) )
| ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(924,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[649,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(925,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(926,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) )
| ! [SX5: $o] :
( ~ ( ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| SX5 )
| ~ ( ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(928,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)],[522,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(929,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)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(930,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( surjFuncSet @ SX0 @ SX1 ) )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(931,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)],[592,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( funcSet @ SX0 @ ( powerset @ SX0 ) ) )
| ~ ( surjective @ SX0 @ ( powerset @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(933,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( ( omegaS @ SX0 )
!= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( powerset @ SX0 ) )
| ~ ( subset @ SX1 @ SX3 )
| ( subset @ ( binintersect @ SX1 @ SX2 ) @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(935,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
| ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 ) ) )
| ( SX1 = SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(936,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(937,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(938,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( kpair @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(939,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)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(940,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)],[610,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(941,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[543,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(942,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 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(943,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(944,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[556,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(945,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(946,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(947,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[534,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(948,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(949,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)],[487,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(950,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[551,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(951,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(952,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[623,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(953,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[492,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(954,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)],[591,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(955,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)],[605,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(956,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)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(957,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[651,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(958,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)],[564,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[365,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(960,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( breln @ SX0 @ SX1
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(962,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)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(963,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(964,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[580,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(965,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( ( breln1invset @ SX0 @ ( breln1compset @ SX0 @ SX1 @ SX2 ) )
= ( breln1compset @ SX0 @ ( breln1invset @ SX0 @ SX2 ) @ ( breln1invset @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(966,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(967,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)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(968,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ~ ( ( in @ ( kpair @ SX3 @ SX4 ) @ SX1 )
| ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) )
| ( in @ ( kpair @ SX3 @ SX4 ) @ ( binunion @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(969,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( breln @ SX0 @ SX1 @ SX3 )
| ~ ! [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)],[460,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(970,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 @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(971,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(972,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)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(973,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)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(974,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[550,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(975,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[640,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(976,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( binintersect @ SX1 @ SX2 ) )
| ( in @ SX3 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(977,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[627,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(978,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)],[430,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(979,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binunion @ SX1 @ SX2 ) )
= ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(980,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)],[634,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(981,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)],[433,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(982,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(983,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(984,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)],[521,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(985,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)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(986,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)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(987,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[622,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(988,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 @ ( powerset @ SX0 ) )
| ( ( setminus @ SX0 @ ( binintersect @ ( binunion @ SX1 @ SX2 ) @ ( binunion @ SX3 @ SX4 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SX0 @ SX1 ) @ ( setminus @ SX0 @ SX2 ) ) @ ( binintersect @ ( setminus @ SX0 @ SX3 ) @ ( setminus @ SX0 @ SX4 ) ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(989,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)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(990,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)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(991,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(992,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(993,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)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(994,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)],[654,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(995,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)],[488,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(996,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(997,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)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintTransitive,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionCommutes,breln1unionE,breln1unionEcases,breln1unionI,breln1unionIL,breln1unionIR,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundation2,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,image1E,image1Equiv,image1Ex,image1Ex1,image1I,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,injFuncInInjFuncSet,injFuncSetFuncIn,injFuncSetFuncInj,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,leftInvIsSurj,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinself,notinself2,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omegaSclos,omegaSp,omega__Cong,peano0notS,peanoSinj,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,surjCantorThm,surjFuncSetFuncIn,surjFuncSetFuncSurj,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,transitiveset,transitivesetOp1,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5,woz2A,woz2B,woz2Ex,woz2W]) ).
thf(998,plain,
! [SV1: $i] :
( ( ! [SY3: $i] :
( ( SV1 != SY3 )
| ( in @ SV1 @ ( setadjoin @ SY3 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(999,plain,
! [SV2: $i] :
( ( ! [SY4: $i] :
( ~ ( ( SV2 != SY4 ) )
| ~ ( in @ SY4 @ ( setadjoin @ SV2 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(1000,plain,
! [SV3: $i] :
( ( ~ ! [SY5: $i] :
( ~ ( in @ SY5 @ SV3 )
| ( subset @ SY5 @ SV3 ) )
| ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(1001,plain,
! [SV4: $i] :
( ( ! [SY9: $i,SY10: $i > $i] :
( ~ ! [SY11: $i] :
( ~ ( in @ SY11 @ SV4 )
| ( in @ ( SY10 @ SY11 ) @ SY9 ) )
| ( in
@ ( lam @ SV4 @ SY9
@ ^ [SX3: $i] : ( SY10 @ SX3 ) )
@ ( funcSet @ SV4 @ SY9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(1002,plain,
! [SV5: $i] :
( ( ~ ! [SY13: $i] :
~ ( in @ SY13 @ SV5 )
| ( SV5 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(1003,plain,
! [SV6: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( in @ SY15 @ SV6 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY14 )
| ( ( ksnd @ ( kpair @ SY15 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(1004,plain,
! [SV7: $i] :
( ( ! [SY17: $i > $o,SY18: $i] :
( ~ ( in @ SY18
@ ( dsetconstr @ SV7
@ ^ [SX3: $i] : ( SY17 @ SX3 ) ) )
| ( in @ SY18 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(1005,plain,
! [SV8: $i] :
( ( ! [SY20: $i > $o,SY21: $i] :
( ~ ( in @ SY21 @ SV8 )
| ~ ( SY20 @ SY21 )
| ~ ! [SY22: $i] :
( ~ ( in @ SY22 @ SV8 )
| ~ ( SY20 @ SY22 )
| ( SY22 = SY21 ) )
| ( ex1 @ SV8
@ ^ [SX3: $i] : ( SY20 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(1006,plain,
! [SV9: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( func @ SV9 @ SY24 @ SY25 )
| ! [SY26: $i] :
( ~ ( in @ SY26 @ SV9 )
| ( ( ap @ SV9 @ SY24 @ SY25 @ SY26 )
= ( ap @ SV9 @ SY24 @ SY25 @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(1007,plain,
! [SV10: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( in @ SY28 @ SV10 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SY27 )
| ( subset @ ( setadjoin @ SY28 @ ( setadjoin @ SY29 @ emptyset ) ) @ ( binunion @ SV10 @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(1008,plain,
! [SV11: $i] :
( ( ! [SY30: $i,SY31: $i] :
( ~ ( func @ SV11 @ SY30 @ SY31 )
| ! [SY32: $i] :
( ~ ( func @ SV11 @ SY30 @ SY32 )
| ~ ! [SY33: $i] :
( ~ ( in @ SY33 @ SV11 )
| ( ( ap @ SV11 @ SY30 @ SY31 @ SY33 )
= ( ap @ SV11 @ SY30 @ SY32 @ SY33 ) ) )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV11 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY30 )
| ~ ( in @ ( kpair @ SY34 @ SX5 ) @ SY32 )
| ( in @ ( kpair @ SY34 @ SX5 ) @ SY31 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(1009,plain,
! [SV12: $i] :
( ( ~ ( iskpair @ SV12 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV12 )
@ ^ [SY36: $i] :
( SV12
= ( kpair @ ( kfst @ SV12 ) @ SY36 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(1010,plain,
! [SV13: $i] :
( ( ! [SY37: $i] : ( in @ SY37 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SY37 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(1011,plain,
! [SV14: $i] :
( ( ! [SY38: $i,SY39: $i > $i] :
( ~ ! [SY40: $i] :
( ~ ( in @ SY40 @ SV14 )
| ( in @ ( SY39 @ SY40 ) @ SY38 ) )
| ( func @ SV14 @ SY38
@ ( dpsetconstr @ SV14 @ SY38
@ ^ [SX3: $i,SX4: $i] :
( ( SY39 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(1012,plain,
! [SV15: $i] :
( ( ! [SY43: $i] :
( ( SV15 != SY43 )
| ( ( setunion @ SV15 )
= ( setunion @ SY43 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(1013,plain,
! [SV16: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( func @ SV16 @ SY44 @ SY45 )
| ( in @ SY45 @ ( funcSet @ SV16 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(1014,plain,
! [SV17: $i] :
( ( ! [SY46: $i] :
( ~ ( in @ SY46 @ ( powerset @ SV17 ) )
| ! [SY47: $i] :
( ~ ( in @ SY47 @ ( powerset @ SV17 ) )
| ! [SY48: $i] :
( ~ ( in @ SY48 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SY46 @ SY47 ) @ ( powerset @ ( binintersect @ ( binunion @ SY46 @ SY48 ) @ ( binunion @ SY47 @ SY48 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(1015,plain,
! [SV18: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( binintersect @ SV18 @ ( binunion @ SY49 @ SY50 ) )
= ( binunion @ ( binintersect @ SV18 @ SY49 ) @ ( binintersect @ SV18 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(1016,plain,
! [SV19: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ~ ( breln @ SV19 @ SY51 @ SY52 )
| ! [SY53: $i > $o] :
( ~ ! [SY54: $i] :
( ~ ( in @ SY54 @ SV19 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY51 )
| ~ ( in @ ( kpair @ SY54 @ SX5 ) @ SY52 )
| ( SY53 @ ( kpair @ SY54 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY52 )
| ( SY53 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(1017,plain,
! [SV20: $i] :
( ( ! [SY57: $i] :
( ~ ( in @ SY57 @ ( powerset @ SV20 ) )
| ! [SY58: $i] :
( ~ ( in @ SY58 @ ( powerset @ SV20 ) )
| ! [SY59: $i] :
( ~ ( in @ SY59 @ SV20 )
| ~ ~ ( in @ SY59 @ ( binunion @ SY57 @ SY58 ) )
| ~ ( in @ SY59 @ SY58 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(1018,plain,
! [SV21: $i] :
( ( ! [SY60: $i] :
( ~ ( in @ SY60 @ ( powerset @ SV21 ) )
| ! [SY61: $i] :
( ~ ( in @ SY61 @ ( powerset @ SV21 ) )
| ~ ( subset @ SY60 @ ( setminus @ SV21 @ SY61 ) )
| ( subset @ SY61 @ ( setminus @ SV21 @ SY60 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(1019,plain,
! [SV22: $i] :
( ( ~ ( in @ SV22 @ omega )
| ( in @ ( setadjoin @ SV22 @ SV22 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(1020,plain,
! [SV23: $i] :
( ( ! [SY62: $i] :
( ~ ( in @ SY62 @ SV23 )
| ( in @ ( setadjoin @ SY62 @ emptyset ) @ ( powerset @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(1021,plain,
! [SV24: $i] :
( ( ! [SY63: $i] :
( ( SV24 != SY63 )
| ! [SY64: $i,SY65: $i] :
( ( SY64 != SY65 )
| ~ ( ~ ( ~ ( in @ SY64 @ SV24 )
| ( in @ SY65 @ SY63 ) )
| ~ ( ~ ( in @ SY65 @ SY63 )
| ( in @ SY64 @ SV24 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(1022,plain,
! [SV25: $i] :
( ( ~ ( in @ SV25 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(1023,plain,
! [SV26: $i] :
( ( ! [SY67: $i > $o] :
( ~ ~ ~ ! [SY68: $i] :
~ ~ ( ~ ( in @ SY68 @ SV26 )
| ~ ( SY67 @ SY68 ) )
| ! [SY69: $i] :
( ~ ( in @ SY69 @ SV26 )
| ~ ( SY67 @ SY69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(1024,plain,
! [SV27: $i] :
( ( ! [SY70: $i > $o] :
( ~ ! [SY71: $i] :
( ~ ( in @ SY71 @ SV27 )
| ~ ( SY70 @ SY71 ) )
| ~ ~ ! [SY72: $i] :
~ ~ ( ~ ( in @ SY72 @ SV27 )
| ~ ( SY70 @ SY72 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(1025,plain,
! [SV28: $i] :
( ( ! [SY73: $i,SY74: $i] :
( ~ ( in @ SY74 @ ( funcSet @ SV28 @ SY73 ) )
| ! [SY75: $i] :
( ~ ( in @ SY75 @ SV28 )
| ( in @ ( ap @ SV28 @ SY73 @ SY74 @ SY75 ) @ SY73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(1026,plain,
! [SV29: $i] :
( ( ! [SY76: $i,SY77: $i] :
( ~ ( in @ SY77 @ ( funcSet @ SV29 @ SY76 ) )
| ( ( lam @ SV29 @ SY76
@ ^ [SY78: $i] : ( ap @ SV29 @ SY76 @ SY77 @ SY78 ) )
= SY77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(1027,plain,
! [SV30: $i] :
( ( in @ emptyset @ ( powerset @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1028,plain,
! [SV31: $i] :
( ( ! [SY79: $i,SY80: $i] :
~ ( ~ ( ~ ( in @ SY80 @ ( setadjoin @ SV31 @ SY79 ) )
| ( SY80 = SV31 )
| ( in @ SY80 @ SY79 ) )
| ~ ( ~ ( ( SY80 = SV31 )
| ( in @ SY80 @ SY79 ) )
| ( in @ SY80 @ ( setadjoin @ SV31 @ SY79 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1029,plain,
! [SV32: $i] :
( ( ~ ( in @ SV32 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1030,plain,
! [SV33: $i] :
( ( ! [SY81: $i] :
( ~ ( in @ SY81 @ ( powerset @ SV33 ) )
| ( subset @ SY81 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1031,plain,
! [SV34: $i] :
( ( ! [SY82: $i] :
( ~ ( in @ SY82 @ ( powerset @ SV34 ) )
| ! [SY83: $i] :
( ~ ( in @ SY83 @ ( powerset @ SV34 ) )
| ! [SY84: $i] :
( ~ ( in @ SY84 @ SV34 )
| ~ ~ ( in @ SY84 @ ( binunion @ SY82 @ SY83 ) )
| ~ ( in @ SY84 @ SY82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1032,plain,
! [SV35: $i] :
( ( ! [SY85: $i] :
( ~ ( in @ SY85 @ ( powerset @ SV35 ) )
| ! [SY86: $i] :
( ~ ( in @ SY86 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SY85 @ SY86 ) )
= ( binunion @ ( setminus @ SV35 @ SY85 ) @ ( setminus @ SV35 @ SY86 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1033,plain,
! [SV36: $i] :
( ( ~ ( in @ SV36 @ omega )
| ( in @ ( omegaS @ SV36 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1034,plain,
! [SV37: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( in @ SY88 @ ( setadjoin @ SV37 @ ( setadjoin @ SY87 @ emptyset ) ) )
| ( SY88 = SV37 )
| ( SY88 = SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1035,plain,
! [SV38: $i] :
( ( ! [SY89: $i] :
( ~ ( in @ SY89 @ ( powerset @ SV38 ) )
| ! [SY90: $i] :
( ~ ( in @ SY90 @ ( powerset @ SV38 ) )
| ( in @ ( setminus @ SY89 @ SY90 ) @ ( powerset @ SV38 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1036,plain,
! [SV39: $i] :
( ( ( dsetconstr @ SV39
@ ^ [SX1: $i] : $true )
= SV39 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1037,plain,
! [SV40: $i] :
( ( ! [SY92: $i] :
( ~ ( breln1 @ SV40 @ SY92 )
| ! [SY93: $i] :
( ~ ( breln1 @ SV40 @ SY93 )
| ! [SY94: $i] :
( ~ ( in @ SY94 @ SV40 )
| ! [SY95: $i] :
( ~ ( in @ SY95 @ SV40 )
| ~ ( in @ ( kpair @ SY94 @ SY95 ) @ ( breln1compset @ SV40 @ SY92 @ SY93 ) )
| ~ ! [SY96: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY96 @ SV40 )
| ~ ( in @ ( kpair @ SY94 @ SY96 ) @ SY92 ) )
| ~ ( in @ ( kpair @ SY96 @ SY95 ) @ SY93 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1038,plain,
! [SV41: $i] :
( ( ! [SY97: $i] :
( ~ ( breln1 @ SV41 @ SY97 )
| ! [SY98: $i] :
( ~ ( breln1 @ SV41 @ SY98 )
| ! [SY99: $i] :
( ~ ( breln1 @ SV41 @ SY99 )
| ( ( breln1compset @ SV41 @ ( binunion @ SY97 @ SY98 ) @ SY99 )
= ( binunion @ ( breln1compset @ SV41 @ SY97 @ SY99 ) @ ( breln1compset @ SV41 @ SY98 @ SY99 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(1039,plain,
! [SV42: $i] :
( ( ! [SY100: $i] :
( ~ ( in @ SY100 @ ( powerset @ SV42 ) )
| ! [SY101: $i] :
( ~ ( in @ SY101 @ ( powerset @ SV42 ) )
| ! [SY102: $i] :
( ~ ( in @ SY102 @ SV42 )
| ~ ( in @ SY102 @ ( binunion @ ( setminus @ SV42 @ SY100 ) @ ( setminus @ SV42 @ SY101 ) ) )
| ( in @ SY102 @ ( setminus @ SV42 @ ( binintersect @ SY100 @ SY101 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1040,plain,
! [SV43: $i] :
( ( ! [SY103: $i > $i,SY104: $i] :
( ~ ~ ! [SY105: $i] :
~ ~ ( ~ ( in @ SY105 @ SV43 )
| ( SY104
!= ( SY103 @ SY105 ) ) )
| ( in @ SY104
@ ( image1 @ SV43
@ ^ [SX3: $i] : ( SY103 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1041,plain,
! [SV44: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( in @ SY108 @ ( injFuncSet @ SV44 @ SY107 ) )
| ( in @ SY108 @ ( funcSet @ SV44 @ SY107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1042,plain,
! [SV45: $i] :
( ( ! [SY109: $i] :
( ~ ( breln1 @ SV45 @ SY109 )
| ! [SY110: $i] :
( ~ ( breln1 @ SV45 @ SY110 )
| ( breln1 @ SV45 @ ( binunion @ SY109 @ SY110 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1043,plain,
! [SV46: $i] :
( ( ! [SY111: $i,SY112: $i,SY113: $i] :
( ( ( kpair @ SV46 @ SY111 )
!= ( kpair @ SY112 @ SY113 ) )
| ( SV46 = SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1044,plain,
! [SV47: $i] :
( ( ! [SY114: $i] :
~ ( ~ ( ~ ( in @ SY114 @ ( setunion @ SV47 ) )
| ~ ! [SY115: $i] :
~ ~ ( ~ ( in @ SY114 @ SY115 )
| ~ ( in @ SY115 @ SV47 ) ) )
| ~ ( ~ ~ ! [SY116: $i] :
~ ~ ( ~ ( in @ SY114 @ SY116 )
| ~ ( in @ SY116 @ SV47 ) )
| ( in @ SY114 @ ( setunion @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(1045,plain,
! [SV48: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( in @ SY118 @ ( setadjoin @ SV48 @ SY117 ) )
| ( SY118 = SV48 )
| ( in @ SY118 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1046,plain,
! [SV49: $i] :
( ( ! [SY119: $i] :
( ~ ( breln1 @ SV49 @ SY119 )
| ! [SY120: $i] :
( ~ ( breln1 @ SV49 @ SY120 )
| ( ( binunion @ SY119 @ SY120 )
= ( binunion @ SY120 @ SY119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1047,plain,
! [SV50: $i] :
( ( in @ SV50 @ ( powerset @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1048,plain,
! [SV51: $i] :
( ( ~ ( in @ SV51 @ omega )
| ! [SY121: $i] :
( ~ ( in @ SY121 @ omega )
| ( ( omegaS @ SV51 )
!= ( omegaS @ SY121 ) )
| ( SV51 = SY121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(1049,plain,
! [SV52: $i] :
( ( ! [SY122: $i] :
( ~ ( in @ SY122 @ ( powerset @ SV52 ) )
| ! [SY123: $i] :
( ~ ( in @ SY123 @ ( powerset @ SV52 ) )
| ! [SY124: $i] :
( ~ ( in @ SY124 @ SV52 )
| ~ ( in @ SY124 @ ( setminus @ SV52 @ SY122 ) )
| ~ ( in @ SY124 @ ( setminus @ SV52 @ SY123 ) )
| ( in @ SY124 @ ( setminus @ SV52 @ ( binunion @ SY122 @ SY123 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(1050,plain,
! [SV53: $i] :
( ( ! [SY125: $i] :
( ~ ( in @ SY125 @ ( powerset @ SV53 ) )
| ! [SY126: $i] :
( ~ ( in @ SY126 @ ( powerset @ SV53 ) )
| ~ ( subset @ SY125 @ SY126 )
| ( subset @ ( setminus @ SV53 @ SY126 ) @ ( setminus @ SV53 @ SY125 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1051,plain,
! [SV54: $i] :
( ( ! [SY127: $i] :
( ~ ( in @ SY127 @ ( powerset @ SV54 ) )
| ! [SY128: $i] :
( ~ ( in @ SY128 @ ( powerset @ SV54 ) )
| ~ ( subset @ ( setminus @ SV54 @ SY128 ) @ ( setminus @ SV54 @ SY127 ) )
| ( subset @ SY127 @ SY128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1052,plain,
! [SV55: $i] :
( ( ! [SY129: $i] :
( ~ ( in @ SY129 @ ( powerset @ SV55 ) )
| ! [SY130: $i] :
( ~ ( in @ SY130 @ ( powerset @ SV55 ) )
| ~ ( subset @ SY129 @ ( setminus @ SV55 @ SY130 ) )
| ! [SY131: $i] :
( ~ ( in @ SY131 @ SV55 )
| ~ ( in @ SY131 @ SY130 )
| ( in @ SY131 @ ( setminus @ SV55 @ SY129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1053,plain,
! [SV56: $i] :
( ( ! [SY132: $i] :
( ~ ( in @ SY132 @ ( powerset @ SV56 ) )
| ( SY132
= ( setminus @ SV56 @ ( setminus @ SV56 @ SY132 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1054,plain,
! [SV57: $i] :
( ( ! [SY133: $i] :
( ~ ( in @ SY133 @ ( powerset @ SV57 ) )
| ! [SY134: $i] :
( ~ ( in @ SY134 @ ( powerset @ SV57 ) )
| ! [SY135: $i] :
( ~ ( in @ SY135 @ SV57 )
| ~ ( in @ SY135 @ ( setminus @ SV57 @ ( binunion @ SY133 @ SY134 ) ) )
| ~ ( in @ SY135 @ SY133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1055,plain,
! [SV58: $i] :
( ( ! [SY136: $i > $o] :
( ~ ~ ~ ! [SY137: $i] :
~ ~ ( ~ ( in @ SY137 @ SV58 )
| ~ ( SY136 @ SY137 ) )
| ! [SY138: $i] :
( ~ ( in @ SY138 @ SV58 )
| ~ ( SY136 @ SY138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1056,plain,
! [SV59: $i] :
( ( ! [SY139: $i,SY140: $i] :
( ~ ( in @ SY140 @ ( setminus @ SV59 @ SY139 ) )
| ~ ( in @ SY140 @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1057,plain,
! [SV60: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( in @ SY142 @ ( setadjoin @ SV60 @ ( setadjoin @ SY141 @ emptyset ) ) )
| ( SY142 = SV60 )
| ( SY142 = SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1058,plain,
! [SV61: $i] :
( ( ! [SY143: $i > $o] :
( ~ ~ ! [SY144: $i] :
( ~ ( in @ SY144 @ SV61 )
| ( SY143 @ SY144 ) )
| ~ ! [SY145: $i] :
~ ~ ( ~ ( in @ SY145 @ SV61 )
| ~ ~ ( SY143 @ SY145 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1059,plain,
! [SV62: $i] :
( ( ! [SY146: $i,SY147: $i > $i] :
( ~ ! [SY148: $i] :
( ~ ( in @ SY148 @ SV62 )
| ( in @ ( SY147 @ SY148 ) @ SY146 ) )
| ! [SY149: $i] :
( ~ ( in @ SY149 @ SV62 )
| ( ( ap @ SV62 @ SY146
@ ( lam @ SV62 @ SY146
@ ^ [SX4: $i] : ( SY147 @ SX4 ) )
@ SY149 )
= ( SY147 @ SY149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1060,plain,
! [SV63: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ~ ( in @ SY152 @ SV63 )
| ~ ( in @ SY152 @ ( setminus @ SV63 @ SY151 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1061,plain,
! [SV64: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV64 @ emptyset ) ) @ SV64 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1062,plain,
! [SV65: $i] :
( ( ! [SY153: $i] :
( ~ ( in @ SY153 @ ( powerset @ SV65 ) )
| ( in @ ( setminus @ SV65 @ SY153 ) @ ( powerset @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1063,plain,
! [SV66: $i] :
( ( ! [SY154: $i] :
( ~ ( in @ SY154 @ ( powerset @ SV66 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ ( powerset @ SV66 ) )
| ! [SY156: $i] :
( ~ ( in @ SY156 @ SV66 )
| ~ ~ ( in @ SY156 @ SY154 )
| ~ ~ ( in @ SY156 @ SY155 )
| ~ ( in @ SY156 @ ( binunion @ SY154 @ SY155 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1064,plain,
! [SV67: $i] :
( ( ! [SY157: $i] :
( ( SV67 != SY157 )
| ! [SY158: $i,SY159: $i] :
( ( SY158 != SY159 )
| ~ ( in @ SY158 @ SV67 )
| ( in @ SY159 @ SY157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1065,plain,
! [SV68: $i] :
( ( ~ ( iskpair @ SV68 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV68 )
@ ^ [SY160: $i] : ( in @ ( setadjoin @ SY160 @ emptyset ) @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1066,plain,
! [SV69: $i] :
( ( ! [SY161: $i,SY162: $i] :
( ~ ( in @ SY162 @ SY161 )
| ~ ( in @ SY162 @ ( setminus @ SV69 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(1067,plain,
! [SV70: $i] :
( ( ! [SY163: $o,SY164: $i] :
( ~ ( in @ SY164 @ SV70 )
| ! [SY165: $i] :
( ~ ( in @ SY165 @ SV70 )
| ~ ~ SY163
| ( ( dsetconstr @ SV70
@ ^ [SX4: $i] :
( ~ ( ~ SY163
| ( SX4 != SY164 ) )
| ~ ( ~ ~ SY163
| ( SX4 != SY165 ) ) ) )
= ( setadjoin @ SY165 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1068,plain,
! [SV71: $o] :
( ( ~ SV71
| ( set2prop @ ( prop2set @ SV71 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[739]) ).
thf(1069,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[739]) ).
thf(1070,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[739]) ).
thf(1071,plain,
! [SV72: $i] :
( ( ~ ( in @ SV72 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1072,plain,
! [SV73: $i] :
( ( ~ ~ ! [SY167: $i] :
~ ( in @ SY167 @ SV73 )
| ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1073,plain,
! [SV74: $i] :
( ( ! [SY170: $i] :
( ( kfst @ ( kpair @ SV74 @ SY170 ) )
= SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1074,plain,
! [SV75: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ( func @ SV75 @ SY171 @ SY172 )
| ! [SY173: $i] :
( ~ ( in @ SY173 @ SV75 )
| ( in @ ( ap @ SV75 @ SY171 @ SY172 @ SY173 ) @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1075,plain,
! [SV76: $i] :
( ( ! [SY174: $i] :
( ~ ( in @ SY174 @ ( powerset @ SV76 ) )
| ! [SY175: $i] :
( ~ ( in @ SY175 @ ( powerset @ SV76 ) )
| ! [SY176: $i] :
( ~ ( in @ SY176 @ SV76 )
| ~ ( in @ SY174 @ ( powerset @ SY175 ) )
| ~ ( in @ SY176 @ SY174 )
| ( in @ SY176 @ SY175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1076,plain,
! [SV77: $i] :
( ( ! [SY177: $i] :
( ~ ( in @ SY177 @ ( powerset @ SV77 ) )
| ! [SY178: $i] :
( ~ ( in @ SY178 @ ( powerset @ SV77 ) )
| ! [SY179: $i] :
( ~ ( in @ SY179 @ SV77 )
| ~ ( subset @ SY177 @ ( setminus @ SV77 @ SY178 ) )
| ~ ( in @ SY179 @ SY178 )
| ~ ( in @ SY179 @ SY177 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1077,plain,
! [SV78: $i] :
( ( ! [SY180: $i,SY181: $i,SY182: $i] :
( ~ ( in @ ( kpair @ SY181 @ SY182 ) @ ( cartprod @ SV78 @ SY180 ) )
| ( in @ SY182 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1078,plain,
! [SV79: $i] :
( ( ! [SY183: $i,SY184: $i] :
( ~ ( in @ SY184 @ SV79 )
| ! [SY185: $i] :
( ~ ( in @ SY185 @ SY183 )
| ( in @ ( kpair @ SY184 @ SY185 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SY183 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1079,plain,
! [SV80: $i] :
( ( ! [SY186: $i] :
( ~ ( in @ SY186 @ ( powerset @ SV80 ) )
| ! [SY187: $i] :
( ~ ( in @ SY187 @ ( powerset @ SV80 ) )
| ( in @ ( setminus @ SV80 @ SY186 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SY186 @ SY187 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1080,plain,
! [SV81: $i] :
( ( ! [SY188: $i] :
( ~ ( in @ SY188 @ SV81 )
| ( subset @ ( setadjoin @ SY188 @ emptyset ) @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1081,plain,
! [SV82: $i] :
( ( ! [SY189: $i] :
( ~ ( in @ SY189 @ ( powerset @ SV82 ) )
| ! [SY190: $i] :
( ~ ( in @ SY190 @ ( powerset @ SV82 ) )
| ! [SY191: $i] :
( ~ ( in @ SY191 @ SV82 )
| ~ ~ ( in @ SY191 @ SY189 )
| ~ ( in @ SY191 @ ( binintersect @ SY189 @ SY190 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1082,plain,
! [SV83: $i] :
( ( ! [SY192: $i,SY193: $i > $i > $o,SY194: $i,SY195: $i] :
( ~ ( in @ ( kpair @ SY194 @ SY195 )
@ ( dpsetconstr @ SV83 @ SY192
@ ^ [SX5: $i,SX6: $i] : ( SY193 @ SX5 @ SX6 ) ) )
| ( SY193 @ SY194 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1083,plain,
! [SV84: $i] :
( ( ! [SY198: $i,SY199: $i] :
( ~ ( func @ SV84 @ SY198 @ SY199 )
| ! [SY200: $i] :
( ~ ( in @ SY200 @ SV84 )
| ( singleton
@ ( dsetconstr @ SY198
@ ^ [SX4: $i] : ( in @ ( kpair @ SY200 @ SX4 ) @ SY199 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1084,plain,
! [SV85: $i] :
( ( ! [SY202: $i,SY203: $i] :
( ~ ~ ( in @ SY203 @ ( setminus @ SV85 @ SY202 ) )
| ~ ( in @ SY203 @ SV85 )
| ( in @ SY203 @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1085,plain,
! [SV86: $i] :
( ( ! [SY204: $i] :
( ( ( setadjoin @ SV86 @ emptyset )
!= ( setadjoin @ SY204 @ emptyset ) )
| ( SV86 = SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1086,plain,
! [SV87: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( in @ SY206 @ SV87 )
| ~ ~ ( in @ SY206 @ SY205 )
| ( in @ SY206 @ ( symdiff @ SV87 @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1087,plain,
! [SV88: $i] :
( ( ! [SY207: $i] : ( in @ SV88 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV88 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV88 @ ( setadjoin @ SY207 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1088,plain,
! [SV89: $i] :
( ( ! [SY208: $i,SY209: $i > $i] :
( ~ ! [SY210: $i] :
( ~ ( in @ SY210 @ SV89 )
| ( in @ ( SY209 @ SY210 ) @ SY208 ) )
| ( ( lam @ SV89 @ SY208
@ ^ [SX3: $i] : ( SY209 @ SX3 ) )
= ( lam @ SV89 @ SY208
@ ^ [SX3: $i] : ( SY209 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1089,plain,
! [SV90: $i] :
( ( ! [SY213: $i] :
( ( SV90 != SY213 )
| ( subset @ SY213 @ SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1090,plain,
! [SV91: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ( in @ SY215 @ ( funcSet @ SV91 @ SY214 ) )
| ! [SY216: $i] :
( ~ ( in @ SY216 @ SV91 )
| ( in @ ( kpair @ SY216 @ ( ap @ SV91 @ SY214 @ SY215 @ SY216 ) ) @ SY215 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1091,plain,
! [SV92: $i] :
( ( ~ ( in @ SV92 @ omega )
| ( in @ ( setadjoin @ SV92 @ SV92 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1092,plain,
! [SV93: $i] :
( ( ! [SY217: $i] :
( ~ ( breln1 @ SV93 @ SY217 )
| ! [SY218: $i] :
( ~ ( breln1 @ SV93 @ SY218 )
| ! [SY219: $i] :
( ~ ( in @ SY219 @ SV93 )
| ! [SY220: $i] :
( ~ ( in @ SY220 @ SV93 )
| ~ ( in @ ( kpair @ SY219 @ SY220 ) @ ( binunion @ SY217 @ SY218 ) )
| ( in @ ( kpair @ SY219 @ SY220 ) @ SY217 )
| ( in @ ( kpair @ SY219 @ SY220 ) @ SY218 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1093,plain,
! [SV94: $i] :
( ( ! [SY221: $o,SY222: $i] :
( ~ ( in @ SY222 @ SV94 )
| ! [SY223: $i] :
( ~ ( in @ SY223 @ SV94 )
| ~ SY221
| ( in @ SY222
@ ( dsetconstr @ SV94
@ ^ [SX4: $i] :
( ~ ( ~ SY221
| ( SX4 != SY222 ) )
| ~ ( ~ ~ SY221
| ( SX4 != SY223 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1094,plain,
! [SV95: $i] :
( ( ! [SY225: $i] :
( ~ ! [SY226: $i] :
( ~ ( in @ SY226 @ SY225 )
| ( in @ SY226 @ SV95 ) )
| ( in @ SY225 @ ( powerset @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1095,plain,
! [SV96: $i] :
( ( ! [SY227: $i] : ( in @ SY227 @ ( setadjoin @ SV96 @ ( setadjoin @ SY227 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1096,plain,
! [SV97: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ~ ( in @ SY229 @ ( symdiff @ SV97 @ SY228 ) )
| ! [SY230: $o] :
( ~ ( ~ ( in @ SY229 @ SV97 )
| ~ ~ ( in @ SY229 @ SY228 )
| SY230 )
| ~ ( ~ ~ ( in @ SY229 @ SV97 )
| ~ ( in @ SY229 @ SY228 )
| SY230 )
| SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1097,plain,
! [SV98: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ( in @ SY232 @ ( setminus @ SV98 @ SY231 ) )
| ( in @ SY232 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1098,plain,
! [SV99: $i] :
( ( ! [SY233: $i] :
( ~ ( breln1 @ SV99 @ SY233 )
| ! [SY234: $i] :
( ~ ( breln1 @ SV99 @ SY234 )
| ! [SY235: $i] :
( ~ ( in @ SY235 @ SV99 )
| ! [SY236: $i] :
( ~ ( in @ SY236 @ SV99 )
| ~ ( in @ ( kpair @ SY235 @ SY236 ) @ ( breln1compset @ SV99 @ SY233 @ SY234 ) )
| ! [SY237: $o] :
( ~ ! [SY238: $i] :
( ~ ( in @ SY238 @ SV99 )
| ~ ( in @ ( kpair @ SY235 @ SY238 ) @ SY233 )
| ~ ( in @ ( kpair @ SY238 @ SY236 ) @ SY234 )
| SY237 )
| SY237 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1099,plain,
! [SV100: $i] :
( ( ! [SY239: $i] :
( ~ ( in @ SY239 @ ( breln1Set @ SV100 ) )
| ( breln1 @ SV100 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1100,plain,
! [SV101: $i] :
( ( ~ ( singleton @ SV101 )
| ( in @ ( setunion @ SV101 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1101,plain,
! [SV102: $i] :
( ( ! [SY240: $i,SY241: $i,SY242: $i] :
( ( ( kpair @ SV102 @ SY240 )
!= ( kpair @ SY241 @ SY242 ) )
| ( SY240 = SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1102,plain,
! [SV103: $i] :
( ( ! [SY243: $i] :
( ~ ( breln1 @ SV103 @ SY243 )
| ( breln1 @ SV103 @ ( breln1invset @ SV103 @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1103,plain,
! [SV104: $i] :
( ( ! [SY244: $i] :
( ~ ( in @ SV104 @ SY244 )
| ~ ( in @ SY244 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1104,plain,
! [SV105: $i] :
( ( ! [SY245: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV105 @ ( setadjoin @ SY245 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1105,plain,
! [SV106: $i] :
( ( ! [SY246: $i,SY247: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV106 @ SY246
@ ^ [SX3: $i,SX4: $i] : ( SY247 @ SX3 @ SX4 ) )
@ ( cartprod @ SV106 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1106,plain,
! [SV107: $i > $o] :
( ( ! [SY250: $i > $o] :
( ~ ! [SY251: $i,SY252: $i] :
( ( SY251 != SY252 )
| ~ ( ~ ( ~ ( SV107 @ SY251 )
| ( SY250 @ SY252 ) )
| ~ ( ~ ( SY250 @ SY252 )
| ( SV107 @ SY251 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY250 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY250 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY250 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY250 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1107,plain,
! [SV108: $i] :
( ( ! [SY261: $i] :
( ~ ( in @ SY261 @ ( powerset @ SV108 ) )
| ! [SY262: $i] :
( ~ ( in @ SY262 @ ( powerset @ SV108 ) )
| ! [SY263: $i] :
( ~ ( in @ SY263 @ ( powerset @ SV108 ) )
| ~ ( subset @ SY261 @ SY262 )
| ~ ( subset @ SY261 @ SY263 )
| ( subset @ SY261 @ ( binintersect @ SY262 @ SY263 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1108,plain,
! [SV109: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( in @ SY265 @ ( funcSet @ SV109 @ SY264 ) )
| ! [SY266: $i] :
( ~ ( in @ SY266 @ ( funcSet @ SV109 @ SY264 ) )
| ~ ! [SY267: $i] :
( ~ ( in @ SY267 @ SV109 )
| ( ( ap @ SV109 @ SY264 @ SY265 @ SY267 )
= ( ap @ SV109 @ SY264 @ SY266 @ SY267 ) ) )
| ( SY265 = SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1109,plain,
! [SV110: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( in @ SY269 @ ( cartprod @ SV110 @ SY268 ) )
| ( iskpair @ SY269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1110,plain,
! [SV111: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( in @ SY271 @ ( cartprod @ SV111 @ SY270 ) )
| ~ ! [SY272: $i] :
~ ~ ( ~ ( in @ SY272 @ SV111 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY270 )
| ( SY271
!= ( kpair @ SY272 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1111,plain,
! [SV112: $i] :
( ( ! [SY274: $i] : ( subset @ ( binintersect @ SV112 @ SY274 ) @ SY274 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1112,plain,
! [SV113: $i] :
( ( ~ ( ( SV113 != emptyset ) )
| ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV113 )
| ( ( binintersect @ SY275 @ SV113 )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1113,plain,
! [SV114: $i] :
( ( ! [SY276: $i] :
( ~ ( in @ SY276 @ ( powerset @ SV114 ) )
| ( subset @ SY276 @ ( setminus @ SV114 @ ( setminus @ SV114 @ SY276 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1114,plain,
! [SV115: $i] :
( ( ! [SY277: $i,SY278: $i] :
( ~ ( in @ ( setadjoin @ SY278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SY277 @ emptyset ) ) @ emptyset ) ) )
| ( SV115 = SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1115,plain,
! [SV116: $i] :
( ( ! [SY279: $i] :
( ~ ( in @ SY279 @ ( powerset @ SV116 ) )
| ! [SY280: $i] :
( ~ ( in @ SY280 @ ( powerset @ SV116 ) )
| ( subset @ ( setminus @ SV116 @ SY279 ) @ ( setminus @ SV116 @ ( binintersect @ SY279 @ SY280 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1116,plain,
! [SV117: $i] :
( ( ! [SY281: $i] :
( ~ ( in @ SY281 @ ( powerset @ SV117 ) )
| ! [SY282: $i] :
( ~ ( in @ SY282 @ ( powerset @ SV117 ) )
| ! [SY283: $i] :
( ~ ( in @ SY283 @ ( powerset @ SV117 ) )
| ! [SY284: $i] :
( ~ ( in @ SY284 @ SV117 )
| ~ ( in @ SY284 @ ( binintersect @ SY281 @ SY282 ) )
| ( in @ SY284 @ ( binintersect @ ( binunion @ SY281 @ SY283 ) @ ( binunion @ SY282 @ SY283 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1117,plain,
! [SV118: $i] :
( ( ! [SY285: $i > $o] :
( ~ ! [SY286: $i] :
( ~ ( in @ SY286 @ SV118 )
| ! [SY287: $i] :
( ~ ( in @ SY287 @ SV118 )
| ~ ( SY285 @ SY286 )
| ~ ( SY285 @ SY287 )
| ( SY286 = SY287 ) ) )
| ~ ~ ! [SY288: $i] :
~ ~ ( ~ ( in @ SY288 @ SV118 )
| ~ ( SY285 @ SY288 ) )
| ( ex1 @ SV118
@ ^ [SX2: $i] : ( SY285 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1118,plain,
! [SV119: $i] :
( ( ! [SY290: $i > $i] :
~ ! [SY291: $i] :
~ ! [SY292: $i] :
~ ( ~ ( ~ ( in @ SY292 @ SY291 )
| ~ ! [SY293: $i] :
~ ~ ( ~ ( in @ SY293 @ SV119 )
| ( SY292
!= ( SY290 @ SY293 ) ) ) )
| ~ ( ~ ~ ! [SY294: $i] :
~ ~ ( ~ ( in @ SY294 @ SV119 )
| ( SY292
!= ( SY290 @ SY294 ) ) )
| ( in @ SY292 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1119,plain,
! [SV120: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ~ ( func @ SV120 @ SY295 @ SY296 )
| ! [SY297: $i] :
( ~ ( in @ SY297 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY295
@ ^ [SX4: $i] : ( in @ ( kpair @ SY297 @ SX4 ) @ SY296 ) ) )
@ SY295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1120,plain,
! [SV121: $i] :
( ( ! [SY299: $i] :
( ~ ! [SY300: $i] :
~ ( ~ ( ~ ( in @ SY300 @ SV121 )
| ( in @ SY300 @ SY299 ) )
| ~ ( ~ ( in @ SY300 @ SY299 )
| ( in @ SY300 @ SV121 ) ) )
| ( SV121 = SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1121,plain,
! [SV122: $i] :
( ( ! [SY301: $i] :
( ~ ! [SY302: $i] :
( ~ ( in @ SY302 @ SV122 )
| ( in @ SY302 @ SY301 ) )
| ( subset @ SV122 @ SY301 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1122,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ( subset @ SX0 @ sK1_X ) )
| ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(1123,plain,
! [SV123: $i] :
( ( ! [SY303: $i] :
( ~ ( subset @ SY303 @ SV123 )
| ( in @ SY303 @ ( powerset @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1124,plain,
! [SV124: $i] :
( ( ! [SY304: $i,SY305: $i > $i] :
( ~ ! [SY306: $i] :
( ~ ( in @ SY306 @ SV124 )
| ( in @ ( SY305 @ SY306 ) @ SY304 ) )
| ( func @ SV124 @ SY304
@ ( lam @ SV124 @ SY304
@ ^ [SX3: $i] : ( SY305 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1125,plain,
! [SV125: $i] :
( ( ! [SY308: $o,SY309: $i] :
( ~ ( in @ SY309 @ SV125 )
| ! [SY310: $i] :
( ~ ( in @ SY310 @ SV125 )
| ~ SY308
| ( ( dsetconstr @ SV125
@ ^ [SX4: $i] :
( ~ ( ~ SY308
| ( SX4 != SY309 ) )
| ~ ( ~ ~ SY308
| ( SX4 != SY310 ) ) ) )
= ( setadjoin @ SY309 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1126,plain,
! [SV126: $i] :
( ( ! [SY312: $i] :
( ~ ( in @ SY312 @ ( setunion @ SV126 ) )
| ! [SY313: $o] :
( ~ ! [SY314: $i] :
( ~ ( in @ SY312 @ SY314 )
| ~ ( in @ SY314 @ SV126 )
| SY313 )
| SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1127,plain,
! [SV127: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( in @ SY316 @ ( cartprod @ SV127 @ SY315 ) )
| ( in @ ( ksnd @ SY316 ) @ SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1128,plain,
! [SV128: $i] :
( ( ! [SY317: $i] :
( ~ ( breln1 @ SV128 @ SY317 )
| ! [SY318: $i] :
( ~ ( breln1 @ SV128 @ SY318 )
| ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SY317 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1129,plain,
! [SV129: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( subset @ SV129 @ SY320 )
| ( subset @ SV129 @ ( setadjoin @ SY319 @ SY320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1130,plain,
! [SV130: $i] :
( ( ! [SY321: $i] : ( in @ SV130 @ ( setadjoin @ SV130 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1131,plain,
! [SV131: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( in @ SY323 @ SV131 )
| ~ ~ ( in @ SY323 @ SY322 )
| ~ ( subset @ SV131 @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1132,plain,
! [SV132: $i] :
( ( ! [SY324: $i,SY325: $i,SY326: $i] :
( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SY324 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY325 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY325 @ ( setadjoin @ SY326 @ emptyset ) ) @ emptyset ) ) )
| ( SY325 != SY326 )
| ( SY324 = SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1133,plain,
! [SV133: $i] :
( ( ! [SY327: $i] :
( ~ ( in @ SY327 @ ( powerset @ SV133 ) )
| ! [SY328: $i] :
( ~ ( in @ SY328 @ ( powerset @ SV133 ) )
| ! [SY329: $i] :
( ~ ( in @ SY329 @ SV133 )
| ~ ( in @ SY329 @ ( setminus @ SV133 @ ( binintersect @ SY327 @ SY328 ) ) )
| ( in @ SY329 @ ( binunion @ ( setminus @ SV133 @ SY327 ) @ ( setminus @ SV133 @ SY328 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1134,plain,
! [SV134: $i] :
( ( ! [SY330: $i] :
( ~ ( in @ SY330 @ ( powerset @ SV134 ) )
| ! [SY331: $i] :
( ~ ( in @ SY331 @ ( powerset @ SV134 ) )
| ! [SY332: $i] :
( ~ ( in @ SY332 @ ( powerset @ SV134 ) )
| ! [SY333: $i] :
( ~ ( in @ SY333 @ ( powerset @ SV134 ) )
| ~ ( subset @ SY330 @ SY332 )
| ~ ( subset @ SY331 @ SY333 )
| ( subset @ ( binintersect @ SY330 @ SY331 ) @ ( binintersect @ SY332 @ SY333 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1135,plain,
! [SV135: $i] :
( ( ! [SY334: $i] : ( subset @ ( setminus @ SV135 @ SY334 ) @ SV135 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1136,plain,
! [SV136: $i > $o] :
( ( ~ ~ ! [SY335: $i] :
~ ~ ( ~ ( SV136 @ SY335 )
| ~ ! [SY336: $i] :
( ~ ( SV136 @ SY336 )
| ( SY335 = SY336 ) ) )
| ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1137,plain,
! [SV137: $i] :
( ( ! [SY339: $i] :
( ( ( setminus @ SV137 @ SY339 )
!= emptyset )
| ( subset @ SV137 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1138,plain,
! [SV138: $i > $o] :
( ( ~ ~ ! [SY340: $i] :
~ ~ ( ~ ( SV138 @ SY340 )
| ~ ! [SY341: $i] :
( ~ ( SV138 @ SY341 )
| ( SY340 = SY341 ) ) )
| ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1139,plain,
! [SV139: $i] :
( ( ! [SY344: $i,SY345: $i] :
( ~ ( func @ SV139 @ SY344 @ SY345 )
| ! [SY346: $i] :
( ~ ( func @ SV139 @ SY344 @ SY346 )
| ~ ! [SY347: $i] :
( ~ ( in @ SY347 @ SV139 )
| ( ( ap @ SV139 @ SY344 @ SY345 @ SY347 )
= ( ap @ SV139 @ SY344 @ SY346 @ SY347 ) ) )
| ( SY345 = SY346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1140,plain,
! [SV140: $i] :
( ( ! [SY348: $i > $i] :
~ ! [SY349: $i] :
~ ~ ( ~ ! [SY350: $i] :
~ ( ~ ( ~ ( in @ SY350 @ SY349 )
| ~ ! [SY351: $i] :
~ ~ ( ~ ( in @ SY351 @ SV140 )
| ( SY350
!= ( SY348 @ SY351 ) ) ) )
| ~ ( ~ ~ ! [SY352: $i] :
~ ~ ( ~ ( in @ SY352 @ SV140 )
| ( SY350
!= ( SY348 @ SY352 ) ) )
| ( in @ SY350 @ SY349 ) ) )
| ~ ! [SY353: $i] :
( ~ ! [SY354: $i] :
~ ( ~ ( ~ ( in @ SY354 @ SY353 )
| ~ ! [SY355: $i] :
~ ~ ( ~ ( in @ SY355 @ SV140 )
| ( SY354
!= ( SY348 @ SY355 ) ) ) )
| ~ ( ~ ~ ! [SY356: $i] :
~ ~ ( ~ ( in @ SY356 @ SV140 )
| ( SY354
!= ( SY348 @ SY356 ) ) )
| ( in @ SY354 @ SY353 ) ) )
| ( SY349 = SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1141,plain,
! [SV141: $i] :
( ( ! [SY357: $i,SY358: $i > $i > $o,SY359: $i,SY360: $i] :
( ~ ( in @ ( kpair @ SY359 @ SY360 )
@ ( dpsetconstr @ SV141 @ SY357
@ ^ [SX5: $i,SX6: $i] : ( SY358 @ SX5 @ SX6 ) ) )
| ( in @ SY359 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1142,plain,
! [SV142: $i] :
( ( ! [SY363: $i,SY364: $i,SY365: $i] :
( ~ ( in @ ( kpair @ SY364 @ SY365 ) @ ( cartprod @ SV142 @ SY363 ) )
| ( in @ SY364 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1143,plain,
! [SV143: $i] :
( ( ! [SY366: $i] :
( ~ ( in @ SY366 @ ( powerset @ SV143 ) )
| ! [SY367: $i] :
( ~ ( in @ SY367 @ ( powerset @ SV143 ) )
| ! [SY368: $i] :
( ~ ( in @ SY368 @ ( powerset @ SV143 ) )
| ~ ( subset @ SY367 @ SY368 )
| ( subset @ ( binintersect @ SY366 @ SY367 ) @ SY368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1144,plain,
! [SV144: $i] :
( ( ! [SY369: $i > $o] :
( ~ ( ex1 @ SV144
@ ^ [SX2: $i] : ( SY369 @ SX2 ) )
| ~ ! [SY371: $i] :
~ ~ ( ~ ( in @ SY371 @ SV144 )
| ~ ( SY369 @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1145,plain,
! [SV145: $i] :
( ( ! [SY372: $i] :
( ~ ! [SY373: $i] :
( ~ ( in @ SY373 @ SV145 )
| ( in @ SY373 @ SY372 ) )
| ( subset @ SV145 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1146,plain,
! [SV146: $i] :
( ( ! [SY374: $i] :
( ~ ( breln1 @ SV146 @ SY374 )
| ! [SY375: $i > $o] :
( ~ ! [SY376: $i] :
( ~ ( in @ SY376 @ SV146 )
| ! [SY377: $i] :
( ~ ( in @ SY377 @ SV146 )
| ~ ( in @ ( kpair @ SY376 @ SY377 ) @ SY374 )
| ( SY375 @ ( kpair @ SY376 @ SY377 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY374 )
| ( SY375 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1147,plain,
! [SV147: $i] :
( ( ! [SY379: $i] :
( ( SV147 != SY379 )
| ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SY379 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1148,plain,
! [SV148: $i] :
( ( ! [SY380: $i > $i,SY381: $i] :
( ~ ( in @ SY381
@ ( image1 @ SV148
@ ^ [SX3: $i] : ( SY380 @ SX3 ) ) )
| ~ ! [SY383: $i] :
~ ~ ( ~ ( in @ SY383 @ SV148 )
| ( SY381
!= ( SY380 @ SY383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1149,plain,
! [SV149: $i] :
( ( ! [SY384: $i] :
( ~ ( in @ SY384 @ ( powerset @ SV149 ) )
| ! [SY385: $i] :
( ~ ( in @ SY385 @ ( powerset @ SV149 ) )
| ~ ! [SY386: $i] :
( ~ ( in @ SY386 @ SV149 )
| ~ ( in @ SY386 @ SY384 )
| ( in @ SY386 @ SY385 ) )
| ~ ! [SY387: $i] :
( ~ ( in @ SY387 @ SV149 )
| ~ ( in @ SY387 @ SY385 )
| ( in @ SY387 @ SY384 ) )
| ( SY384 = SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1150,plain,
! [SV150: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( in @ SY389 @ ( injFuncSet @ SV150 @ SY388 ) )
| ( injective @ SV150 @ SY388 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1151,plain,
! [SV151: $i] :
( ( ! [SY390: $i > $o] :
( in
@ ( dsetconstr @ SV151
@ ^ [SX2: $i] : ( SY390 @ SX2 ) )
@ ( powerset @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1152,plain,
! [SV152: $i] :
( ( ! [SY392: $i] :
( ( ( binintersect @ SV152 @ SY392 )
!= SY392 )
| ( subset @ SY392 @ SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1153,plain,
! [SV153: $i] :
( ( ! [SY393: $i > $o] :
( ~ ~ ! [SY394: $i] :
~ ~ ( ~ ( in @ SY394 @ SV153 )
| ~ ( SY393 @ SY394 ) )
| ( ( dsetconstr @ SV153
@ ^ [SX2: $i] : ( SY393 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1154,plain,
! [SV154: $i] :
( ( ! [SY396: $i] :
( ~ ( breln1 @ SV154 @ SY396 )
| ! [SY397: $i] :
( ~ ( breln1 @ SV154 @ SY397 )
| ! [SY398: $i] :
( ~ ( breln1 @ SV154 @ SY398 )
| ( ( breln1compset @ SV154 @ ( binunion @ SY396 @ SY397 ) @ SY398 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY398 ) @ ( breln1invset @ SV154 @ SY397 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY398 ) @ ( breln1invset @ SV154 @ SY396 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1155,plain,
! [SV155: $i > $o] :
( ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ( SV155 @ SY399 )
| ~ ! [SY400: $i] :
( ~ ( SV155 @ SY400 )
| ( SY399 = SY400 ) ) )
| ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1156,plain,
! [SV156: $i] :
( ( ! [SY403: $i] :
( ~ ( breln1 @ SV156 @ SY403 )
| ! [SY404: $i > $o] :
( ~ ! [SY405: $i] :
( ~ ( in @ SY405 @ SV156 )
| ! [SY406: $i] :
( ~ ( in @ SY406 @ SV156 )
| ~ ( in @ ( kpair @ SY405 @ SY406 ) @ SY403 )
| ( SY404 @ ( kpair @ SY405 @ SY406 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY403 )
| ( SY404 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1157,plain,
! [SV157: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( in @ SY409 @ SV157 )
| ! [SY410: $i] :
( ~ ( in @ SY410 @ SY408 )
| ( in @ ( kpair @ SY409 @ SY410 ) @ ( cartprod @ SV157 @ SY408 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1158,plain,
! [SV158: $i] :
( ( ! [SY411: $o,SY412: $i] :
( ~ ( in @ SY412 @ SV158 )
| ! [SY413: $i] :
( ~ ( in @ SY413 @ SV158 )
| ~ ~ SY411
| ( in @ SY413
@ ( dsetconstr @ SV158
@ ^ [SX4: $i] :
( ~ ( ~ SY411
| ( SX4 != SY412 ) )
| ~ ( ~ ~ SY411
| ( SX4 != SY413 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1159,plain,
! [SV159: $i] :
( ( ! [SY415: $i,SY416: $i] :
( ~ ( in @ SY415 @ ( powerset @ SV159 ) )
| ~ ( in @ SY416 @ SY415 )
| ( in @ SY416 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1160,plain,
! [SV160: $i] :
( ( ! [SY417: $i,SY418: $i] :
( ~ ( in @ SY418 @ SV160 )
| ~ ~ ( in @ SY418 @ SY417 )
| ( SV160 != SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1161,plain,
! [SV161: $i] :
( ( ! [SY419: $i,SY420: $i] :
( ~ ( subset @ SV161 @ SY419 )
| ~ ( subset @ SY419 @ SY420 )
| ( subset @ SV161 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1162,plain,
! [SV162: $i] :
( ( ! [SY421: $i] :
( ~ ( in @ SY421 @ ( powerset @ SV162 ) )
| ( in @ ( powerset @ SY421 ) @ ( powerset @ ( powerset @ SV162 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1163,plain,
! [SV163: $i] :
( ( ! [SY422: $i] :
( ~ ( in @ SY422 @ ( powerset @ SV163 ) )
| ! [SY423: $i] :
( ~ ( in @ SY423 @ SV163 )
| ~ ~ ( in @ SY423 @ ( setminus @ SV163 @ SY422 ) )
| ( in @ SY423 @ SY422 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1164,plain,
! [SV164: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( in @ SY425 @ SV164 )
| ~ ~ ( in @ SY425 @ SY424 )
| ( in @ SY425 @ ( setminus @ SV164 @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1165,plain,
! [SV165: $i] :
( ( ! [SY426: $i > $o,SY427: $i] :
( ~ ( in @ SY427 @ SV165 )
| ~ ( SY426 @ SY427 )
| ( ( dsetconstr @ SV165
@ ^ [SX3: $i] : ( SY426 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1166,plain,
! [SV166: $i > $o] :
( ( ~ ~ ! [SY429: $i] :
~ ( SV166 @ SY429 )
| ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1167,plain,
! [SV167: $i > $o] :
( ( ~ ~ ! [SY434: $i] :
~ ~ ( ~ ( SV167 @ SY434 )
| ~ ! [SY435: $i] :
( ~ ( SV167 @ SY435 )
| ( SY434 = SY435 ) ) )
| ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1168,plain,
! [SV168: $i] :
( ( ! [SY438: $i,SY439: $i] :
( ~ ( breln @ SV168 @ SY438 @ SY439 )
| ! [SY440: $i] :
( ~ ( breln @ SV168 @ SY438 @ SY440 )
| ~ ! [SY441: $i] :
( ~ ( in @ SY441 @ SV168 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY438 )
| ~ ( in @ ( kpair @ SY441 @ SX5 ) @ SY439 )
| ( in @ ( kpair @ SY441 @ SX5 ) @ SY440 ) ) )
| ~ ! [SY443: $i] :
( ~ ( in @ SY443 @ SV168 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY438 )
| ~ ( in @ ( kpair @ SY443 @ SX5 ) @ SY440 )
| ( in @ ( kpair @ SY443 @ SX5 ) @ SY439 ) ) )
| ( SY439 = SY440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1169,plain,
! [SV169: $i] :
( ( ! [SY445: $i] : ( subset @ ( binintersect @ SV169 @ SY445 ) @ SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1170,plain,
! [SV170: $i] :
( ( ! [SY446: $i > $i,SY447: $i] :
~ ( ~ ( ~ ( in @ SY447
@ ( image1 @ SV170
@ ^ [SX3: $i] : ( SY446 @ SX3 ) ) )
| ~ ! [SY449: $i] :
~ ~ ( ~ ( in @ SY449 @ SV170 )
| ( SY447
!= ( SY446 @ SY449 ) ) ) )
| ~ ( ~ ~ ! [SY450: $i] :
~ ~ ( ~ ( in @ SY450 @ SV170 )
| ( SY447
!= ( SY446 @ SY450 ) ) )
| ( in @ SY447
@ ( image1 @ SV170
@ ^ [SX3: $i] : ( SY446 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1171,plain,
! [SV171: $i] :
( ( ! [SY452: $i] :
( ~ ( in @ SY452 @ ( powerset @ SV171 ) )
| ! [SY453: $i] :
( ~ ( in @ SY453 @ ( powerset @ SV171 ) )
| ! [SY454: $i] :
( ~ ( in @ SY454 @ SV171 )
| ~ ~ ( in @ SY454 @ SY453 )
| ~ ( in @ SY454 @ ( binintersect @ SY452 @ SY453 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1172,plain,
! [SV172: $i] :
( ( ! [SY455: $i,SY456: $i > $i] :
( ~ ! [SY457: $i] :
( ~ ( in @ SY457 @ SV172 )
| ( in @ ( SY456 @ SY457 ) @ SY455 ) )
| ! [SY458: $i] :
( ~ ( in @ SY458 @ SV172 )
| ( ( ap @ SV172 @ SY455
@ ( lam @ SV172 @ SY455
@ ^ [SX4: $i] : ( SY456 @ SX4 ) )
@ SY458 )
= ( SY456 @ SY458 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1173,plain,
! [SV173: $i] :
( ( ~ ( in @ SV173 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1174,plain,
! [SV174: $i > $o] :
( ( ~ ~ ! [SY460: $i] :
~ ! [SY461: $i] :
~ ( ~ ( ~ ( SV174 @ SY461 )
| ( SY461 = SY460 ) )
| ~ ( ( SY461 != SY460 )
| ( SV174 @ SY461 ) ) )
| ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1175,plain,
! [SV175: $i] :
( ( ! [SY464: $i] :
( ( SV175 != SY464 )
| ! [SY465: $i,SY466: $i] :
( ( SY465 != SY466 )
| ( ( setadjoin @ SV175 @ SY465 )
= ( setadjoin @ SY464 @ SY466 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1176,plain,
! [SV176: $i] :
( ( ! [SY467: $i > $o,SY468: $i] :
( ~ ( in @ SY468 @ SV176 )
| ~ ( ~ ( ~ ( in @ SY468
@ ( dsetconstr @ SV176
@ ^ [SX3: $i] : ( SY467 @ SX3 ) ) )
| ( SY467 @ SY468 ) )
| ~ ( ~ ( SY467 @ SY468 )
| ( in @ SY468
@ ( dsetconstr @ SV176
@ ^ [SX3: $i] : ( SY467 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1177,plain,
! [SV177: $i] :
( ( ! [SY471: $i,SY472: $i] :
( ~ ( in @ SY472 @ SV177 )
| ( in @ SY472 @ ( binunion @ SV177 @ SY471 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1178,plain,
! [SV178: $i] :
( ( ! [SY473: $i] :
( ~ ( in @ SY473 @ ( setunion @ SV178 ) )
| ~ ! [SY474: $i] :
~ ~ ( ~ ( in @ SY474 @ SV178 )
| ~ ( in @ SY473 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1179,plain,
! [SV179: $i] :
( ( ! [SY475: $i] :
( ~ ( in @ SY475 @ ( powerset @ SV179 ) )
| ! [SY476: $i] :
( ~ ( in @ SY476 @ ( powerset @ SV179 ) )
| ! [SY477: $i] :
( ~ ( in @ SY477 @ ( powerset @ SV179 ) )
| ! [SY478: $i] :
( ~ ( in @ SY478 @ SV179 )
| ~ ( in @ SY478 @ ( binintersect @ SY475 @ SY476 ) )
| ( in @ SY478 @ ( binunion @ SY476 @ SY477 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1180,plain,
! [SV180: $i] :
( ( subset @ emptyset @ SV180 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1181,plain,
! [SV181: $i] :
( ( ! [SY479: $o,SY480: $i] :
( ~ ( in @ SY480 @ SV181 )
| ! [SY481: $i] :
( ~ ( in @ SY481 @ SV181 )
| ~ SY479
| ( ( if @ SV181 @ SY479 @ SY480 @ SY481 )
= SY480 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1182,plain,
! [SV182: $i] :
( ( ! [SY482: $i,SY483: $i] :
( ~ ~ ( in @ SY483 @ SV182 )
| ~ ( in @ SY483 @ SY482 )
| ( in @ SY483 @ ( symdiff @ SV182 @ SY482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1183,plain,
! [SV183: $i] :
( ( ! [SY484: $i,SY485: $i] :
( ~ ( breln @ SV183 @ SY484 @ SY485 )
| ! [SY486: $i > $o] :
( ~ ! [SY487: $i] :
( ~ ( in @ SY487 @ SV183 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY484 )
| ~ ( in @ ( kpair @ SY487 @ SX5 ) @ SY485 )
| ( SY486 @ ( kpair @ SY487 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY485 )
| ( SY486 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1184,plain,
! [SV184: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ~ ( subset @ SV184 @ SY490 )
| ~ ~ ( in @ SY491 @ SY490 )
| ~ ( in @ SY491 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1185,plain,
! [SV185: $i] :
( ( ! [SY492: $i] :
( ~ ( subset @ SV185 @ SY492 )
| ~ ( subset @ SY492 @ SV185 )
| ( SV185 = SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1186,plain,
! [SV186: $i] :
( ( ! [SY493: $i] :
( ~ ( in @ SY493 @ ( powerset @ SV186 ) )
| ! [SY494: $i] :
( ~ ( in @ SY494 @ ( powerset @ SV186 ) )
| ( in @ ( binunion @ SY493 @ SY494 ) @ ( powerset @ SV186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1187,plain,
! [SV187: $o] :
( ( ~ SV187
| ( in @ emptyset @ ( prop2set @ SV187 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[858]) ).
thf(1188,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[858]) ).
thf(1189,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[858]) ).
thf(1190,plain,
! [SV188: $i] :
( ( ! [SY495: $i] :
( ~ ( in @ SY495 @ ( powerset @ SV188 ) )
| ! [SY496: $i] :
( ~ ( in @ SY496 @ ( powerset @ SV188 ) )
| ! [SY497: $i] :
( ~ ( in @ SY497 @ SV188 )
| ~ ( in @ SY497 @ ( setminus @ SV188 @ ( binunion @ SY495 @ SY496 ) ) )
| ( in @ SY497 @ ( setminus @ SV188 @ SY495 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1191,plain,
! [SV189: $i] :
( ( ! [SY498: $i > $o] :
( ~ ( ex1 @ SV189
@ ^ [SX2: $i] : ( SY498 @ SX2 ) )
| ! [SY500: $i] :
( ~ ( in @ SY500 @ SV189 )
| ! [SY501: $i] :
( ~ ( in @ SY501 @ SV189 )
| ~ ( SY498 @ SY500 )
| ~ ( SY498 @ SY501 )
| ( SY500 = SY501 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1192,plain,
! [SV190: $i] :
( ( ! [SY502: $o,SY503: $i] :
( ~ ( in @ SY503 @ SV190 )
| ! [SY504: $i] :
( ~ ( in @ SY504 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SX4: $i] :
( ~ ( ~ SY502
| ( SX4 != SY503 ) )
| ~ ( ~ ~ SY502
| ( SX4 != SY504 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1193,plain,
! [SV191: $i > $i > $o] :
( ( ! [SY506: $i] :
( ~ ! [SY507: $i] :
( ~ ( in @ SY507 @ SY506 )
| ~ ! [SY508: $i] :
~ ~ ( ~ ( SV191 @ SY507 @ SY508 )
| ~ ! [SY509: $i] :
( ~ ( SV191 @ SY507 @ SY509 )
| ( SY508 = SY509 ) ) ) )
| ~ ! [SY510: $i] :
~ ! [SY511: $i] :
~ ( ~ ( ~ ( in @ SY511 @ SY510 )
| ~ ! [SY512: $i] :
~ ~ ( ~ ( in @ SY512 @ SY506 )
| ~ ( SV191 @ SY512 @ SY511 ) ) )
| ~ ( ~ ~ ! [SY513: $i] :
~ ~ ( ~ ( in @ SY513 @ SY506 )
| ~ ( SV191 @ SY513 @ SY511 ) )
| ( in @ SY511 @ SY510 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1194,plain,
! [SV192: $i] :
( ( ! [SY514: $i] :
( ~ ~ ( subset @ SV192 @ SY514 )
| ( SV192 != SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1195,plain,
! [SV193: $i] :
( ( ! [SY515: $i] :
( ( SV193 != SY515 )
| ( ( setadjoin @ SV193 @ ( setadjoin @ SY515 @ emptyset ) )
= ( setadjoin @ SV193 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1196,plain,
! [SV194: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( in @ SY517 @ ( surjFuncSet @ SV194 @ SY516 ) )
| ( surjective @ SV194 @ SY516 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1197,plain,
! [SV195: $i] :
( ( ! [SY518: $i] : ( in @ SY518 @ ( setadjoin @ SV195 @ ( setadjoin @ SY518 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1198,plain,
! [SV196: $i] :
( ( ! [SY519: $i,SY520: $i] :
( ~ ( in @ SY520 @ SV196 )
| ( in @ ( setadjoin @ SY520 @ emptyset ) @ ( powerset @ ( binunion @ SV196 @ SY519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1199,plain,
! [SV197: $i] :
( ( ! [SY521: $i] :
( ~ ( breln1 @ SV197 @ SY521 )
| ( SY521
= ( breln1invset @ SV197 @ ( breln1invset @ SV197 @ SY521 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1200,plain,
! [SV198: $i] :
( ( ! [SY522: $i] :
( ~ ( in @ SY522 @ ( powerset @ SV198 ) )
| ! [SY523: $i] :
( ~ ( in @ SY523 @ ( powerset @ SV198 ) )
| ! [SY524: $i] :
( ~ ( in @ SY524 @ SV198 )
| ~ ( in @ SY524 @ ( binintersect @ ( setminus @ SV198 @ SY522 ) @ ( setminus @ SV198 @ SY523 ) ) )
| ( in @ SY524 @ ( setminus @ SV198 @ ( binunion @ SY522 @ SY523 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1201,plain,
! [SV199: $i] :
( ( ! [SY525: $i,SY526: $i] :
( ~ ( in @ SY526 @ ( funcSet @ SV199 @ SY525 ) )
| ~ ( injective @ SV199 @ SY525 @ SY526 )
| ( in @ SY526 @ ( injFuncSet @ SV199 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1202,plain,
! [SV200: $i] :
( ( ~ ! [SY527: $i] :
( ~ ( in @ SY527 @ SV200 )
| ( subset @ SY527 @ SV200 ) )
| ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1203,plain,
! [SV201: $i] :
( ( ! [SY529: $i] : ( in @ SY529 @ ( setadjoin @ SV201 @ ( setadjoin @ SY529 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1204,plain,
! [SV202: $i] :
( ( ! [SY530: $i,SY531: $i > $i] :
( ~ ! [SY532: $i] :
( ~ ( in @ SY532 @ SV202 )
| ( in @ ( SY531 @ SY532 ) @ SY530 ) )
| ! [SY533: $i] :
( ~ ( in @ SY533 @ ( funcSet @ SY530 @ SV202 ) )
| ~ ! [SY534: $i] :
( ~ ( in @ SY534 @ SV202 )
| ( ( ap @ SY530 @ SV202 @ SY533 @ ( SY531 @ SY534 ) )
= SY534 ) )
| ( surjective @ SY530 @ SV202 @ SY533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1205,plain,
! [SV203: $i] :
( ( ~ ( subset @ SV203 @ emptyset )
| ( SV203 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1206,plain,
! [SV204: $i] :
( ( ~ ( singleton @ SV204 )
| ! [SY535: $i] :
( ~ ( in @ SY535 @ SV204 )
| ( ( setunion @ SV204 )
= SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1207,plain,
! [SV205: $i] :
( ( ! [SY536: $i] :
( ~ ( in @ SY536 @ ( powerset @ SV205 ) )
| ! [SY537: $i] :
( ~ ( in @ SY537 @ SV205 )
| ~ ( in @ SY537 @ SY536 )
| ( in @ SY537 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SY536 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1208,plain,
! [SV206: $i] :
( ( ! [SY538: $i] :
( ( ksnd @ ( kpair @ SV206 @ SY538 ) )
= SY538 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(1209,plain,
! [SV207: $i] :
( ( ! [SY539: $i > $o,SY540: $i] :
( ~ ( in @ SY540 @ SV207 )
| ~ ( SY539 @ SY540 )
| ( in @ SY540
@ ( dsetconstr @ SV207
@ ^ [SX3: $i] : ( SY539 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1210,plain,
! [SV208: $i] :
( ( ! [SY542: $i,SY543: $i > $i > $o,SY544: $i,SY545: $i] :
( ~ ( in @ ( kpair @ SY544 @ SY545 )
@ ( dpsetconstr @ SV208 @ SY542
@ ^ [SX5: $i,SX6: $i] : ( SY543 @ SX5 @ SX6 ) ) )
| ( in @ SY545 @ SY542 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1211,plain,
! [SV209: $i] :
( ( ! [SY548: $i] :
( ~ ( breln1 @ SV209 @ SY548 )
| ! [SY549: $i] :
( ~ ( breln1 @ SV209 @ SY549 )
| ~ ! [SY550: $i] :
( ~ ( in @ SY550 @ SV209 )
| ! [SY551: $i] :
( ~ ( in @ SY551 @ SV209 )
| ~ ( in @ ( kpair @ SY550 @ SY551 ) @ SY548 )
| ( in @ ( kpair @ SY550 @ SY551 ) @ SY549 ) ) )
| ( subset @ SY548 @ SY549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1212,plain,
! [SV210: $i] :
( ( ! [SY552: $i] :
( ~ ( in @ SY552 @ SV210 )
| ( in @ SY552 @ ( powerset @ ( setunion @ SV210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1213,plain,
! [SV211: $i] :
( ( ! [SY553: $i] :
( ~ ( in @ SY553 @ ( powerset @ SV211 ) )
| ! [SY554: $i] :
( ~ ( in @ SY554 @ ( powerset @ SV211 ) )
| ! [SY555: $i] :
( ~ ( in @ SY555 @ ( powerset @ SV211 ) )
| ! [SY556: $i] :
( ~ ( in @ SY556 @ SV211 )
| ~ ( in @ SY556 @ ( binintersect @ SY553 @ SY554 ) )
| ( in @ SY556 @ ( binunion @ SY553 @ SY555 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1214,plain,
! [SV212: $i] :
( ( ~ ! [SY557: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SY557 )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY558 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY560: $i,SY561: $i] :
( ~ ~ ( ~ ( in @ SY560 @ SV212 )
| ~ ( in @ SY561 @ SV212 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY557 )
| ~ ( ~ ( ~ ( in @ SY560 @ SX4 )
| ( in @ SY561 @ SX4 ) )
| ~ ( ~ ( in @ SY561 @ SX4 )
| ( in @ SY560 @ SX4 ) ) ) )
| ( SY560 = SY561 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY557 )
| ~ ( in @ SX3 @ SY557 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY567: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY567 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY567 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY557 )
| ~ ( in @ SX4 @ SY567 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY567 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY557 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1215,plain,
! [SV213: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( in @ SY576 @ ( funcSet @ SV213 @ SY575 ) )
| ! [SY577: $i] :
( ~ ( in @ SY577 @ SV213 )
| ( ( ap @ SV213 @ SY575 @ SY576 @ SY577 )
= ( ap @ SV213 @ SY575 @ SY576 @ SY577 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1216,plain,
! [SV214: $i] :
( ( ! [SY578: $o,SY579: $i] :
( ~ ( in @ SY579 @ SV214 )
| ! [SY580: $i] :
( ~ ( in @ SY580 @ SV214 )
| ( in @ ( if @ SV214 @ SY578 @ SY579 @ SY580 ) @ ( setadjoin @ SY579 @ ( setadjoin @ SY580 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1217,plain,
! [SV215: $i] :
( ( ! [SY581: $i,SY582: $i > $i > $o] :
( ~ ! [SY583: $i] :
( ~ ( in @ SY583 @ SV215 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY581 )
| ~ ( SY582 @ SY583 @ SX4 ) ) )
| ! [SY585: $i] :
( ~ ( in @ SY585 @ ( breln1Set @ SY581 ) )
| ~ ( reflwellordering @ SY581 @ SY585 )
| ! [SY586: $i] :
( ~ ( in @ SY586 @ SV215 )
| ( singleton
@ ( dsetconstr @ SY581
@ ^ [SX5: $i] :
~ ( ~ ( SY582 @ SY586 @ SX5 )
| ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SY581 )
| ~ ( SY582 @ SY586 @ SX6 )
| ( in @ ( kpair @ SX5 @ SX6 ) @ SY585 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1218,plain,
! [SV216: $i] :
( ( ! [SY589: $i] :
( ~ ( subset @ SV216 @ SY589 )
| ( in @ SV216 @ ( powerset @ SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1219,plain,
! [SV217: $i > $o] :
( ( ! [SY590: $i] :
( ~ ( in @ SY590 @ emptyset )
| ( SV217 @ SY590 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1220,plain,
! [SV218: $i] :
( ( in @ emptyset @ ( powerset @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1221,plain,
! [SV219: $i] :
( ( subset @ SV219 @ ( setunion @ ( setadjoin @ SV219 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1222,plain,
! [SV220: $i] :
( ( ! [SY591: $i,SY592: $i] :
( ~ ( in @ SY592 @ ( cartprod @ SV220 @ SY591 ) )
| ( in @ ( kfst @ SY592 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1223,plain,
! [SV221: $i] :
( ( ! [SY593: $i] :
( ~ ( subset @ SV221 @ SY593 )
| ( ( setminus @ SV221 @ SY593 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(1224,plain,
! [SV222: $i] :
( ( ! [SY594: $i,SY595: $i] :
( ( ( setadjoin @ SV222 @ ( setadjoin @ SY594 @ emptyset ) )
!= ( setadjoin @ SY595 @ emptyset ) )
| ( SV222 = SY594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1225,plain,
! [SV223: $i] :
( ( ! [SY596: $i] : ( subset @ SY596 @ ( binunion @ SV223 @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1226,plain,
! [SV224: $i] :
( ( ( setunion @ ( setadjoin @ SV224 @ emptyset ) )
= SV224 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(1227,plain,
! [SV225: $i] :
( ( ! [SY597: $i,SY598: $i] :
( ~ ( func @ SV225 @ SY597 @ SY598 )
| ! [SY599: $i] :
( ~ ( in @ SY599 @ SV225 )
| ! [SY600: $i] :
( ~ ( in @ SY600 @ SY597 )
| ~ ( in @ ( kpair @ SY599 @ SY600 ) @ SY598 )
| ( ( ap @ SV225 @ SY597 @ SY598 @ SY599 )
= SY600 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1228,plain,
! [SV226: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV226 )
| ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) )
| ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1229,plain,
! [SV227: $i] :
( ( ! [SY603: $i] :
( ~ ( in @ SY603 @ ( powerset @ SV227 ) )
| ! [SY604: $i] :
( ~ ( in @ SY604 @ ( powerset @ SV227 ) )
| ~ ( subset @ SY603 @ ( setminus @ SV227 @ SY604 ) )
| ( subset @ SY604 @ ( setminus @ SV227 @ SY603 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(1230,plain,
! [SV228: $i] :
( ( ~ ~ ! [SY605: $i] :
~ ( in @ SY605 @ SV228 )
| ( SV228 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1231,plain,
! [SV229: $i] :
( ( ! [SY606: $i] :
( ~ ( in @ SY606 @ ( powerset @ SV229 ) )
| ! [SY607: $i] :
( ~ ( in @ SY607 @ ( powerset @ SV229 ) )
| ( in @ ( setminus @ SV229 @ ( binunion @ SY606 @ SY607 ) ) @ ( powerset @ ( setminus @ SV229 @ SY606 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(1232,plain,
! [SV230: $i] :
( ( ! [SY608: $i] :
( ~ ! [SY609: $i] :
( ~ ( in @ SY609 @ SV230 )
| ( in @ SY609 @ SY608 ) )
| ~ ! [SY610: $i] :
( ~ ( in @ SY610 @ SY608 )
| ( in @ SY610 @ SV230 ) )
| ( SV230 = SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1233,plain,
! [SV231: $i] :
( ( ! [SY611: $i] :
( ~ ( in @ SY611 @ ( powerset @ SV231 ) )
| ( subset @ ( setminus @ SV231 @ ( setminus @ SV231 @ SY611 ) ) @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1234,plain,
! [SV232: $i] :
( ( ! [SY612: $i > $o] :
( ~ ~ ! [SY613: $i] :
( ~ ( in @ SY613 @ SV232 )
| ( SY612 @ SY613 ) )
| ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV232 )
| ~ ~ ( SY612 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1235,plain,
! [SV233: $i] :
( ( ! [SY615: $i,SY616: $i] :
( ~ ( in @ SY616 @ ( funcSet @ SV233 @ SY615 ) )
| ( func @ SV233 @ SY615 @ SY616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1236,plain,
! [SV234: $i] :
( ( ! [SY617: $i] :
( ~ ( breln1 @ SV234 @ SY617 )
| ! [SY618: $i] :
( ~ ( breln1 @ SV234 @ SY618 )
| ! [SY619: $i] :
( ~ ( in @ SY619 @ SV234 )
| ! [SY620: $i] :
( ~ ( in @ SY620 @ SV234 )
| ! [SY621: $i] :
( ~ ( in @ SY621 @ SV234 )
| ~ ( in @ ( kpair @ SY619 @ SY621 ) @ SY617 )
| ~ ( in @ ( kpair @ SY621 @ SY620 ) @ SY618 )
| ( in @ ( kpair @ SY619 @ SY620 ) @ ( breln1compset @ SV234 @ SY617 @ SY618 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1237,plain,
! [SV235: $i] :
( ( ! [SY622: $i] :
( ~ ~ ~ ! [SY623: $i] :
~ ~ ( ~ ( in @ SY623 @ SV235 )
| ~ ( in @ SY623 @ SY622 ) )
| ( ( binintersect @ SV235 @ SY622 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1238,plain,
! [SV236: $i] :
( ( ! [SY624: $i,SY625: $i] :
( ~ ( in @ SY625 @ SV236 )
| ~ ( in @ SY625 @ SY624 )
| ( in @ SY625 @ ( binintersect @ SV236 @ SY624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1239,plain,
! [SV237: $i] :
( ( ! [SY626: $i,SY627: $i,SY628: $i] :
( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SY626 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY627 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY627 @ ( setadjoin @ SY628 @ emptyset ) ) @ emptyset ) ) )
| ( SV237 = SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1240,plain,
! [SV238: $i] :
( ( ! [SY629: $i,SY630: $i > $i > $o,SY631: $i] :
( ~ ( in @ SY631 @ SV238 )
| ! [SY632: $i] :
( ~ ( in @ SY632 @ SY629 )
| ~ ( in @ ( kpair @ SY631 @ SY632 )
@ ( dpsetconstr @ SV238 @ SY629
@ ^ [SX5: $i,SX6: $i] : ( SY630 @ SX5 @ SX6 ) ) )
| ( SY630 @ SY631 @ SY632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1241,plain,
! [SV239: $i] :
( ( ! [SY635: $i,SY636: $i] :
( ~ ( in @ SY636 @ SV239 )
| ! [SY637: $i] :
( ~ ( in @ SY637 @ SY635 )
| ( in @ ( setadjoin @ SY636 @ ( setadjoin @ SY637 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SY635 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1242,plain,
! [SV240: $i] :
( ( ! [SY638: $i] :
( ~ ( in @ SY638 @ ( powerset @ SV240 ) )
| ! [SY639: $i] :
( ~ ( in @ SY639 @ ( powerset @ SV240 ) )
| ( in @ ( setminus @ SV240 @ ( binunion @ SY638 @ SY639 ) ) @ ( powerset @ ( setminus @ SV240 @ SY638 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1243,plain,
! [SV241: $i] :
( ( ! [SY640: $o,SY641: $i] :
( ~ ( in @ SY641 @ SV241 )
| ! [SY642: $i] :
( ~ ( in @ SY642 @ SV241 )
| ( in @ ( if @ SV241 @ SY640 @ SY641 @ SY642 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1244,plain,
! [SV242: $i] :
( ( ! [SY643: $i > $i > $o] :
( breln1 @ SV242
@ ( dpsetconstr @ SV242 @ SV242
@ ^ [SX2: $i,SX3: $i] : ( SY643 @ SX2 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1245,plain,
! [SV243: $i] :
( ( ! [SY646: $i,SY647: $i] :
( ~ ( func @ SV243 @ SY646 @ SY647 )
| ( ( lam @ SV243 @ SY646
@ ^ [SY648: $i] : ( ap @ SV243 @ SY646 @ SY647 @ SY648 ) )
= SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1246,plain,
! [SV244: $i] :
( ( ! [SY649: $i > $o] :
( subset
@ ( dsetconstr @ SV244
@ ^ [SX2: $i] : ( SY649 @ SX2 ) )
@ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1247,plain,
! [SV245: $i] :
( ( ! [SY651: $i > $o] :
( ~ ! [SY652: $i] :
( ~ ( in @ SY652 @ SV245 )
| ! [SY653: $i] :
( ~ ( in @ SY653 @ SV245 )
| ~ ( SY651 @ SY652 )
| ~ ( SY651 @ SY653 )
| ( SY652 = SY653 ) ) )
| ~ ~ ! [SY654: $i] :
~ ~ ( ~ ( in @ SY654 @ SV245 )
| ~ ( SY651 @ SY654 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SX2: $i] : ( SY651 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1248,plain,
! [SV246: $i] :
( ( ! [SY656: $i,SY657: $i,SY658: $i] :
( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SY656 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY657 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY657 @ ( setadjoin @ SY658 @ emptyset ) ) @ emptyset ) ) )
| ( SY656 = SY658 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(1249,plain,
! [SV247: $i] :
( ( ! [SY659: $i] :
( ~ ( subset @ SV247 @ SY659 )
| ( subset @ ( powerset @ SV247 ) @ ( powerset @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1250,plain,
! [SV248: $i] :
( ( ! [SY660: $i] :
~ ( ~ ( ~ ( in @ SY660 @ ( powerset @ SV248 ) )
| ! [SY661: $i] :
( ~ ( in @ SY661 @ SY660 )
| ( in @ SY661 @ SV248 ) ) )
| ~ ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SY660 )
| ( in @ SY662 @ SV248 ) )
| ( in @ SY660 @ ( powerset @ SV248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1251,plain,
! [SV249: $i] :
( ( ~ ( in @ SV249 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1252,plain,
! [SV250: $i] :
( ( ! [SY663: $i,SY664: $i] :
( ~ ( in @ SY664 @ ( funcSet @ SV250 @ SY663 ) )
| ! [SY665: $i] :
( ~ ( in @ SY665 @ SV250 )
| ! [SY666: $i] :
( ~ ( in @ SY666 @ SY663 )
| ~ ( in @ ( kpair @ SY665 @ SY666 ) @ SY664 )
| ( ( ap @ SV250 @ SY663 @ SY664 @ SY665 )
= SY666 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1253,plain,
! [SV251: $i] :
( ( ! [SY667: $i] :
( ~ ( breln1 @ SV251 @ SY667 )
| ! [SY668: $i] :
( ~ ( in @ SY668 @ SV251 )
| ! [SY669: $i] :
( ~ ( in @ SY669 @ SV251 )
| ~ ( in @ ( kpair @ SY668 @ SY669 ) @ SY667 )
| ( in @ ( kpair @ SY669 @ SY668 ) @ ( breln1invset @ SV251 @ SY667 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1254,plain,
! [SV252: $i] :
( ( ! [SY670: $i] :
( ~ ( breln1 @ SV252 @ SY670 )
| ! [SY671: $i] :
( ~ ( in @ SY671 @ SV252 )
| ! [SY672: $i] :
( ~ ( in @ SY672 @ SV252 )
| ~ ( in @ ( kpair @ SY672 @ SY671 ) @ ( breln1invset @ SV252 @ SY670 ) )
| ( in @ ( kpair @ SY671 @ SY672 ) @ SY670 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1255,plain,
! [SV253: $o] :
( ( ! [SY673: $i] :
( ~ ( in @ SY673 @ ( prop2set @ SV253 ) )
| SV253 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1256,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1257,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[924]) ).
thf(1258,plain,
! [SV254: $i] :
( ( ! [SY674: $i,SY675: $i] :
( ~ ( in @ SY675 @ ( binintersect @ SV254 @ SY674 ) )
| ( in @ SY675 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1259,plain,
! [SV255: $i] :
( ( ! [SY676: $i] :
( ~ ( breln1 @ SV255 @ SY676 )
| ! [SY677: $i] :
( ~ ( breln1 @ SV255 @ SY677 )
| ! [SY678: $i] :
( ~ ( in @ SY678 @ SV255 )
| ! [SY679: $i] :
( ~ ( in @ SY679 @ SV255 )
| ~ ( in @ ( kpair @ SY678 @ SY679 ) @ ( binunion @ SY676 @ SY677 ) )
| ! [SX5: $o] :
( ~ ( ~ ( in @ ( kpair @ SY678 @ SY679 ) @ SY676 )
| SX5 )
| ~ ( ~ ( in @ ( kpair @ SY678 @ SY679 ) @ SY677 )
| SX5 )
| SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1260,plain,
! [SV256: $i] :
( ( ! [SY681: $i,SY682: $i] :
( ~ ( in @ SY682 @ SY681 )
| ( in @ SY682 @ ( setadjoin @ SV256 @ SY681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1261,plain,
! [SV257: $i] :
( ( ! [SY683: $i,SY684: $i] :
( ~ ( in @ SY684 @ SV257 )
| ! [SY685: $i] :
( ~ ( in @ SY685 @ SY683 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY684 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY684 @ ( setadjoin @ SY685 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SY683 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1262,plain,
! [SV258: $i] :
( ( ! [SY686: $i] :
( ~ ( in @ SY686 @ ( powerset @ SV258 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ ( powerset @ SV258 ) )
| ! [SY688: $i] :
( ~ ( in @ SY688 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SY686 @ SY687 ) @ ( powerset @ ( binintersect @ ( binunion @ SY686 @ SY688 ) @ ( binunion @ SY687 @ SY688 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1263,plain,
! [SV259: $i] :
( ( ! [SY689: $i,SY690: $i] :
( ~ ( in @ SY690 @ ( surjFuncSet @ SV259 @ SY689 ) )
| ( in @ SY690 @ ( funcSet @ SV259 @ SY689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1264,plain,
! [SV260: $i > $o] :
( ( ! [SY691: $i > $o] :
( ~ ! [SY692: $i,SY693: $i] :
( ( SY692 != SY693 )
| ~ ( ~ ( ~ ( SV260 @ SY692 )
| ( SY691 @ SY693 ) )
| ~ ( ~ ( SY691 @ SY693 )
| ( SV260 @ SY692 ) ) ) )
| ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY691 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY691 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SX2: $i] : ( SY691 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1265,plain,
! [SV261: $i] :
( ( ! [SY700: $i] :
( ~ ( in @ SY700 @ ( funcSet @ SV261 @ ( powerset @ SV261 ) ) )
| ~ ( surjective @ SV261 @ ( powerset @ SV261 ) @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1266,plain,
! [SV262: $i] :
( ( ~ ( in @ SV262 @ omega )
| ( ( omegaS @ SV262 )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1267,plain,
! [SV263: $i] :
( ( ! [SY701: $i] :
( ~ ( in @ SY701 @ ( powerset @ SV263 ) )
| ! [SY702: $i] :
( ~ ( in @ SY702 @ ( powerset @ SV263 ) )
| ! [SY703: $i] :
( ~ ( in @ SY703 @ ( powerset @ SV263 ) )
| ~ ( subset @ SY701 @ SY703 )
| ( subset @ ( binintersect @ SY701 @ SY702 ) @ SY703 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1268,plain,
! [SV264: $i] :
( ( ! [SY704: $i] :
( ~ ( breln1 @ SV264 @ SY704 )
| ! [SY705: $i] :
( ~ ( breln1 @ SV264 @ SY705 )
| ~ ! [SY706: $i] :
( ~ ( in @ SY706 @ SV264 )
| ! [SY707: $i] :
( ~ ( in @ SY707 @ SV264 )
| ~ ( in @ ( kpair @ SY706 @ SY707 ) @ SY704 )
| ( in @ ( kpair @ SY706 @ SY707 ) @ SY705 ) ) )
| ~ ! [SY708: $i] :
( ~ ( in @ SY708 @ SV264 )
| ! [SY709: $i] :
( ~ ( in @ SY709 @ SV264 )
| ~ ( in @ ( kpair @ SY708 @ SY709 ) @ SY705 )
| ( in @ ( kpair @ SY708 @ SY709 ) @ SY704 ) ) )
| ( SY704 = SY705 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1269,plain,
! [SV265: $i] :
( ( ! [SY710: $i,SY711: $i] :
( ~ ( in @ SY711 @ SV265 )
| ~ ( in @ SY711 @ SY710 )
| ~ ( in @ SY711 @ ( symdiff @ SV265 @ SY710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1270,plain,
! [SV266: $i] :
( ( ! [SY712: $i,SY713: $i] :
( ~ ( in @ SY713 @ ( cartprod @ SV266 @ SY712 ) )
| ( ( kpair @ ( kfst @ SY713 ) @ ( ksnd @ SY713 ) )
= SY713 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1271,plain,
! [SV267: $i] :
( ( ! [SY714: $i] : ( iskpair @ ( kpair @ SV267 @ SY714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1272,plain,
! [SV268: $i] :
( ( ! [SY715: $i] :
( ~ ( in @ SY715 @ ( powerset @ SV268 ) )
| ! [SY716: $i] :
( ~ ( in @ SY716 @ SV268 )
| ~ ( in @ SY716 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SY715 ) ) )
| ( in @ SY716 @ SY715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1273,plain,
! [SV269: $i] :
( ( ! [SY717: $i > $o] :
( ~ ~ ! [SY718: $i] :
~ ~ ( ~ ( in @ SY718 @ SV269 )
| ~ ~ ( SY717 @ SY718 ) )
| ~ ! [SY719: $i] :
( ~ ( in @ SY719 @ SV269 )
| ( SY717 @ SY719 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1274,plain,
! [SV270: $i] :
( ( ! [SY720: $i,SY721: $i] :
( ~ ~ ( in @ SY721 @ ( setminus @ SV270 @ SY720 ) )
| ~ ~ ( in @ SY721 @ SY720 )
| ~ ( in @ SY721 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1275,plain,
! [SV271: $i] :
( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ ( powerset @ SV271 ) )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ ( powerset @ SV271 ) )
| ! [SY724: $i] :
( ~ ( in @ SY724 @ SV271 )
| ~ ( in @ SY724 @ ( setminus @ SV271 @ ( binunion @ SY722 @ SY723 ) ) )
| ( in @ SY724 @ ( setminus @ SV271 @ SY723 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1276,plain,
! [SV272: $i] :
( ( ~ ! [SY725: $i] :
~ ( in @ SY725 @ SV272 )
| ( SV272 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1277,plain,
! [SV273: $i] :
( ( ! [SY726: $i] :
( ~ ( subset @ SV273 @ SY726 )
| ( ( binintersect @ SV273 @ SY726 )
= SV273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1278,plain,
! [SV274: $i] :
( ( ! [SY727: $i] :
( ~ ( breln1 @ SV274 @ SY727 )
| ! [SY728: $i] :
( ~ ( breln1 @ SV274 @ SY728 )
| ! [SY729: $i] :
( ~ ( in @ SY729 @ SV274 )
| ! [SY730: $i] :
( ~ ( in @ SY730 @ SV274 )
| ~ ( in @ ( kpair @ SY729 @ SY730 ) @ SY727 )
| ( in @ ( kpair @ SY729 @ SY730 ) @ ( binunion @ SY727 @ SY728 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1279,plain,
! [SV275: $i] :
( ( ! [SY731: $i,SY732: $i] :
( ~ ( in @ SY732 @ ( binintersect @ SV275 @ SY731 ) )
| ( in @ SY732 @ SY731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1280,plain,
! [SV276: $i] :
( ( ! [SY733: $i,SY734: $i] :
( ~ ~ ( in @ SY734 @ SV276 )
| ~ ~ ( in @ SY734 @ SY733 )
| ~ ( in @ SY734 @ ( symdiff @ SV276 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1281,plain,
! [SV277: $i] :
( ( ! [SY735: $i] : ( subset @ SY735 @ ( setadjoin @ SV277 @ SY735 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1282,plain,
! [SV278: $i] :
( ( ! [SY736: $i,SY737: $i] :
( ~ ( in @ SY737 @ SV278 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY736 )
| ( ( kfst @ ( kpair @ SY737 @ SX3 ) )
= SY737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1283,plain,
! [SV279: $i] :
( ( ! [SY739: $i] :
( ~ ( subset @ SY739 @ SV279 )
| ( ( binintersect @ SV279 @ SY739 )
= SY739 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1284,plain,
! [SV280: $i] :
( ( ! [SY740: $i,SY741: $i] :
( ~ ( in @ SY741 @ SY740 )
| ( in @ SY741 @ ( binunion @ SV280 @ SY740 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1285,plain,
! [SV281: $i] :
( ( ~ ( ( SV281 != emptyset ) )
| ~ ! [SY742: $i] :
~ ~ ( ~ ( in @ SY742 @ SV281 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1286,plain,
! [SV282: $i] :
( ( ~ ( iskpair @ SV282 )
| ( ( kpair @ ( kfst @ SV282 ) @ ( ksnd @ SV282 ) )
= SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1287,plain,
! [SV283: $i] :
( ( ! [SY743: $i] :
( ( SV283 != SY743 )
| ! [SY744: $i > $o,SY745: $i > $o] :
( ~ ! [SY746: $i] :
( ~ ( in @ SY746 @ SV283 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY743 )
| ( SY746 != SX5 )
| ~ ( ~ ( ~ ( SY744 @ SY746 )
| ( SY745 @ SX5 ) )
| ~ ( ~ ( SY745 @ SX5 )
| ( SY744 @ SY746 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SX4: $i] : ( SY744 @ SX4 ) )
= ( dsetconstr @ SY743
@ ^ [SX4: $i] : ( SY745 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1288,plain,
! [SV284: $i > $o] :
( ( ~ ~ ! [SY750: $i] :
~ ~ ( ~ ( SV284 @ SY750 )
| ~ ! [SY751: $i] :
( ~ ( SV284 @ SY751 )
| ( SY750 = SY751 ) ) )
| ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1289,plain,
! [SV285: $i] :
( ( ! [SY754: $i] :
( ~ ( in @ SY754 @ ( powerset @ SV285 ) )
| ! [SY755: $i] :
( ~ ( in @ SY755 @ ( powerset @ SV285 ) )
| ! [SY756: $i] :
( ~ ( in @ SY756 @ SV285 )
| ~ ( in @ SY756 @ ( setminus @ SV285 @ SY754 ) )
| ~ ( in @ SY756 @ ( binintersect @ SY754 @ SY755 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1290,plain,
! [SV286: $i] :
( ( ! [SY757: $i > $o,SY758: $i] :
( ~ ( in @ SY758
@ ( dsetconstr @ SV286
@ ^ [SX3: $i] : ( SY757 @ SX3 ) ) )
| ( SY757 @ SY758 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1291,plain,
! [SV287: $i] :
( ( ! [SY760: $i,SY761: $i,SY762: $o] :
( ~ ( in @ SY761 @ ( binunion @ SV287 @ SY760 ) )
| ~ ( ~ ( in @ SY761 @ SV287 )
| SY762 )
| ~ ( ~ ( in @ SY761 @ SY760 )
| SY762 )
| SY762 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1292,plain,
! [SV288: $i] :
( ( ! [SY763: $i] :
( ~ ( breln1 @ SV288 @ SY763 )
| ! [SY764: $i] :
( ~ ( breln1 @ SV288 @ SY764 )
| ! [SY765: $i] :
( ~ ( in @ SY765 @ SV288 )
| ! [SY766: $i] :
( ~ ( in @ SY766 @ SV288 )
| ~ ( in @ ( kpair @ SY765 @ SY766 ) @ SY764 )
| ( in @ ( kpair @ SY765 @ SY766 ) @ ( binunion @ SY763 @ SY764 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1293,plain,
! [SV289: $i] :
( ( ! [SY767: $i] :
( ( SV289 != SY767 )
| ( ( powerset @ SV289 )
= ( powerset @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1294,plain,
! [SV290: $i] :
( ( ! [SY768: $i,SY769: $i > $i > $o] :
( breln @ SV290 @ SY768
@ ( dpsetconstr @ SV290 @ SY768
@ ^ [SX3: $i,SX4: $i] : ( SY769 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1295,plain,
! [SV291: $i] :
( ( ! [SY772: $o,SY773: $i] :
( ~ ( in @ SY773 @ SV291 )
| ! [SY774: $i] :
( ~ ( in @ SY774 @ SV291 )
| ~ ~ SY772
| ( ( if @ SV291 @ SY772 @ SY773 @ SY774 )
= SY774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1296,plain,
! [SV292: $i] :
( ( ! [SY775: $i] : ( in @ SV292 @ ( setadjoin @ SV292 @ ( setadjoin @ SY775 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1297,plain,
! [SV293: $i] :
( ( subset @ SV293 @ SV293 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1298,plain,
! [SV294: $i] :
( ( ! [SY776: $i] :
( ~ ( breln1 @ SV294 @ SY776 )
| ! [SY777: $i] :
( ~ ( breln1 @ SV294 @ SY777 )
| ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SY776 @ SY777 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SY777 ) @ ( breln1invset @ SV294 @ SY776 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1299,plain,
! [SV295: $i] :
( ( ! [SY778: $i] : ( subset @ SV295 @ ( binunion @ SV295 @ SY778 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1300,plain,
! [SV296: $i] :
( ( ! [SY779: $i] :
( ~ ( in @ SY779 @ ( powerset @ SV296 ) )
| ! [SY780: $i] :
( ~ ( in @ SY780 @ ( powerset @ SV296 ) )
| ~ ! [SY781: $i] :
( ~ ( in @ SY781 @ SV296 )
| ~ ( in @ SY781 @ SY779 )
| ( in @ SY781 @ SY780 ) )
| ( in @ SY779 @ ( powerset @ SY780 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1301,plain,
! [SV297: $i] :
( ( ! [SY782: $i] :
( ~ ( breln1 @ SV297 @ SY782 )
| ! [SY783: $i] :
( ~ ( breln1 @ SV297 @ SY783 )
| ! [SY784: $i] :
( ~ ( in @ SY784 @ SV297 )
| ! [SY785: $i] :
( ~ ( in @ SY785 @ SV297 )
| ~ ( ( in @ ( kpair @ SY784 @ SY785 ) @ SY782 )
| ( in @ ( kpair @ SY784 @ SY785 ) @ SY783 ) )
| ( in @ ( kpair @ SY784 @ SY785 ) @ ( binunion @ SY782 @ SY783 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1302,plain,
! [SV298: $i] :
( ( ! [SY786: $i,SY787: $i] :
( ~ ( breln @ SV298 @ SY786 @ SY787 )
| ! [SY788: $i] :
( ~ ( breln @ SV298 @ SY786 @ SY788 )
| ~ ! [SY789: $i] :
( ~ ( in @ SY789 @ SV298 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY786 )
| ~ ( in @ ( kpair @ SY789 @ SX5 ) @ SY787 )
| ( in @ ( kpair @ SY789 @ SX5 ) @ SY788 ) ) )
| ( subset @ SY787 @ SY788 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1303,plain,
! [SV299: $i] :
( ( ! [SY791: $i] :
( ~ ( in @ SY791 @ ( powerset @ SV299 ) )
| ! [SY792: $i] :
( ~ ( in @ SY792 @ ( powerset @ SV299 ) )
| ! [SY793: $i] :
( ~ ( in @ SY793 @ SV299 )
| ~ ( in @ SY793 @ ( setminus @ SV299 @ ( binunion @ SY791 @ SY792 ) ) )
| ( in @ SY793 @ ( binintersect @ ( setminus @ SV299 @ SY791 ) @ ( setminus @ SV299 @ SY792 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1304,plain,
! [SV300: $i > $o] :
( ( ~ ~ ! [SY794: $i] :
~ ~ ( ~ ( SV300 @ SY794 )
| ~ ! [SY795: $i] :
( ~ ( SV300 @ SY795 )
| ( SY794 = SY795 ) ) )
| ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1305,plain,
! [SV301: $i] :
( ( ! [SY797: $i] :
( ~ ( in @ SY797 @ ( powerset @ SV301 ) )
| ! [SY798: $i] :
( ~ ( in @ SY798 @ ( powerset @ SV301 ) )
| ! [SY799: $i] :
( ~ ( in @ SY799 @ SV301 )
| ~ ( in @ SY799 @ ( setminus @ SV301 @ SY797 ) )
| ( in @ SY799 @ ( setminus @ SV301 @ ( binintersect @ SY797 @ SY798 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1306,plain,
! [SV302: $i] :
( ( ! [SY800: $i] :
( ~ ( in @ SY800 @ ( powerset @ SV302 ) )
| ! [SY801: $i] :
( ~ ( in @ SY801 @ ( powerset @ SV302 ) )
| ! [SY802: $i] :
( ~ ( in @ SY802 @ SV302 )
| ~ ( in @ SY802 @ ( setminus @ SV302 @ ( binunion @ SY800 @ SY801 ) ) )
| ( in @ SY802 @ ( setminus @ SV302 @ SY800 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1307,plain,
! [SV303: $i] :
( ( ! [SY803: $i] :
( ( ( binintersect @ SV303 @ SY803 )
!= SV303 )
| ( subset @ SV303 @ SY803 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1308,plain,
! [SV304: $i] :
( ( ~ ( ( SV304 != emptyset ) )
| ~ ! [SY804: $i] :
~ ( in @ SY804 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1309,plain,
! [SV305: $i] :
( ( ! [SY805: $i] :
( ~ ( in @ SY805 @ ( powerset @ SV305 ) )
| ! [SY806: $i] :
( ~ ( in @ SY806 @ ( powerset @ SV305 ) )
| ! [SY807: $i] :
( ~ ( in @ SY807 @ ( binintersect @ SY805 @ SY806 ) )
| ( in @ SY807 @ SV305 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1310,plain,
! [SV306: $i] :
( ( ! [SY808: $i,SY809: $i] :
( ~ ( in @ SY808 @ SY809 )
| ~ ( in @ SY809 @ SV306 )
| ( in @ SY808 @ ( setunion @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1311,plain,
! [SV307: $i] :
( ( ! [SY810: $i] :
( ~ ( in @ SY810 @ ( powerset @ SV307 ) )
| ! [SY811: $i] :
( ~ ( in @ SY811 @ SV307 )
| ~ ( in @ SY811 @ SY810 )
| ~ ( in @ SY811 @ ( setminus @ SV307 @ SY810 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1312,plain,
! [SV308: $i] :
( ( ! [SY812: $i] :
( ~ ( in @ SY812 @ ( powerset @ SV308 ) )
| ! [SY813: $i] :
( ~ ( in @ SY813 @ ( powerset @ SV308 ) )
| ( ( setminus @ SV308 @ ( binunion @ SY812 @ SY813 ) )
= ( binintersect @ ( setminus @ SV308 @ SY812 ) @ ( setminus @ SV308 @ SY813 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[979]) ).
thf(1313,plain,
! [SV309: $i] :
( ( ! [SY814: $i,SY815: $i] :
( ~ ( in @ SY815 @ ( setadjoin @ SV309 @ SY814 ) )
| ! [SY816: $o] :
( ~ ( ( SY815 != SV309 )
| SY816 )
| ~ ( ~ ( in @ SY815 @ SY814 )
| SY816 )
| SY816 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1314,plain,
! [SV310: $i] :
( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ ( powerset @ SV310 ) )
| ! [SY818: $i] :
( ~ ( in @ SY818 @ ( powerset @ SV310 ) )
| ~ ! [SY819: $i] :
( ~ ( in @ SY819 @ SV310 )
| ~ ( in @ SY819 @ SY817 )
| ( in @ SY819 @ SY818 ) )
| ( subset @ SY817 @ SY818 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1315,plain,
! [SV311: $i] :
( ( ! [SY820: $i] :
( ~ ( in @ SV311 @ ( setadjoin @ SY820 @ emptyset ) )
| ( in @ SY820 @ ( setadjoin @ SV311 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1316,plain,
! [SV312: $i] :
( ( ! [SY821: $i,SY822: $i] :
( ~ ( in @ SY822 @ ( binunion @ SV312 @ SY821 ) )
| ( in @ SY822 @ SV312 )
| ( in @ SY822 @ SY821 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1317,plain,
! [SV313: $i] :
( ( ! [SY823: $i,SY824: $i] :
( ~ ( in @ SY824 @ SV313 )
| ! [SY825: $i] :
( ~ ( in @ SY825 @ SY823 )
| ( in @ ( setadjoin @ ( setadjoin @ SY824 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY824 @ ( setadjoin @ SY825 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SY823 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1318,plain,
! [SV314: $i] :
( ( ! [SY826: $i,SY827: $i > $i > $o,SY828: $i] :
( ~ ( in @ SY828 @ SV314 )
| ! [SY829: $i] :
( ~ ( in @ SY829 @ SY826 )
| ~ ( SY827 @ SY828 @ SY829 )
| ( in @ ( kpair @ SY828 @ SY829 )
@ ( dpsetconstr @ SV314 @ SY826
@ ^ [SX5: $i,SX6: $i] : ( SY827 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1319,plain,
! [SV315: $i] :
( ( ! [SY832: $i] :
( ~ ( in @ SY832 @ ( powerset @ SV315 ) )
| ! [SY833: $i] :
( ~ ( in @ SY833 @ ( powerset @ SV315 ) )
| ! [SY834: $o,SY835: $i] :
( ~ ( in @ SY835 @ SV315 )
| ~ ( in @ SY835 @ ( binunion @ SY832 @ SY833 ) )
| ~ ( ~ ( in @ SY835 @ SY832 )
| SY834 )
| ~ ( ~ ( in @ SY835 @ SY833 )
| SY834 )
| SY834 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1320,plain,
! [SV316: $i] :
( ( ! [SY836: $i] :
( ~ ( in @ SV316 @ ( setadjoin @ SY836 @ emptyset ) )
| ( SV316 = SY836 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1321,plain,
! [SV317: $i] :
( ( ! [SY837: $i] :
( ~ ( in @ SY837 @ ( powerset @ SV317 ) )
| ! [SY838: $i] :
( ~ ( in @ SY838 @ ( powerset @ SV317 ) )
| ! [SY839: $i] :
( ~ ( in @ SY839 @ ( powerset @ SV317 ) )
| ! [SY840: $i] :
( ~ ( in @ SY840 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SY837 @ SY838 ) @ ( binunion @ SY839 @ SY840 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SY837 ) @ ( setminus @ SV317 @ SY838 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY839 ) @ ( setminus @ SV317 @ SY840 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1322,plain,
! [SV318: $i] :
( ( ! [SY841: $i] :
( ~ ( in @ SY841 @ ( powerset @ SV318 ) )
| ! [SY842: $i] :
( ~ ( in @ SY842 @ ( powerset @ SV318 ) )
| ! [SY843: $i] :
( ~ ( in @ SY843 @ SV318 )
| ~ ( subset @ SY841 @ SY842 )
| ~ ~ ( in @ SY843 @ SY842 )
| ~ ( in @ SY843 @ SY841 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1323,plain,
! [SV319: $i] :
( ( ! [SY844: $i,SY845: $i] :
( ~ ( func @ SV319 @ SY844 @ SY845 )
| ! [SY846: $i] :
( ~ ( in @ SY846 @ SV319 )
| ( in @ ( kpair @ SY846 @ ( ap @ SV319 @ SY844 @ SY845 @ SY846 ) ) @ SY845 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[990]) ).
thf(1324,plain,
! [SV320: $i] :
( ( ! [SY847: $i,SY848: $i] :
( ~ ( subset @ SV320 @ SY847 )
| ~ ( in @ SY848 @ SV320 )
| ( in @ SY848 @ SY847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1325,plain,
! [SV321: $i] :
( ( ! [SY849: $i,SY850: $i] :
( ~ ( subset @ SY850 @ SV321 )
| ~ ( subset @ SY850 @ SY849 )
| ( subset @ SY850 @ ( binintersect @ SV321 @ SY849 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1326,plain,
! [SV322: $i] :
( ( ! [SY851: $i] :
( ~ ( in @ SY851 @ ( powerset @ SV322 ) )
| ! [SY852: $i] :
( ~ ( in @ SY852 @ ( powerset @ SV322 ) )
| ( in @ ( binintersect @ SY851 @ SY852 ) @ ( powerset @ SV322 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1327,plain,
! [SV323: $i > $o] :
( ( ~ ~ ! [SY853: $i] :
~ ~ ( ~ ( SV323 @ SY853 )
| ~ ! [SY854: $i] :
( ~ ( SV323 @ SY854 )
| ( SY853 = SY854 ) ) )
| ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1328,plain,
! [SV324: $i] :
( ( ! [SY856: $i,SY857: $i] :
( ~ ( in @ SY857 @ SV324 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY856 )
| ( ( kpair @ SY857 @ SX3 )
= ( kpair @ SY857 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1329,plain,
! [SV325: $i] :
( ( ! [SY859: $i] :
( ( SV325 != SY859 )
| ( subset @ SV325 @ SY859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1330,plain,
! [SV326: $i] :
( ( ! [SY860: $i] :
( ~ ( in @ SY860 @ ( powerset @ SV326 ) )
| ! [SY861: $i] :
( ~ ( in @ SY861 @ ( powerset @ SV326 ) )
| ( in @ ( setminus @ SV326 @ SY860 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SY860 @ SY861 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1331,plain,
! [SV327: $i,SV1: $i] :
( ( ( SV1 != SV327 )
| ( in @ SV1 @ ( setadjoin @ SV327 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1332,plain,
! [SV328: $i,SV2: $i] :
( ( ~ ( ( SV2 != SV328 ) )
| ~ ( in @ SV328 @ ( setadjoin @ SV2 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1333,plain,
! [SV3: $i] :
( ( ( ~ ! [SY5: $i] :
( ~ ( in @ SY5 @ SV3 )
| ( subset @ SY5 @ SV3 ) ) )
= $true )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1334,plain,
! [SV329: $i,SV4: $i] :
( ( ! [SY862: $i > $i] :
( ~ ! [SY863: $i] :
( ~ ( in @ SY863 @ SV4 )
| ( in @ ( SY862 @ SY863 ) @ SV329 ) )
| ( in
@ ( lam @ SV4 @ SV329
@ ^ [SX3: $i] : ( SY862 @ SX3 ) )
@ ( funcSet @ SV4 @ SV329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1335,plain,
! [SV5: $i] :
( ( ( ~ ! [SY13: $i] :
~ ( in @ SY13 @ SV5 ) )
= $true )
| ( ( SV5 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1002]) ).
thf(1336,plain,
! [SV330: $i,SV6: $i] :
( ( ! [SY865: $i] :
( ~ ( in @ SY865 @ SV6 )
| ! [SY866: $i] :
( ~ ( in @ SY866 @ SV330 )
| ( ( ksnd @ ( kpair @ SY865 @ SY866 ) )
= SY866 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1003]) ).
thf(1337,plain,
! [SV331: $i > $o,SV7: $i] :
( ( ! [SY867: $i] :
( ~ ( in @ SY867
@ ( dsetconstr @ SV7
@ ^ [SY868: $i] : ( SV331 @ SY868 ) ) )
| ( in @ SY867 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1338,plain,
! [SV332: $i > $o,SV8: $i] :
( ( ! [SY869: $i] :
( ~ ( in @ SY869 @ SV8 )
| ~ ( SV332 @ SY869 )
| ~ ! [SY870: $i] :
( ~ ( in @ SY870 @ SV8 )
| ~ ( SV332 @ SY870 )
| ( SY870 = SY869 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1005]) ).
thf(1339,plain,
! [SV333: $i,SV9: $i] :
( ( ! [SY872: $i] :
( ~ ( func @ SV9 @ SV333 @ SY872 )
| ! [SY873: $i] :
( ~ ( in @ SY873 @ SV9 )
| ( ( ap @ SV9 @ SV333 @ SY872 @ SY873 )
= ( ap @ SV9 @ SV333 @ SY872 @ SY873 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1340,plain,
! [SV334: $i,SV10: $i] :
( ( ! [SY874: $i] :
( ~ ( in @ SY874 @ SV10 )
| ! [SY875: $i] :
( ~ ( in @ SY875 @ SV334 )
| ( subset @ ( setadjoin @ SY874 @ ( setadjoin @ SY875 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1341,plain,
! [SV335: $i,SV11: $i] :
( ( ! [SY876: $i] :
( ~ ( func @ SV11 @ SV335 @ SY876 )
| ! [SY877: $i] :
( ~ ( func @ SV11 @ SV335 @ SY877 )
| ~ ! [SY878: $i] :
( ~ ( in @ SY878 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SY876 @ SY878 )
= ( ap @ SV11 @ SV335 @ SY877 @ SY878 ) ) )
| ! [SY879: $i] :
( ~ ( in @ SY879 @ SV11 )
| ! [SY880: $i] :
( ~ ( in @ SY880 @ SV335 )
| ~ ( in @ ( kpair @ SY879 @ SY880 ) @ SY877 )
| ( in @ ( kpair @ SY879 @ SY880 ) @ SY876 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1342,plain,
! [SV12: $i] :
( ( ( ~ ( iskpair @ SV12 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV12 )
@ ^ [SY36: $i] :
( SV12
= ( kpair @ ( kfst @ SV12 ) @ SY36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1343,plain,
! [SV13: $i,SV336: $i] :
( ( in @ SV336 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV336 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1344,plain,
! [SV337: $i,SV14: $i] :
( ( ! [SY881: $i > $i] :
( ~ ! [SY882: $i] :
( ~ ( in @ SY882 @ SV14 )
| ( in @ ( SY881 @ SY882 ) @ SV337 ) )
| ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SX3: $i,SX4: $i] :
( ( SY881 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1345,plain,
! [SV338: $i,SV15: $i] :
( ( ( SV15 != SV338 )
| ( ( setunion @ SV15 )
= ( setunion @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1346,plain,
! [SV339: $i,SV16: $i] :
( ( ! [SY885: $i] :
( ~ ( func @ SV16 @ SV339 @ SY885 )
| ( in @ SY885 @ ( funcSet @ SV16 @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1347,plain,
! [SV17: $i,SV340: $i] :
( ( ~ ( in @ SV340 @ ( powerset @ SV17 ) )
| ! [SY886: $i] :
( ~ ( in @ SY886 @ ( powerset @ SV17 ) )
| ! [SY887: $i] :
( ~ ( in @ SY887 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SY886 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY887 ) @ ( binunion @ SY886 @ SY887 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1348,plain,
! [SV341: $i,SV18: $i] :
( ( ! [SY888: $i] :
( ( binintersect @ SV18 @ ( binunion @ SV341 @ SY888 ) )
= ( binunion @ ( binintersect @ SV18 @ SV341 ) @ ( binintersect @ SV18 @ SY888 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1349,plain,
! [SV342: $i,SV19: $i] :
( ( ! [SY889: $i] :
( ~ ( breln @ SV19 @ SV342 @ SY889 )
| ! [SY890: $i > $o] :
( ~ ! [SY891: $i] :
( ~ ( in @ SY891 @ SV19 )
| ! [SY892: $i] :
( ~ ( in @ SY892 @ SV342 )
| ~ ( in @ ( kpair @ SY891 @ SY892 ) @ SY889 )
| ( SY890 @ ( kpair @ SY891 @ SY892 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY889 )
| ( SY890 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1350,plain,
! [SV20: $i,SV343: $i] :
( ( ~ ( in @ SV343 @ ( powerset @ SV20 ) )
| ! [SY894: $i] :
( ~ ( in @ SY894 @ ( powerset @ SV20 ) )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ SV20 )
| ~ ~ ( in @ SY895 @ ( binunion @ SV343 @ SY894 ) )
| ~ ( in @ SY895 @ SY894 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1351,plain,
! [SV21: $i,SV344: $i] :
( ( ~ ( in @ SV344 @ ( powerset @ SV21 ) )
| ! [SY896: $i] :
( ~ ( in @ SY896 @ ( powerset @ SV21 ) )
| ~ ( subset @ SV344 @ ( setminus @ SV21 @ SY896 ) )
| ( subset @ SY896 @ ( setminus @ SV21 @ SV344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1352,plain,
! [SV22: $i] :
( ( ( ~ ( in @ SV22 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV22 @ SV22 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1019]) ).
thf(1353,plain,
! [SV23: $i,SV345: $i] :
( ( ~ ( in @ SV345 @ SV23 )
| ( in @ ( setadjoin @ SV345 @ emptyset ) @ ( powerset @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1354,plain,
! [SV346: $i,SV24: $i] :
( ( ( SV24 != SV346 )
| ! [SY897: $i,SY898: $i] :
( ( SY897 != SY898 )
| ~ ( ~ ( ~ ( in @ SY897 @ SV24 )
| ( in @ SY898 @ SV346 ) )
| ~ ( ~ ( in @ SY898 @ SV346 )
| ( in @ SY897 @ SV24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1021]) ).
thf(1355,plain,
! [SV25: $i] :
( ( ( ~ ( in @ SV25 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1356,plain,
! [SV347: $i > $o,SV26: $i] :
( ( ~ ~ ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV26 )
| ~ ( SV347 @ SY899 ) )
| ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1023]) ).
thf(1357,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ~ ! [SY901: $i] :
( ~ ( in @ SY901 @ SV27 )
| ~ ( SV348 @ SY901 ) )
| ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1358,plain,
! [SV349: $i,SV28: $i] :
( ( ! [SY903: $i] :
( ~ ( in @ SY903 @ ( funcSet @ SV28 @ SV349 ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV28 )
| ( in @ ( ap @ SV28 @ SV349 @ SY903 @ SY904 ) @ SV349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1359,plain,
! [SV350: $i,SV29: $i] :
( ( ! [SY905: $i] :
( ~ ( in @ SY905 @ ( funcSet @ SV29 @ SV350 ) )
| ( ( lam @ SV29 @ SV350
@ ^ [SY906: $i] : ( ap @ SV29 @ SV350 @ SY905 @ SY906 ) )
= SY905 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1360,plain,
! [SV351: $i,SV31: $i] :
( ( ! [SY907: $i] :
~ ( ~ ( ~ ( in @ SY907 @ ( setadjoin @ SV31 @ SV351 ) )
| ( SY907 = SV31 )
| ( in @ SY907 @ SV351 ) )
| ~ ( ~ ( ( SY907 = SV31 )
| ( in @ SY907 @ SV351 ) )
| ( in @ SY907 @ ( setadjoin @ SV31 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1361,plain,
! [SV32: $i] :
( ( in @ SV32 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1362,plain,
! [SV33: $i,SV352: $i] :
( ( ~ ( in @ SV352 @ ( powerset @ SV33 ) )
| ( subset @ SV352 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1363,plain,
! [SV34: $i,SV353: $i] :
( ( ~ ( in @ SV353 @ ( powerset @ SV34 ) )
| ! [SY908: $i] :
( ~ ( in @ SY908 @ ( powerset @ SV34 ) )
| ! [SY909: $i] :
( ~ ( in @ SY909 @ SV34 )
| ~ ~ ( in @ SY909 @ ( binunion @ SV353 @ SY908 ) )
| ~ ( in @ SY909 @ SV353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1364,plain,
! [SV35: $i,SV354: $i] :
( ( ~ ( in @ SV354 @ ( powerset @ SV35 ) )
| ! [SY910: $i] :
( ~ ( in @ SY910 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SY910 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SY910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1365,plain,
! [SV36: $i] :
( ( ( ~ ( in @ SV36 @ omega ) )
= $true )
| ( ( in @ ( omegaS @ SV36 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1366,plain,
! [SV355: $i,SV37: $i] :
( ( ! [SY911: $i] :
( ~ ( in @ SY911 @ ( setadjoin @ SV37 @ ( setadjoin @ SV355 @ emptyset ) ) )
| ( SY911 = SV37 )
| ( SY911 = SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1367,plain,
! [SV38: $i,SV356: $i] :
( ( ~ ( in @ SV356 @ ( powerset @ SV38 ) )
| ! [SY912: $i] :
( ~ ( in @ SY912 @ ( powerset @ SV38 ) )
| ( in @ ( setminus @ SV356 @ SY912 ) @ ( powerset @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1368,plain,
! [SV357: $i,SV40: $i] :
( ( ~ ( breln1 @ SV40 @ SV357 )
| ! [SY913: $i] :
( ~ ( breln1 @ SV40 @ SY913 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV40 )
| ! [SY915: $i] :
( ~ ( in @ SY915 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY915 ) @ ( breln1compset @ SV40 @ SV357 @ SY913 ) )
| ~ ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY916 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY916 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY916 @ SY915 ) @ SY913 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1369,plain,
! [SV358: $i,SV41: $i] :
( ( ~ ( breln1 @ SV41 @ SV358 )
| ! [SY917: $i] :
( ~ ( breln1 @ SV41 @ SY917 )
| ! [SY918: $i] :
( ~ ( breln1 @ SV41 @ SY918 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SY917 ) @ SY918 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY918 ) @ ( breln1compset @ SV41 @ SY917 @ SY918 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1370,plain,
! [SV42: $i,SV359: $i] :
( ( ~ ( in @ SV359 @ ( powerset @ SV42 ) )
| ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV42 ) )
| ! [SY920: $i] :
( ~ ( in @ SY920 @ SV42 )
| ~ ( in @ SY920 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SY919 ) ) )
| ( in @ SY920 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SY919 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1371,plain,
! [SV360: $i > $i,SV43: $i] :
( ( ! [SY921: $i] :
( ~ ~ ! [SY922: $i] :
~ ~ ( ~ ( in @ SY922 @ SV43 )
| ( SY921
!= ( SV360 @ SY922 ) ) )
| ( in @ SY921
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1372,plain,
! [SV361: $i,SV44: $i] :
( ( ! [SY924: $i] :
( ~ ( in @ SY924 @ ( injFuncSet @ SV44 @ SV361 ) )
| ( in @ SY924 @ ( funcSet @ SV44 @ SV361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1373,plain,
! [SV362: $i,SV45: $i] :
( ( ~ ( breln1 @ SV45 @ SV362 )
| ! [SY925: $i] :
( ~ ( breln1 @ SV45 @ SY925 )
| ( breln1 @ SV45 @ ( binunion @ SV362 @ SY925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1374,plain,
! [SV363: $i,SV46: $i] :
( ( ! [SY926: $i,SY927: $i] :
( ( ( kpair @ SV46 @ SV363 )
!= ( kpair @ SY926 @ SY927 ) )
| ( SV46 = SY926 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1375,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ( ~ ( ~ ( in @ SV364 @ ( setunion @ SV47 ) )
| ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
| ~ ( ~ ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) )
| ( in @ SV364 @ ( setunion @ SV47 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1376,plain,
! [SV365: $i,SV48: $i] :
( ( ! [SY930: $i] :
( ~ ( in @ SY930 @ ( setadjoin @ SV48 @ SV365 ) )
| ( SY930 = SV48 )
| ( in @ SY930 @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1377,plain,
! [SV366: $i,SV49: $i] :
( ( ~ ( breln1 @ SV49 @ SV366 )
| ! [SY931: $i] :
( ~ ( breln1 @ SV49 @ SY931 )
| ( ( binunion @ SV366 @ SY931 )
= ( binunion @ SY931 @ SV366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1378,plain,
! [SV51: $i] :
( ( ( ~ ( in @ SV51 @ omega ) )
= $true )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ omega )
| ( ( omegaS @ SV51 )
!= ( omegaS @ SY121 ) )
| ( SV51 = SY121 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1379,plain,
! [SV52: $i,SV367: $i] :
( ( ~ ( in @ SV367 @ ( powerset @ SV52 ) )
| ! [SY932: $i] :
( ~ ( in @ SY932 @ ( powerset @ SV52 ) )
| ! [SY933: $i] :
( ~ ( in @ SY933 @ SV52 )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SY932 ) )
| ( in @ SY933 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SY932 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1380,plain,
! [SV53: $i,SV368: $i] :
( ( ~ ( in @ SV368 @ ( powerset @ SV53 ) )
| ! [SY934: $i] :
( ~ ( in @ SY934 @ ( powerset @ SV53 ) )
| ~ ( subset @ SV368 @ SY934 )
| ( subset @ ( setminus @ SV53 @ SY934 ) @ ( setminus @ SV53 @ SV368 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1381,plain,
! [SV54: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ ( powerset @ SV54 ) )
| ! [SY935: $i] :
( ~ ( in @ SY935 @ ( powerset @ SV54 ) )
| ~ ( subset @ ( setminus @ SV54 @ SY935 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1382,plain,
! [SV55: $i,SV370: $i] :
( ( ~ ( in @ SV370 @ ( powerset @ SV55 ) )
| ! [SY936: $i] :
( ~ ( in @ SY936 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV370 @ ( setminus @ SV55 @ SY936 ) )
| ! [SY937: $i] :
( ~ ( in @ SY937 @ SV55 )
| ~ ( in @ SY937 @ SY936 )
| ( in @ SY937 @ ( setminus @ SV55 @ SV370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1383,plain,
! [SV56: $i,SV371: $i] :
( ( ~ ( in @ SV371 @ ( powerset @ SV56 ) )
| ( SV371
= ( setminus @ SV56 @ ( setminus @ SV56 @ SV371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1384,plain,
! [SV57: $i,SV372: $i] :
( ( ~ ( in @ SV372 @ ( powerset @ SV57 ) )
| ! [SY938: $i] :
( ~ ( in @ SY938 @ ( powerset @ SV57 ) )
| ! [SY939: $i] :
( ~ ( in @ SY939 @ SV57 )
| ~ ( in @ SY939 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SY938 ) ) )
| ~ ( in @ SY939 @ SV372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1385,plain,
! [SV373: $i > $o,SV58: $i] :
( ( ~ ~ ~ ! [SY940: $i] :
~ ~ ( ~ ( in @ SY940 @ SV58 )
| ~ ( SV373 @ SY940 ) )
| ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1386,plain,
! [SV374: $i,SV59: $i] :
( ( ! [SY942: $i] :
( ~ ( in @ SY942 @ ( setminus @ SV59 @ SV374 ) )
| ~ ( in @ SY942 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1387,plain,
! [SV375: $i,SV60: $i] :
( ( ! [SY943: $i] :
( ~ ( in @ SY943 @ ( setadjoin @ SV60 @ ( setadjoin @ SV375 @ emptyset ) ) )
| ( SY943 = SV60 )
| ( SY943 = SV375 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1388,plain,
! [SV376: $i > $o,SV61: $i] :
( ( ~ ~ ! [SY944: $i] :
( ~ ( in @ SY944 @ SV61 )
| ( SV376 @ SY944 ) )
| ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1058]) ).
thf(1389,plain,
! [SV377: $i,SV62: $i] :
( ( ! [SY946: $i > $i] :
( ~ ! [SY947: $i] :
( ~ ( in @ SY947 @ SV62 )
| ( in @ ( SY946 @ SY947 ) @ SV377 ) )
| ! [SY948: $i] :
( ~ ( in @ SY948 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SX4: $i] : ( SY946 @ SX4 ) )
@ SY948 )
= ( SY946 @ SY948 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1390,plain,
! [SV378: $i,SV63: $i] :
( ( ! [SY950: $i] :
( ~ ~ ( in @ SY950 @ SV63 )
| ~ ( in @ SY950 @ ( setminus @ SV63 @ SV378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1060]) ).
thf(1391,plain,
! [SV65: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ ( powerset @ SV65 ) )
| ( in @ ( setminus @ SV65 @ SV379 ) @ ( powerset @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1392,plain,
! [SV66: $i,SV380: $i] :
( ( ~ ( in @ SV380 @ ( powerset @ SV66 ) )
| ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV66 ) )
| ! [SY952: $i] :
( ~ ( in @ SY952 @ SV66 )
| ~ ~ ( in @ SY952 @ SV380 )
| ~ ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ ( binunion @ SV380 @ SY951 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1393,plain,
! [SV381: $i,SV67: $i] :
( ( ( SV67 != SV381 )
| ! [SY953: $i,SY954: $i] :
( ( SY953 != SY954 )
| ~ ( in @ SY953 @ SV67 )
| ( in @ SY954 @ SV381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1394,plain,
! [SV68: $i] :
( ( ( ~ ( iskpair @ SV68 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV68 )
@ ^ [SY160: $i] : ( in @ ( setadjoin @ SY160 @ emptyset ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1395,plain,
! [SV69: $i,SV382: $i] :
( ( ! [SY955: $i] :
( ~ ( in @ SY955 @ SV382 )
| ~ ( in @ SY955 @ ( setminus @ SV69 @ SV382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1396,plain,
! [SV383: $o,SV70: $i] :
( ( ! [SY956: $i] :
( ~ ( in @ SY956 @ SV70 )
| ! [SY957: $i] :
( ~ ( in @ SY957 @ SV70 )
| ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY958: $i] :
( ~ ( ~ SV383
| ( SY958 != SY956 ) )
| ~ ( ~ ~ SV383
| ( SY958 != SY957 ) ) ) )
= ( setadjoin @ SY957 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1067]) ).
thf(1397,plain,
! [SV70: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV70 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV70 )
| ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1067]) ).
thf(1398,plain,
! [SV70: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV70 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV70 )
| ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1067]) ).
thf(1399,plain,
! [SV71: $o] :
( ( ( ~ SV71 ) = $true )
| ( ( set2prop @ ( prop2set @ SV71 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1400,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1401,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1070]) ).
thf(1402,plain,
! [SV72: $i] :
( ( in @ SV72 @ SV72 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1403,plain,
! [SV73: $i] :
( ( ( ~ ~ ! [SY167: $i] :
~ ( in @ SY167 @ SV73 ) )
= $true )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1404,plain,
! [SV384: $i,SV74: $i] :
( ( ( kfst @ ( kpair @ SV74 @ SV384 ) )
= SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1405,plain,
! [SV385: $i,SV75: $i] :
( ( ! [SY959: $i] :
( ~ ( func @ SV75 @ SV385 @ SY959 )
| ! [SY960: $i] :
( ~ ( in @ SY960 @ SV75 )
| ( in @ ( ap @ SV75 @ SV385 @ SY959 @ SY960 ) @ SV385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1406,plain,
! [SV76: $i,SV386: $i] :
( ( ~ ( in @ SV386 @ ( powerset @ SV76 ) )
| ! [SY961: $i] :
( ~ ( in @ SY961 @ ( powerset @ SV76 ) )
| ! [SY962: $i] :
( ~ ( in @ SY962 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SY961 ) )
| ~ ( in @ SY962 @ SV386 )
| ( in @ SY962 @ SY961 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1407,plain,
! [SV77: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ ( powerset @ SV77 ) )
| ! [SY963: $i] :
( ~ ( in @ SY963 @ ( powerset @ SV77 ) )
| ! [SY964: $i] :
( ~ ( in @ SY964 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SY963 ) )
| ~ ( in @ SY964 @ SY963 )
| ~ ( in @ SY964 @ SV387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1408,plain,
! [SV388: $i,SV78: $i] :
( ( ! [SY965: $i,SY966: $i] :
( ~ ( in @ ( kpair @ SY965 @ SY966 ) @ ( cartprod @ SV78 @ SV388 ) )
| ( in @ SY966 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1409,plain,
! [SV389: $i,SV79: $i] :
( ( ! [SY967: $i] :
( ~ ( in @ SY967 @ SV79 )
| ! [SY968: $i] :
( ~ ( in @ SY968 @ SV389 )
| ( in @ ( kpair @ SY967 @ SY968 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1410,plain,
! [SV80: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( powerset @ SV80 ) )
| ! [SY969: $i] :
( ~ ( in @ SY969 @ ( powerset @ SV80 ) )
| ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SY969 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1411,plain,
! [SV81: $i,SV391: $i] :
( ( ~ ( in @ SV391 @ SV81 )
| ( subset @ ( setadjoin @ SV391 @ emptyset ) @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1412,plain,
! [SV82: $i,SV392: $i] :
( ( ~ ( in @ SV392 @ ( powerset @ SV82 ) )
| ! [SY970: $i] :
( ~ ( in @ SY970 @ ( powerset @ SV82 ) )
| ! [SY971: $i] :
( ~ ( in @ SY971 @ SV82 )
| ~ ~ ( in @ SY971 @ SV392 )
| ~ ( in @ SY971 @ ( binintersect @ SV392 @ SY970 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1081]) ).
thf(1413,plain,
! [SV393: $i,SV83: $i] :
( ( ! [SY972: $i > $i > $o,SY973: $i,SY974: $i] :
( ~ ( in @ ( kpair @ SY973 @ SY974 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SX5: $i,SX6: $i] : ( SY972 @ SX5 @ SX6 ) ) )
| ( SY972 @ SY973 @ SY974 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1414,plain,
! [SV394: $i,SV84: $i] :
( ( ! [SY977: $i] :
( ~ ( func @ SV84 @ SV394 @ SY977 )
| ! [SY978: $i] :
( ~ ( in @ SY978 @ SV84 )
| ( singleton
@ ( dsetconstr @ SV394
@ ^ [SX4: $i] : ( in @ ( kpair @ SY978 @ SX4 ) @ SY977 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1083]) ).
thf(1415,plain,
! [SV395: $i,SV85: $i] :
( ( ! [SY980: $i] :
( ~ ~ ( in @ SY980 @ ( setminus @ SV85 @ SV395 ) )
| ~ ( in @ SY980 @ SV85 )
| ( in @ SY980 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1416,plain,
! [SV396: $i,SV86: $i] :
( ( ( ( setadjoin @ SV86 @ emptyset )
!= ( setadjoin @ SV396 @ emptyset ) )
| ( SV86 = SV396 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1417,plain,
! [SV397: $i,SV87: $i] :
( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV87 )
| ~ ~ ( in @ SY981 @ SV397 )
| ( in @ SY981 @ ( symdiff @ SV87 @ SV397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1418,plain,
! [SV398: $i,SV88: $i] :
( ( in @ SV88 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV88 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV88 @ ( setadjoin @ SV398 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1419,plain,
! [SV399: $i,SV89: $i] :
( ( ! [SY982: $i > $i] :
( ~ ! [SY983: $i] :
( ~ ( in @ SY983 @ SV89 )
| ( in @ ( SY982 @ SY983 ) @ SV399 ) )
| ( ( lam @ SV89 @ SV399
@ ^ [SX3: $i] : ( SY982 @ SX3 ) )
= ( lam @ SV89 @ SV399
@ ^ [SX3: $i] : ( SY982 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1420,plain,
! [SV400: $i,SV90: $i] :
( ( ( SV90 != SV400 )
| ( subset @ SV400 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1421,plain,
! [SV401: $i,SV91: $i] :
( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ ( funcSet @ SV91 @ SV401 ) )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV91 )
| ( in @ ( kpair @ SY987 @ ( ap @ SV91 @ SV401 @ SY986 @ SY987 ) ) @ SY986 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1090]) ).
thf(1422,plain,
! [SV92: $i] :
( ( ( ~ ( in @ SV92 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV92 @ SV92 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1423,plain,
! [SV402: $i,SV93: $i] :
( ( ~ ( breln1 @ SV93 @ SV402 )
| ! [SY988: $i] :
( ~ ( breln1 @ SV93 @ SY988 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV93 )
| ! [SY990: $i] :
( ~ ( in @ SY990 @ SV93 )
| ~ ( in @ ( kpair @ SY989 @ SY990 ) @ ( binunion @ SV402 @ SY988 ) )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SV402 )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SY988 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1424,plain,
! [SV403: $o,SV94: $i] :
( ( ! [SY991: $i] :
( ~ ( in @ SY991 @ SV94 )
| ! [SY992: $i] :
( ~ ( in @ SY992 @ SV94 )
| ~ SV403
| ( in @ SY991
@ ( dsetconstr @ SV94
@ ^ [SY993: $i] :
( ~ ( ~ SV403
| ( SY993 != SY991 ) )
| ~ ( ~ ~ SV403
| ( SY993 != SY992 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1093]) ).
thf(1425,plain,
! [SV94: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV94 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV94 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV94
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1093]) ).
thf(1426,plain,
! [SV94: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV94 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV94 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV94
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1093]) ).
thf(1427,plain,
! [SV95: $i,SV404: $i] :
( ( ~ ! [SY994: $i] :
( ~ ( in @ SY994 @ SV404 )
| ( in @ SY994 @ SV95 ) )
| ( in @ SV404 @ ( powerset @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1428,plain,
! [SV96: $i,SV405: $i] :
( ( in @ SV405 @ ( setadjoin @ SV96 @ ( setadjoin @ SV405 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1429,plain,
! [SV406: $i,SV97: $i] :
( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ ( symdiff @ SV97 @ SV406 ) )
| ! [SY996: $o] :
( ~ ( ~ ( in @ SY995 @ SV97 )
| ~ ~ ( in @ SY995 @ SV406 )
| SY996 )
| ~ ( ~ ~ ( in @ SY995 @ SV97 )
| ~ ( in @ SY995 @ SV406 )
| SY996 )
| SY996 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1430,plain,
! [SV407: $i,SV98: $i] :
( ( ! [SY997: $i] :
( ~ ( in @ SY997 @ ( setminus @ SV98 @ SV407 ) )
| ( in @ SY997 @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1431,plain,
! [SV408: $i,SV99: $i] :
( ( ~ ( breln1 @ SV99 @ SV408 )
| ! [SY998: $i] :
( ~ ( breln1 @ SV99 @ SY998 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV99 )
| ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1000 ) @ ( breln1compset @ SV99 @ SV408 @ SY998 ) )
| ! [SY1001: $o] :
( ~ ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1002 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1002 @ SY1000 ) @ SY998 )
| SY1001 )
| SY1001 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1432,plain,
! [SV100: $i,SV409: $i] :
( ( ~ ( in @ SV409 @ ( breln1Set @ SV100 ) )
| ( breln1 @ SV100 @ SV409 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1433,plain,
! [SV101: $i] :
( ( ( ~ ( singleton @ SV101 ) )
= $true )
| ( ( in @ ( setunion @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1434,plain,
! [SV410: $i,SV102: $i] :
( ( ! [SY1003: $i,SY1004: $i] :
( ( ( kpair @ SV102 @ SV410 )
!= ( kpair @ SY1003 @ SY1004 ) )
| ( SV410 = SY1004 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1435,plain,
! [SV411: $i,SV103: $i] :
( ( ~ ( breln1 @ SV103 @ SV411 )
| ( breln1 @ SV103 @ ( breln1invset @ SV103 @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1436,plain,
! [SV412: $i,SV104: $i] :
( ( ~ ( in @ SV104 @ SV412 )
| ~ ( in @ SV412 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1437,plain,
! [SV413: $i,SV105: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV105 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV105 @ ( setadjoin @ SV413 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1438,plain,
! [SV414: $i,SV106: $i] :
( ( ! [SY1005: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV106 @ SV414
@ ^ [SX3: $i,SX4: $i] : ( SY1005 @ SX3 @ SX4 ) )
@ ( cartprod @ SV106 @ SV414 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1439,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ~ ! [SY1008: $i,SY1009: $i] :
( ( SY1008 != SY1009 )
| ~ ( ~ ( ~ ( SV107 @ SY1008 )
| ( SV415 @ SY1009 ) )
| ~ ( ~ ( SV415 @ SY1009 )
| ( SV107 @ SY1008 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1440,plain,
! [SV108: $i,SV416: $i] :
( ( ~ ( in @ SV416 @ ( powerset @ SV108 ) )
| ! [SY1018: $i] :
( ~ ( in @ SY1018 @ ( powerset @ SV108 ) )
| ! [SY1019: $i] :
( ~ ( in @ SY1019 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SY1018 )
| ~ ( subset @ SV416 @ SY1019 )
| ( subset @ SV416 @ ( binintersect @ SY1018 @ SY1019 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1441,plain,
! [SV417: $i,SV109: $i] :
( ( ! [SY1020: $i] :
( ~ ( in @ SY1020 @ ( funcSet @ SV109 @ SV417 ) )
| ! [SY1021: $i] :
( ~ ( in @ SY1021 @ ( funcSet @ SV109 @ SV417 ) )
| ~ ! [SY1022: $i] :
( ~ ( in @ SY1022 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SY1020 @ SY1022 )
= ( ap @ SV109 @ SV417 @ SY1021 @ SY1022 ) ) )
| ( SY1020 = SY1021 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1442,plain,
! [SV418: $i,SV110: $i] :
( ( ! [SY1023: $i] :
( ~ ( in @ SY1023 @ ( cartprod @ SV110 @ SV418 ) )
| ( iskpair @ SY1023 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1443,plain,
! [SV419: $i,SV111: $i] :
( ( ! [SY1024: $i] :
( ~ ( in @ SY1024 @ ( cartprod @ SV111 @ SV419 ) )
| ~ ! [SY1025: $i] :
~ ~ ( ~ ( in @ SY1025 @ SV111 )
| ~ ~ ! [SY1026: $i] :
~ ~ ( ~ ( in @ SY1026 @ SV419 )
| ( SY1024
!= ( kpair @ SY1025 @ SY1026 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1444,plain,
! [SV420: $i,SV112: $i] :
( ( subset @ ( binintersect @ SV112 @ SV420 ) @ SV420 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1445,plain,
! [SV113: $i] :
( ( ( ~ ( ( SV113 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV113 )
| ( ( binintersect @ SY275 @ SV113 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1446,plain,
! [SV114: $i,SV421: $i] :
( ( ~ ( in @ SV421 @ ( powerset @ SV114 ) )
| ( subset @ SV421 @ ( setminus @ SV114 @ ( setminus @ SV114 @ SV421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1113]) ).
thf(1447,plain,
! [SV422: $i,SV115: $i] :
( ( ! [SY1027: $i] :
( ~ ( in @ ( setadjoin @ SY1027 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) ) )
| ( SV115 = SY1027 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1448,plain,
! [SV116: $i,SV423: $i] :
( ( ~ ( in @ SV423 @ ( powerset @ SV116 ) )
| ! [SY1028: $i] :
( ~ ( in @ SY1028 @ ( powerset @ SV116 ) )
| ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SY1028 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1449,plain,
! [SV117: $i,SV424: $i] :
( ( ~ ( in @ SV424 @ ( powerset @ SV117 ) )
| ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV117 ) )
| ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( powerset @ SV117 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV117 )
| ~ ( in @ SY1031 @ ( binintersect @ SV424 @ SY1029 ) )
| ( in @ SY1031 @ ( binintersect @ ( binunion @ SV424 @ SY1030 ) @ ( binunion @ SY1029 @ SY1030 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1450,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV118 )
| ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV118 )
| ~ ( SV425 @ SY1032 )
| ~ ( SV425 @ SY1033 )
| ( SY1032 = SY1033 ) ) )
| ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1451,plain,
! [SV426: $i > $i,SV119: $i] :
( ( ~ ! [SY1036: $i] :
~ ! [SY1037: $i] :
~ ( ~ ( ~ ( in @ SY1037 @ SY1036 )
| ~ ! [SY1038: $i] :
~ ~ ( ~ ( in @ SY1038 @ SV119 )
| ( SY1037
!= ( SV426 @ SY1038 ) ) ) )
| ~ ( ~ ~ ! [SY1039: $i] :
~ ~ ( ~ ( in @ SY1039 @ SV119 )
| ( SY1037
!= ( SV426 @ SY1039 ) ) )
| ( in @ SY1037 @ SY1036 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1452,plain,
! [SV427: $i,SV120: $i] :
( ( ! [SY1040: $i] :
( ~ ( func @ SV120 @ SV427 @ SY1040 )
| ! [SY1041: $i] :
( ~ ( in @ SY1041 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SX4: $i] : ( in @ ( kpair @ SY1041 @ SX4 ) @ SY1040 ) ) )
@ SV427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1453,plain,
! [SV428: $i,SV121: $i] :
( ( ~ ! [SY1043: $i] :
~ ( ~ ( ~ ( in @ SY1043 @ SV121 )
| ( in @ SY1043 @ SV428 ) )
| ~ ( ~ ( in @ SY1043 @ SV428 )
| ( in @ SY1043 @ SV121 ) ) )
| ( SV121 = SV428 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1454,plain,
! [SV429: $i,SV122: $i] :
( ( ~ ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV122 )
| ( in @ SY1044 @ SV429 ) )
| ( subset @ SV122 @ SV429 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1455,plain,
( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ( subset @ SX0 @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1456,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1122]) ).
thf(1457,plain,
! [SV123: $i,SV430: $i] :
( ( ~ ( subset @ SV430 @ SV123 )
| ( in @ SV430 @ ( powerset @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1458,plain,
! [SV431: $i,SV124: $i] :
( ( ! [SY1045: $i > $i] :
( ~ ! [SY1046: $i] :
( ~ ( in @ SY1046 @ SV124 )
| ( in @ ( SY1045 @ SY1046 ) @ SV431 ) )
| ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SX3: $i] : ( SY1045 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1459,plain,
! [SV432: $o,SV125: $i] :
( ( ! [SY1048: $i] :
( ~ ( in @ SY1048 @ SV125 )
| ! [SY1049: $i] :
( ~ ( in @ SY1049 @ SV125 )
| ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1050: $i] :
( ~ ( ~ SV432
| ( SY1050 != SY1048 ) )
| ~ ( ~ ~ SV432
| ( SY1050 != SY1049 ) ) ) )
= ( setadjoin @ SY1048 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1125]) ).
thf(1460,plain,
! [SV125: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV125 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV125 )
| ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1125]) ).
thf(1461,plain,
! [SV125: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV125 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV125 )
| ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1125]) ).
thf(1462,plain,
! [SV126: $i,SV433: $i] :
( ( ~ ( in @ SV433 @ ( setunion @ SV126 ) )
| ! [SY1051: $o] :
( ~ ! [SY1052: $i] :
( ~ ( in @ SV433 @ SY1052 )
| ~ ( in @ SY1052 @ SV126 )
| SY1051 )
| SY1051 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1463,plain,
! [SV434: $i,SV127: $i] :
( ( ! [SY1053: $i] :
( ~ ( in @ SY1053 @ ( cartprod @ SV127 @ SV434 ) )
| ( in @ ( ksnd @ SY1053 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1464,plain,
! [SV435: $i,SV128: $i] :
( ( ~ ( breln1 @ SV128 @ SV435 )
| ! [SY1054: $i] :
( ~ ( breln1 @ SV128 @ SY1054 )
| ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SY1054 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1465,plain,
! [SV436: $i,SV129: $i] :
( ( ! [SY1055: $i] :
( ~ ( subset @ SV129 @ SY1055 )
| ( subset @ SV129 @ ( setadjoin @ SV436 @ SY1055 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1466,plain,
! [SV437: $i,SV130: $i] :
( ( in @ SV130 @ ( setadjoin @ SV130 @ SV437 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1130]) ).
thf(1467,plain,
! [SV438: $i,SV131: $i] :
( ( ! [SY1056: $i] :
( ~ ( in @ SY1056 @ SV131 )
| ~ ~ ( in @ SY1056 @ SV438 )
| ~ ( subset @ SV131 @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1468,plain,
! [SV439: $i,SV132: $i] :
( ( ! [SY1057: $i,SY1058: $i] :
( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1057 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1057 @ ( setadjoin @ SY1058 @ emptyset ) ) @ emptyset ) ) )
| ( SY1057 != SY1058 )
| ( SV439 = SY1058 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1469,plain,
! [SV133: $i,SV440: $i] :
( ( ~ ( in @ SV440 @ ( powerset @ SV133 ) )
| ! [SY1059: $i] :
( ~ ( in @ SY1059 @ ( powerset @ SV133 ) )
| ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV133 )
| ~ ( in @ SY1060 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SY1059 ) ) )
| ( in @ SY1060 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SY1059 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1470,plain,
! [SV134: $i,SV441: $i] :
( ( ~ ( in @ SV441 @ ( powerset @ SV134 ) )
| ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( powerset @ SV134 ) )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( powerset @ SV134 ) )
| ! [SY1063: $i] :
( ~ ( in @ SY1063 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1062 )
| ~ ( subset @ SY1061 @ SY1063 )
| ( subset @ ( binintersect @ SV441 @ SY1061 ) @ ( binintersect @ SY1062 @ SY1063 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1471,plain,
! [SV442: $i,SV135: $i] :
( ( subset @ ( setminus @ SV135 @ SV442 ) @ SV135 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1472,plain,
! [SV136: $i > $o] :
( ( ( ~ ~ ! [SY335: $i] :
~ ~ ( ~ ( SV136 @ SY335 )
| ~ ! [SY336: $i] :
( ~ ( SV136 @ SY336 )
| ( SY335 = SY336 ) ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1473,plain,
! [SV443: $i,SV137: $i] :
( ( ( ( setminus @ SV137 @ SV443 )
!= emptyset )
| ( subset @ SV137 @ SV443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1474,plain,
! [SV138: $i > $o] :
( ( ( ~ ~ ! [SY340: $i] :
~ ~ ( ~ ( SV138 @ SY340 )
| ~ ! [SY341: $i] :
( ~ ( SV138 @ SY341 )
| ( SY340 = SY341 ) ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1138]) ).
thf(1475,plain,
! [SV444: $i,SV139: $i] :
( ( ! [SY1064: $i] :
( ~ ( func @ SV139 @ SV444 @ SY1064 )
| ! [SY1065: $i] :
( ~ ( func @ SV139 @ SV444 @ SY1065 )
| ~ ! [SY1066: $i] :
( ~ ( in @ SY1066 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SY1064 @ SY1066 )
= ( ap @ SV139 @ SV444 @ SY1065 @ SY1066 ) ) )
| ( SY1064 = SY1065 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1139]) ).
thf(1476,plain,
! [SV445: $i > $i,SV140: $i] :
( ( ~ ! [SY1067: $i] :
~ ~ ( ~ ! [SY1068: $i] :
~ ( ~ ( ~ ( in @ SY1068 @ SY1067 )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1068
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1068
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1068 @ SY1067 ) ) )
| ~ ! [SY1071: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1071 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1071 ) ) )
| ( SY1067 = SY1071 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1477,plain,
! [SV446: $i,SV141: $i] :
( ( ! [SY1075: $i > $i > $o,SY1076: $i,SY1077: $i] :
( ~ ( in @ ( kpair @ SY1076 @ SY1077 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SX5: $i,SX6: $i] : ( SY1075 @ SX5 @ SX6 ) ) )
| ( in @ SY1076 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1141]) ).
thf(1478,plain,
! [SV447: $i,SV142: $i] :
( ( ! [SY1080: $i,SY1081: $i] :
( ~ ( in @ ( kpair @ SY1080 @ SY1081 ) @ ( cartprod @ SV142 @ SV447 ) )
| ( in @ SY1080 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1479,plain,
! [SV143: $i,SV448: $i] :
( ( ~ ( in @ SV448 @ ( powerset @ SV143 ) )
| ! [SY1082: $i] :
( ~ ( in @ SY1082 @ ( powerset @ SV143 ) )
| ! [SY1083: $i] :
( ~ ( in @ SY1083 @ ( powerset @ SV143 ) )
| ~ ( subset @ SY1082 @ SY1083 )
| ( subset @ ( binintersect @ SV448 @ SY1082 ) @ SY1083 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1480,plain,
! [SV449: $i > $o,SV144: $i] :
( ( ~ ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
| ~ ! [SY1085: $i] :
~ ~ ( ~ ( in @ SY1085 @ SV144 )
| ~ ( SV449 @ SY1085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1144]) ).
thf(1481,plain,
! [SV450: $i,SV145: $i] :
( ( ~ ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV145 )
| ( in @ SY1086 @ SV450 ) )
| ( subset @ SV145 @ SV450 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1482,plain,
! [SV451: $i,SV146: $i] :
( ( ~ ( breln1 @ SV146 @ SV451 )
| ! [SY1087: $i > $o] :
( ~ ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV146 )
| ! [SY1089: $i] :
( ~ ( in @ SY1089 @ SV146 )
| ~ ( in @ ( kpair @ SY1088 @ SY1089 ) @ SV451 )
| ( SY1087 @ ( kpair @ SY1088 @ SY1089 ) ) ) )
| ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV451 )
| ( SY1087 @ SY1090 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1483,plain,
! [SV452: $i,SV147: $i] :
( ( ( SV147 != SV452 )
| ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV452 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1147]) ).
thf(1484,plain,
! [SV453: $i > $i,SV148: $i] :
( ( ! [SY1091: $i] :
( ~ ( in @ SY1091
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
| ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV148 )
| ( SY1091
!= ( SV453 @ SY1093 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1485,plain,
! [SV149: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ ( powerset @ SV149 ) )
| ! [SY1094: $i] :
( ~ ( in @ SY1094 @ ( powerset @ SV149 ) )
| ~ ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV149 )
| ~ ( in @ SY1095 @ SV454 )
| ( in @ SY1095 @ SY1094 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV149 )
| ~ ( in @ SY1096 @ SY1094 )
| ( in @ SY1096 @ SV454 ) )
| ( SV454 = SY1094 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1486,plain,
! [SV455: $i,SV150: $i] :
( ( ! [SY1097: $i] :
( ~ ( in @ SY1097 @ ( injFuncSet @ SV150 @ SV455 ) )
| ( injective @ SV150 @ SV455 @ SY1097 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1487,plain,
! [SV456: $i > $o,SV151: $i] :
( ( in
@ ( dsetconstr @ SV151
@ ^ [SY1098: $i] : ( SV456 @ SY1098 ) )
@ ( powerset @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1488,plain,
! [SV457: $i,SV152: $i] :
( ( ( ( binintersect @ SV152 @ SV457 )
!= SV457 )
| ( subset @ SV457 @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1489,plain,
! [SV458: $i > $o,SV153: $i] :
( ( ~ ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV153 )
| ~ ( SV458 @ SY1099 ) )
| ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1490,plain,
! [SV459: $i,SV154: $i] :
( ( ~ ( breln1 @ SV154 @ SV459 )
| ! [SY1101: $i] :
( ~ ( breln1 @ SV154 @ SY1101 )
| ! [SY1102: $i] :
( ~ ( breln1 @ SV154 @ SY1102 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SY1101 ) @ SY1102 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SY1101 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1491,plain,
! [SV155: $i > $o] :
( ( ( ~ ~ ! [SY399: $i] :
~ ~ ( ~ ( SV155 @ SY399 )
| ~ ! [SY400: $i] :
( ~ ( SV155 @ SY400 )
| ( SY399 = SY400 ) ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1155]) ).
thf(1492,plain,
! [SV460: $i,SV156: $i] :
( ( ~ ( breln1 @ SV156 @ SV460 )
| ! [SY1103: $i > $o] :
( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV156 )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV156 )
| ~ ( in @ ( kpair @ SY1104 @ SY1105 ) @ SV460 )
| ( SY1103 @ ( kpair @ SY1104 @ SY1105 ) ) ) )
| ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV460 )
| ( SY1103 @ SY1106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1493,plain,
! [SV461: $i,SV157: $i] :
( ( ! [SY1107: $i] :
( ~ ( in @ SY1107 @ SV157 )
| ! [SY1108: $i] :
( ~ ( in @ SY1108 @ SV461 )
| ( in @ ( kpair @ SY1107 @ SY1108 ) @ ( cartprod @ SV157 @ SV461 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1494,plain,
! [SV462: $o,SV158: $i] :
( ( ! [SY1109: $i] :
( ~ ( in @ SY1109 @ SV158 )
| ! [SY1110: $i] :
( ~ ( in @ SY1110 @ SV158 )
| ~ ~ SV462
| ( in @ SY1110
@ ( dsetconstr @ SV158
@ ^ [SY1111: $i] :
( ~ ( ~ SV462
| ( SY1111 != SY1109 ) )
| ~ ( ~ ~ SV462
| ( SY1111 != SY1110 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1158]) ).
thf(1495,plain,
! [SV158: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV158 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV158 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV158
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1158]) ).
thf(1496,plain,
! [SV158: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV158 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV158 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV158
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1158]) ).
thf(1497,plain,
! [SV159: $i,SV463: $i] :
( ( ! [SY1112: $i] :
( ~ ( in @ SV463 @ ( powerset @ SV159 ) )
| ~ ( in @ SY1112 @ SV463 )
| ( in @ SY1112 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1498,plain,
! [SV464: $i,SV160: $i] :
( ( ! [SY1113: $i] :
( ~ ( in @ SY1113 @ SV160 )
| ~ ~ ( in @ SY1113 @ SV464 )
| ( SV160 != SV464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1160]) ).
thf(1499,plain,
! [SV465: $i,SV161: $i] :
( ( ! [SY1114: $i] :
( ~ ( subset @ SV161 @ SV465 )
| ~ ( subset @ SV465 @ SY1114 )
| ( subset @ SV161 @ SY1114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1500,plain,
! [SV162: $i,SV466: $i] :
( ( ~ ( in @ SV466 @ ( powerset @ SV162 ) )
| ( in @ ( powerset @ SV466 ) @ ( powerset @ ( powerset @ SV162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1501,plain,
! [SV163: $i,SV467: $i] :
( ( ~ ( in @ SV467 @ ( powerset @ SV163 ) )
| ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV163 )
| ~ ~ ( in @ SY1115 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SY1115 @ SV467 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1502,plain,
! [SV468: $i,SV164: $i] :
( ( ! [SY1116: $i] :
( ~ ( in @ SY1116 @ SV164 )
| ~ ~ ( in @ SY1116 @ SV468 )
| ( in @ SY1116 @ ( setminus @ SV164 @ SV468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1164]) ).
thf(1503,plain,
! [SV469: $i > $o,SV165: $i] :
( ( ! [SY1117: $i] :
( ~ ( in @ SY1117 @ SV165 )
| ~ ( SV469 @ SY1117 )
| ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1504,plain,
! [SV166: $i > $o] :
( ( ( ~ ~ ! [SY429: $i] :
~ ( SV166 @ SY429 ) )
= $true )
| ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1505,plain,
! [SV167: $i > $o] :
( ( ( ~ ~ ! [SY434: $i] :
~ ~ ( ~ ( SV167 @ SY434 )
| ~ ! [SY435: $i] :
( ~ ( SV167 @ SY435 )
| ( SY434 = SY435 ) ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1506,plain,
! [SV470: $i,SV168: $i] :
( ( ! [SY1119: $i] :
( ~ ( breln @ SV168 @ SV470 @ SY1119 )
| ! [SY1120: $i] :
( ~ ( breln @ SV168 @ SV470 @ SY1120 )
| ~ ! [SY1121: $i] :
( ~ ( in @ SY1121 @ SV168 )
| ! [SY1122: $i] :
( ~ ( in @ SY1122 @ SV470 )
| ~ ( in @ ( kpair @ SY1121 @ SY1122 ) @ SY1119 )
| ( in @ ( kpair @ SY1121 @ SY1122 ) @ SY1120 ) ) )
| ~ ! [SY1123: $i] :
( ~ ( in @ SY1123 @ SV168 )
| ! [SY1124: $i] :
( ~ ( in @ SY1124 @ SV470 )
| ~ ( in @ ( kpair @ SY1123 @ SY1124 ) @ SY1120 )
| ( in @ ( kpair @ SY1123 @ SY1124 ) @ SY1119 ) ) )
| ( SY1119 = SY1120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1507,plain,
! [SV471: $i,SV169: $i] :
( ( subset @ ( binintersect @ SV169 @ SV471 ) @ SV169 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1508,plain,
! [SV472: $i > $i,SV170: $i] :
( ( ! [SY1125: $i] :
~ ( ~ ( ~ ( in @ SY1125
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
| ~ ! [SY1127: $i] :
~ ~ ( ~ ( in @ SY1127 @ SV170 )
| ( SY1125
!= ( SV472 @ SY1127 ) ) ) )
| ~ ( ~ ~ ! [SY1128: $i] :
~ ~ ( ~ ( in @ SY1128 @ SV170 )
| ( SY1125
!= ( SV472 @ SY1128 ) ) )
| ( in @ SY1125
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1509,plain,
! [SV171: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ ( powerset @ SV171 ) )
| ! [SY1130: $i] :
( ~ ( in @ SY1130 @ ( powerset @ SV171 ) )
| ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV171 )
| ~ ~ ( in @ SY1131 @ SY1130 )
| ~ ( in @ SY1131 @ ( binintersect @ SV473 @ SY1130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1171]) ).
thf(1510,plain,
! [SV474: $i,SV172: $i] :
( ( ! [SY1132: $i > $i] :
( ~ ! [SY1133: $i] :
( ~ ( in @ SY1133 @ SV172 )
| ( in @ ( SY1132 @ SY1133 ) @ SV474 ) )
| ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SX4: $i] : ( SY1132 @ SX4 ) )
@ SY1134 )
= ( SY1132 @ SY1134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1172]) ).
thf(1511,plain,
! [SV173: $i] :
( ( in @ SV173 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1512,plain,
! [SV174: $i > $o] :
( ( ( ~ ~ ! [SY460: $i] :
~ ! [SY461: $i] :
~ ( ~ ( ~ ( SV174 @ SY461 )
| ( SY461 = SY460 ) )
| ~ ( ( SY461 != SY460 )
| ( SV174 @ SY461 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1513,plain,
! [SV475: $i,SV175: $i] :
( ( ( SV175 != SV475 )
| ! [SY1136: $i,SY1137: $i] :
( ( SY1136 != SY1137 )
| ( ( setadjoin @ SV175 @ SY1136 )
= ( setadjoin @ SV475 @ SY1137 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1514,plain,
! [SV476: $i > $o,SV176: $i] :
( ( ! [SY1138: $i] :
( ~ ( in @ SY1138 @ SV176 )
| ~ ( ~ ( ~ ( in @ SY1138
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SY1138 ) )
| ~ ( ~ ( SV476 @ SY1138 )
| ( in @ SY1138
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1176]) ).
thf(1515,plain,
! [SV477: $i,SV177: $i] :
( ( ! [SY1141: $i] :
( ~ ( in @ SY1141 @ SV177 )
| ( in @ SY1141 @ ( binunion @ SV177 @ SV477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1177]) ).
thf(1516,plain,
! [SV178: $i,SV478: $i] :
( ( ~ ( in @ SV478 @ ( setunion @ SV178 ) )
| ~ ! [SY1142: $i] :
~ ~ ( ~ ( in @ SY1142 @ SV178 )
| ~ ( in @ SV478 @ SY1142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1178]) ).
thf(1517,plain,
! [SV179: $i,SV479: $i] :
( ( ~ ( in @ SV479 @ ( powerset @ SV179 ) )
| ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( powerset @ SV179 ) )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( powerset @ SV179 ) )
| ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV179 )
| ~ ( in @ SY1145 @ ( binintersect @ SV479 @ SY1143 ) )
| ( in @ SY1145 @ ( binunion @ SY1143 @ SY1144 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1179]) ).
thf(1518,plain,
! [SV480: $o,SV181: $i] :
( ( ! [SY1146: $i] :
( ~ ( in @ SY1146 @ SV181 )
| ! [SY1147: $i] :
( ~ ( in @ SY1147 @ SV181 )
| ~ SV480
| ( ( if @ SV181 @ SV480 @ SY1146 @ SY1147 )
= SY1146 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1181]) ).
thf(1519,plain,
! [SV181: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV181 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV181 )
| ~ $true
| ( ( if @ SV181 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1181]) ).
thf(1520,plain,
! [SV181: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV181 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV181 )
| ~ $false
| ( ( if @ SV181 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1181]) ).
thf(1521,plain,
! [SV481: $i,SV182: $i] :
( ( ! [SY1148: $i] :
( ~ ~ ( in @ SY1148 @ SV182 )
| ~ ( in @ SY1148 @ SV481 )
| ( in @ SY1148 @ ( symdiff @ SV182 @ SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1182]) ).
thf(1522,plain,
! [SV482: $i,SV183: $i] :
( ( ! [SY1149: $i] :
( ~ ( breln @ SV183 @ SV482 @ SY1149 )
| ! [SY1150: $i > $o] :
( ~ ! [SY1151: $i] :
( ~ ( in @ SY1151 @ SV183 )
| ! [SY1152: $i] :
( ~ ( in @ SY1152 @ SV482 )
| ~ ( in @ ( kpair @ SY1151 @ SY1152 ) @ SY1149 )
| ( SY1150 @ ( kpair @ SY1151 @ SY1152 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1149 )
| ( SY1150 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1183]) ).
thf(1523,plain,
! [SV483: $i,SV184: $i] :
( ( ! [SY1154: $i] :
( ~ ( subset @ SV184 @ SV483 )
| ~ ~ ( in @ SY1154 @ SV483 )
| ~ ( in @ SY1154 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1524,plain,
! [SV484: $i,SV185: $i] :
( ( ~ ( subset @ SV185 @ SV484 )
| ~ ( subset @ SV484 @ SV185 )
| ( SV185 = SV484 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1185]) ).
thf(1525,plain,
! [SV186: $i,SV485: $i] :
( ( ~ ( in @ SV485 @ ( powerset @ SV186 ) )
| ! [SY1155: $i] :
( ~ ( in @ SY1155 @ ( powerset @ SV186 ) )
| ( in @ ( binunion @ SV485 @ SY1155 ) @ ( powerset @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1186]) ).
thf(1526,plain,
! [SV187: $o] :
( ( ( ~ SV187 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1187]) ).
thf(1527,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1188]) ).
thf(1528,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1529,plain,
! [SV188: $i,SV486: $i] :
( ( ~ ( in @ SV486 @ ( powerset @ SV188 ) )
| ! [SY1156: $i] :
( ~ ( in @ SY1156 @ ( powerset @ SV188 ) )
| ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV188 )
| ~ ( in @ SY1157 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SY1156 ) ) )
| ( in @ SY1157 @ ( setminus @ SV188 @ SV486 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1190]) ).
thf(1530,plain,
! [SV487: $i > $o,SV189: $i] :
( ( ~ ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
| ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV189 )
| ! [SY1160: $i] :
( ~ ( in @ SY1160 @ SV189 )
| ~ ( SV487 @ SY1159 )
| ~ ( SV487 @ SY1160 )
| ( SY1159 = SY1160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1191]) ).
thf(1531,plain,
! [SV488: $o,SV190: $i] :
( ( ! [SY1161: $i] :
( ~ ( in @ SY1161 @ SV190 )
| ! [SY1162: $i] :
( ~ ( in @ SY1162 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1163: $i] :
( ~ ( ~ SV488
| ( SY1163 != SY1161 ) )
| ~ ( ~ ~ SV488
| ( SY1163 != SY1162 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1532,plain,
! [SV190: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV190 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1533,plain,
! [SV190: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV190 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1192]) ).
thf(1534,plain,
! [SV191: $i > $i > $o,SV489: $i] :
( ( ~ ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV489 )
| ~ ! [SY508: $i] :
~ ~ ( ~ ( SV191 @ SY1164 @ SY508 )
| ~ ! [SY509: $i] :
( ~ ( SV191 @ SY1164 @ SY509 )
| ( SY508 = SY509 ) ) ) )
| ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1193]) ).
thf(1535,plain,
! [SV490: $i,SV192: $i] :
( ( ~ ~ ( subset @ SV192 @ SV490 )
| ( SV192 != SV490 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1536,plain,
! [SV491: $i,SV193: $i] :
( ( ( SV193 != SV491 )
| ( ( setadjoin @ SV193 @ ( setadjoin @ SV491 @ emptyset ) )
= ( setadjoin @ SV193 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1195]) ).
thf(1537,plain,
! [SV492: $i,SV194: $i] :
( ( ! [SY1171: $i] :
( ~ ( in @ SY1171 @ ( surjFuncSet @ SV194 @ SV492 ) )
| ( surjective @ SV194 @ SV492 @ SY1171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1196]) ).
thf(1538,plain,
! [SV195: $i,SV493: $i] :
( ( in @ SV493 @ ( setadjoin @ SV195 @ ( setadjoin @ SV493 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1197]) ).
thf(1539,plain,
! [SV494: $i,SV196: $i] :
( ( ! [SY1172: $i] :
( ~ ( in @ SY1172 @ SV196 )
| ( in @ ( setadjoin @ SY1172 @ emptyset ) @ ( powerset @ ( binunion @ SV196 @ SV494 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1198]) ).
thf(1540,plain,
! [SV495: $i,SV197: $i] :
( ( ~ ( breln1 @ SV197 @ SV495 )
| ( SV495
= ( breln1invset @ SV197 @ ( breln1invset @ SV197 @ SV495 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1541,plain,
! [SV198: $i,SV496: $i] :
( ( ~ ( in @ SV496 @ ( powerset @ SV198 ) )
| ! [SY1173: $i] :
( ~ ( in @ SY1173 @ ( powerset @ SV198 ) )
| ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV198 )
| ~ ( in @ SY1174 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SY1173 ) ) )
| ( in @ SY1174 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SY1173 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1200]) ).
thf(1542,plain,
! [SV497: $i,SV199: $i] :
( ( ! [SY1175: $i] :
( ~ ( in @ SY1175 @ ( funcSet @ SV199 @ SV497 ) )
| ~ ( injective @ SV199 @ SV497 @ SY1175 )
| ( in @ SY1175 @ ( injFuncSet @ SV199 @ SV497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1201]) ).
thf(1543,plain,
! [SV200: $i] :
( ( ( ~ ! [SY527: $i] :
( ~ ( in @ SY527 @ SV200 )
| ( subset @ SY527 @ SV200 ) ) )
= $true )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1544,plain,
! [SV201: $i,SV498: $i] :
( ( in @ SV498 @ ( setadjoin @ SV201 @ ( setadjoin @ SV498 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1203]) ).
thf(1545,plain,
! [SV499: $i,SV202: $i] :
( ( ! [SY1176: $i > $i] :
( ~ ! [SY1177: $i] :
( ~ ( in @ SY1177 @ SV202 )
| ( in @ ( SY1176 @ SY1177 ) @ SV499 ) )
| ! [SY1178: $i] :
( ~ ( in @ SY1178 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1179: $i] :
( ~ ( in @ SY1179 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1178 @ ( SY1176 @ SY1179 ) )
= SY1179 ) )
| ( surjective @ SV499 @ SV202 @ SY1178 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1546,plain,
! [SV203: $i] :
( ( ( ~ ( subset @ SV203 @ emptyset ) )
= $true )
| ( ( SV203 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1205]) ).
thf(1547,plain,
! [SV204: $i] :
( ( ( ~ ( singleton @ SV204 ) )
= $true )
| ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV204 )
| ( ( setunion @ SV204 )
= SY535 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1206]) ).
thf(1548,plain,
! [SV205: $i,SV500: $i] :
( ( ~ ( in @ SV500 @ ( powerset @ SV205 ) )
| ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV205 )
| ~ ( in @ SY1180 @ SV500 )
| ( in @ SY1180 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1207]) ).
thf(1549,plain,
! [SV501: $i,SV206: $i] :
( ( ( ksnd @ ( kpair @ SV206 @ SV501 ) )
= SV501 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1208]) ).
thf(1550,plain,
! [SV502: $i > $o,SV207: $i] :
( ( ! [SY1181: $i] :
( ~ ( in @ SY1181 @ SV207 )
| ~ ( SV502 @ SY1181 )
| ( in @ SY1181
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1209]) ).
thf(1551,plain,
! [SV503: $i,SV208: $i] :
( ( ! [SY1183: $i > $i > $o,SY1184: $i,SY1185: $i] :
( ~ ( in @ ( kpair @ SY1184 @ SY1185 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SX5: $i,SX6: $i] : ( SY1183 @ SX5 @ SX6 ) ) )
| ( in @ SY1185 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1210]) ).
thf(1552,plain,
! [SV504: $i,SV209: $i] :
( ( ~ ( breln1 @ SV209 @ SV504 )
| ! [SY1188: $i] :
( ~ ( breln1 @ SV209 @ SY1188 )
| ~ ! [SY1189: $i] :
( ~ ( in @ SY1189 @ SV209 )
| ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV209 )
| ~ ( in @ ( kpair @ SY1189 @ SY1190 ) @ SV504 )
| ( in @ ( kpair @ SY1189 @ SY1190 ) @ SY1188 ) ) )
| ( subset @ SV504 @ SY1188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1211]) ).
thf(1553,plain,
! [SV210: $i,SV505: $i] :
( ( ~ ( in @ SV505 @ SV210 )
| ( in @ SV505 @ ( powerset @ ( setunion @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1212]) ).
thf(1554,plain,
! [SV211: $i,SV506: $i] :
( ( ~ ( in @ SV506 @ ( powerset @ SV211 ) )
| ! [SY1191: $i] :
( ~ ( in @ SY1191 @ ( powerset @ SV211 ) )
| ! [SY1192: $i] :
( ~ ( in @ SY1192 @ ( powerset @ SV211 ) )
| ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV211 )
| ~ ( in @ SY1193 @ ( binintersect @ SV506 @ SY1191 ) )
| ( in @ SY1193 @ ( binunion @ SV506 @ SY1192 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1213]) ).
thf(1555,plain,
! [SV212: $i] :
( ( ! [SY557: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY558: $i] :
( ~ ( in @ SY558 @ SY557 )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY558 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY560: $i,SY561: $i] :
( ~ ~ ( ~ ( in @ SY560 @ SV212 )
| ~ ( in @ SY561 @ SV212 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY557 )
| ~ ( ~ ( ~ ( in @ SY560 @ SX4 )
| ( in @ SY561 @ SX4 ) )
| ~ ( ~ ( in @ SY561 @ SX4 )
| ( in @ SY560 @ SX4 ) ) ) )
| ( SY560 = SY561 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY557 )
| ~ ( in @ SX3 @ SY557 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY567: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY567 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY567 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY557 )
| ~ ( in @ SX4 @ SY567 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY567 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY557 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1556,plain,
! [SV507: $i,SV213: $i] :
( ( ! [SY1194: $i] :
( ~ ( in @ SY1194 @ ( funcSet @ SV213 @ SV507 ) )
| ! [SY1195: $i] :
( ~ ( in @ SY1195 @ SV213 )
| ( ( ap @ SV213 @ SV507 @ SY1194 @ SY1195 )
= ( ap @ SV213 @ SV507 @ SY1194 @ SY1195 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1215]) ).
thf(1557,plain,
! [SV508: $o,SV214: $i] :
( ( ! [SY1196: $i] :
( ~ ( in @ SY1196 @ SV214 )
| ! [SY1197: $i] :
( ~ ( in @ SY1197 @ SV214 )
| ( in @ ( if @ SV214 @ SV508 @ SY1196 @ SY1197 ) @ ( setadjoin @ SY1196 @ ( setadjoin @ SY1197 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1216]) ).
thf(1558,plain,
! [SV214: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV214 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV214 )
| ( in @ ( if @ SV214 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1216]) ).
thf(1559,plain,
! [SV214: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV214 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV214 )
| ( in @ ( if @ SV214 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1216]) ).
thf(1560,plain,
! [SV509: $i,SV215: $i] :
( ( ! [SY1198: $i > $i > $o] :
( ~ ! [SY1199: $i] :
( ~ ( in @ SY1199 @ SV215 )
| ~ ! [SY1200: $i] :
~ ~ ( ~ ( in @ SY1200 @ SV509 )
| ~ ( SY1198 @ SY1199 @ SY1200 ) ) )
| ! [SY1201: $i] :
( ~ ( in @ SY1201 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1201 )
| ! [SY1202: $i] :
( ~ ( in @ SY1202 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1203: $i] :
~ ( ~ ( SY1198 @ SY1202 @ SY1203 )
| ~ ! [SY1204: $i] :
( ~ ( in @ SY1204 @ SV509 )
| ~ ( SY1198 @ SY1202 @ SY1204 )
| ( in @ ( kpair @ SY1203 @ SY1204 ) @ SY1201 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1217]) ).
thf(1561,plain,
! [SV510: $i,SV216: $i] :
( ( ~ ( subset @ SV216 @ SV510 )
| ( in @ SV216 @ ( powerset @ SV510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1218]) ).
thf(1562,plain,
! [SV217: $i > $o,SV511: $i] :
( ( ~ ( in @ SV511 @ emptyset )
| ( SV217 @ SV511 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1563,plain,
! [SV512: $i,SV220: $i] :
( ( ! [SY1205: $i] :
( ~ ( in @ SY1205 @ ( cartprod @ SV220 @ SV512 ) )
| ( in @ ( kfst @ SY1205 ) @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1564,plain,
! [SV513: $i,SV221: $i] :
( ( ~ ( subset @ SV221 @ SV513 )
| ( ( setminus @ SV221 @ SV513 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1565,plain,
! [SV514: $i,SV222: $i] :
( ( ! [SY1206: $i] :
( ( ( setadjoin @ SV222 @ ( setadjoin @ SV514 @ emptyset ) )
!= ( setadjoin @ SY1206 @ emptyset ) )
| ( SV222 = SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1224]) ).
thf(1566,plain,
! [SV223: $i,SV515: $i] :
( ( subset @ SV515 @ ( binunion @ SV223 @ SV515 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1225]) ).
thf(1567,plain,
! [SV516: $i,SV225: $i] :
( ( ! [SY1207: $i] :
( ~ ( func @ SV225 @ SV516 @ SY1207 )
| ! [SY1208: $i] :
( ~ ( in @ SY1208 @ SV225 )
| ! [SY1209: $i] :
( ~ ( in @ SY1209 @ SV516 )
| ~ ( in @ ( kpair @ SY1208 @ SY1209 ) @ SY1207 )
| ( ( ap @ SV225 @ SV516 @ SY1207 @ SY1208 )
= SY1209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1227]) ).
thf(1568,plain,
! [SV226: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV226 )
| ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) ) )
= $true )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1569,plain,
! [SV227: $i,SV517: $i] :
( ( ~ ( in @ SV517 @ ( powerset @ SV227 ) )
| ! [SY1210: $i] :
( ~ ( in @ SY1210 @ ( powerset @ SV227 ) )
| ~ ( subset @ SV517 @ ( setminus @ SV227 @ SY1210 ) )
| ( subset @ SY1210 @ ( setminus @ SV227 @ SV517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1229]) ).
thf(1570,plain,
! [SV228: $i] :
( ( ( ~ ~ ! [SY605: $i] :
~ ( in @ SY605 @ SV228 ) )
= $true )
| ( ( SV228 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1571,plain,
! [SV229: $i,SV518: $i] :
( ( ~ ( in @ SV518 @ ( powerset @ SV229 ) )
| ! [SY1211: $i] :
( ~ ( in @ SY1211 @ ( powerset @ SV229 ) )
| ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SY1211 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1231]) ).
thf(1572,plain,
! [SV519: $i,SV230: $i] :
( ( ~ ! [SY1212: $i] :
( ~ ( in @ SY1212 @ SV230 )
| ( in @ SY1212 @ SV519 ) )
| ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1232]) ).
thf(1573,plain,
! [SV231: $i,SV520: $i] :
( ( ~ ( in @ SV520 @ ( powerset @ SV231 ) )
| ( subset @ ( setminus @ SV231 @ ( setminus @ SV231 @ SV520 ) ) @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1233]) ).
thf(1574,plain,
! [SV521: $i > $o,SV232: $i] :
( ( ~ ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SV232 )
| ( SV521 @ SY1214 ) )
| ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1575,plain,
! [SV522: $i,SV233: $i] :
( ( ! [SY1216: $i] :
( ~ ( in @ SY1216 @ ( funcSet @ SV233 @ SV522 ) )
| ( func @ SV233 @ SV522 @ SY1216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1576,plain,
! [SV523: $i,SV234: $i] :
( ( ~ ( breln1 @ SV234 @ SV523 )
| ! [SY1217: $i] :
( ~ ( breln1 @ SV234 @ SY1217 )
| ! [SY1218: $i] :
( ~ ( in @ SY1218 @ SV234 )
| ! [SY1219: $i] :
( ~ ( in @ SY1219 @ SV234 )
| ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV234 )
| ~ ( in @ ( kpair @ SY1218 @ SY1220 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1220 @ SY1219 ) @ SY1217 )
| ( in @ ( kpair @ SY1218 @ SY1219 ) @ ( breln1compset @ SV234 @ SV523 @ SY1217 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1577,plain,
! [SV524: $i,SV235: $i] :
( ( ~ ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV235 )
| ~ ( in @ SY1221 @ SV524 ) )
| ( ( binintersect @ SV235 @ SV524 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1578,plain,
! [SV525: $i,SV236: $i] :
( ( ! [SY1222: $i] :
( ~ ( in @ SY1222 @ SV236 )
| ~ ( in @ SY1222 @ SV525 )
| ( in @ SY1222 @ ( binintersect @ SV236 @ SV525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1579,plain,
! [SV526: $i,SV237: $i] :
( ( ! [SY1223: $i,SY1224: $i] :
( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SV526 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1223 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1223 @ ( setadjoin @ SY1224 @ emptyset ) ) @ emptyset ) ) )
| ( SV237 = SY1223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1580,plain,
! [SV527: $i,SV238: $i] :
( ( ! [SY1225: $i > $i > $o,SY1226: $i] :
( ~ ( in @ SY1226 @ SV238 )
| ! [SY1227: $i] :
( ~ ( in @ SY1227 @ SV527 )
| ~ ( in @ ( kpair @ SY1226 @ SY1227 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SX5: $i,SX6: $i] : ( SY1225 @ SX5 @ SX6 ) ) )
| ( SY1225 @ SY1226 @ SY1227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1581,plain,
! [SV528: $i,SV239: $i] :
( ( ! [SY1230: $i] :
( ~ ( in @ SY1230 @ SV239 )
| ! [SY1231: $i] :
( ~ ( in @ SY1231 @ SV528 )
| ( in @ ( setadjoin @ SY1230 @ ( setadjoin @ SY1231 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1241]) ).
thf(1582,plain,
! [SV240: $i,SV529: $i] :
( ( ~ ( in @ SV529 @ ( powerset @ SV240 ) )
| ! [SY1232: $i] :
( ~ ( in @ SY1232 @ ( powerset @ SV240 ) )
| ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SY1232 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1583,plain,
! [SV530: $o,SV241: $i] :
( ( ! [SY1233: $i] :
( ~ ( in @ SY1233 @ SV241 )
| ! [SY1234: $i] :
( ~ ( in @ SY1234 @ SV241 )
| ( in @ ( if @ SV241 @ SV530 @ SY1233 @ SY1234 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1243]) ).
thf(1584,plain,
! [SV241: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV241 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV241 )
| ( in @ ( if @ SV241 @ $true @ SX0 @ SX1 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1243]) ).
thf(1585,plain,
! [SV241: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV241 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV241 )
| ( in @ ( if @ SV241 @ $false @ SX0 @ SX1 ) @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1243]) ).
thf(1586,plain,
! [SV531: $i > $i > $o,SV242: $i] :
( ( breln1 @ SV242
@ ( dpsetconstr @ SV242 @ SV242
@ ^ [SY1235: $i,SY1236: $i] : ( SV531 @ SY1235 @ SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1244]) ).
thf(1587,plain,
! [SV532: $i,SV243: $i] :
( ( ! [SY1237: $i] :
( ~ ( func @ SV243 @ SV532 @ SY1237 )
| ( ( lam @ SV243 @ SV532
@ ^ [SY1238: $i] : ( ap @ SV243 @ SV532 @ SY1237 @ SY1238 ) )
= SY1237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1245]) ).
thf(1588,plain,
! [SV533: $i > $o,SV244: $i] :
( ( subset
@ ( dsetconstr @ SV244
@ ^ [SY1239: $i] : ( SV533 @ SY1239 ) )
@ SV244 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1589,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ~ ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV245 )
| ! [SY1241: $i] :
( ~ ( in @ SY1241 @ SV245 )
| ~ ( SV534 @ SY1240 )
| ~ ( SV534 @ SY1241 )
| ( SY1240 = SY1241 ) ) )
| ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1590,plain,
! [SV535: $i,SV246: $i] :
( ( ! [SY1244: $i,SY1245: $i] :
( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SV535 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY1244 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1244 @ ( setadjoin @ SY1245 @ emptyset ) ) @ emptyset ) ) )
| ( SV535 = SY1245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1248]) ).
thf(1591,plain,
! [SV536: $i,SV247: $i] :
( ( ~ ( subset @ SV247 @ SV536 )
| ( subset @ ( powerset @ SV247 ) @ ( powerset @ SV536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1249]) ).
thf(1592,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ( ~ ( ~ ( in @ SV537 @ ( powerset @ SV248 ) )
| ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) )
| ~ ( ~ ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) )
| ( in @ SV537 @ ( powerset @ SV248 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1250]) ).
thf(1593,plain,
! [SV249: $i] :
( ( ( ~ ( in @ SV249 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1594,plain,
! [SV538: $i,SV250: $i] :
( ( ! [SY1248: $i] :
( ~ ( in @ SY1248 @ ( funcSet @ SV250 @ SV538 ) )
| ! [SY1249: $i] :
( ~ ( in @ SY1249 @ SV250 )
| ! [SY1250: $i] :
( ~ ( in @ SY1250 @ SV538 )
| ~ ( in @ ( kpair @ SY1249 @ SY1250 ) @ SY1248 )
| ( ( ap @ SV250 @ SV538 @ SY1248 @ SY1249 )
= SY1250 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1595,plain,
! [SV539: $i,SV251: $i] :
( ( ~ ( breln1 @ SV251 @ SV539 )
| ! [SY1251: $i] :
( ~ ( in @ SY1251 @ SV251 )
| ! [SY1252: $i] :
( ~ ( in @ SY1252 @ SV251 )
| ~ ( in @ ( kpair @ SY1251 @ SY1252 ) @ SV539 )
| ( in @ ( kpair @ SY1252 @ SY1251 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1596,plain,
! [SV540: $i,SV252: $i] :
( ( ~ ( breln1 @ SV252 @ SV540 )
| ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SV252 )
| ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV252 )
| ~ ( in @ ( kpair @ SY1254 @ SY1253 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SY1253 @ SY1254 ) @ SV540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1597,plain,
! [SV253: $o,SV541: $i] :
( ( ~ ( in @ SV541 @ ( prop2set @ SV253 ) )
| SV253 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1598,plain,
! [SV542: $i] :
( ( ~ ( in @ SV542 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1599,plain,
! [SV543: $i] :
( ( ~ ( in @ SV543 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1257]) ).
thf(1600,plain,
! [SV544: $i,SV254: $i] :
( ( ! [SY1255: $i] :
( ~ ( in @ SY1255 @ ( binintersect @ SV254 @ SV544 ) )
| ( in @ SY1255 @ SV254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1601,plain,
! [SV545: $i,SV255: $i] :
( ( ~ ( breln1 @ SV255 @ SV545 )
| ! [SY1256: $i] :
( ~ ( breln1 @ SV255 @ SY1256 )
| ! [SY1257: $i] :
( ~ ( in @ SY1257 @ SV255 )
| ! [SY1258: $i] :
( ~ ( in @ SY1258 @ SV255 )
| ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ ( binunion @ SV545 @ SY1256 ) )
| ! [SY1259: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SV545 )
| SY1259 )
| ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SY1256 )
| SY1259 )
| SY1259 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1602,plain,
! [SV256: $i,SV546: $i] :
( ( ! [SY1260: $i] :
( ~ ( in @ SY1260 @ SV546 )
| ( in @ SY1260 @ ( setadjoin @ SV256 @ SV546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1603,plain,
! [SV547: $i,SV257: $i] :
( ( ! [SY1261: $i] :
( ~ ( in @ SY1261 @ SV257 )
| ! [SY1262: $i] :
( ~ ( in @ SY1262 @ SV547 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1261 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1261 @ ( setadjoin @ SY1262 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1261]) ).
thf(1604,plain,
! [SV258: $i,SV548: $i] :
( ( ~ ( in @ SV548 @ ( powerset @ SV258 ) )
| ! [SY1263: $i] :
( ~ ( in @ SY1263 @ ( powerset @ SV258 ) )
| ! [SY1264: $i] :
( ~ ( in @ SY1264 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SY1263 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1264 ) @ ( binunion @ SY1263 @ SY1264 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1262]) ).
thf(1605,plain,
! [SV549: $i,SV259: $i] :
( ( ! [SY1265: $i] :
( ~ ( in @ SY1265 @ ( surjFuncSet @ SV259 @ SV549 ) )
| ( in @ SY1265 @ ( funcSet @ SV259 @ SV549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1263]) ).
thf(1606,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ~ ! [SY1266: $i,SY1267: $i] :
( ( SY1266 != SY1267 )
| ~ ( ~ ( ~ ( SV260 @ SY1266 )
| ( SV550 @ SY1267 ) )
| ~ ( ~ ( SV550 @ SY1267 )
| ( SV260 @ SY1266 ) ) ) )
| ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1607,plain,
! [SV261: $i,SV551: $i] :
( ( ~ ( in @ SV551 @ ( funcSet @ SV261 @ ( powerset @ SV261 ) ) )
| ~ ( surjective @ SV261 @ ( powerset @ SV261 ) @ SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1265]) ).
thf(1608,plain,
! [SV262: $i] :
( ( ( ~ ( in @ SV262 @ omega ) )
= $true )
| ( ( ( omegaS @ SV262 )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1609,plain,
! [SV263: $i,SV552: $i] :
( ( ~ ( in @ SV552 @ ( powerset @ SV263 ) )
| ! [SY1274: $i] :
( ~ ( in @ SY1274 @ ( powerset @ SV263 ) )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1275 )
| ( subset @ ( binintersect @ SV552 @ SY1274 ) @ SY1275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1267]) ).
thf(1610,plain,
! [SV553: $i,SV264: $i] :
( ( ~ ( breln1 @ SV264 @ SV553 )
| ! [SY1276: $i] :
( ~ ( breln1 @ SV264 @ SY1276 )
| ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV264 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV264 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV553 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SY1276 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV264 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV264 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SY1276 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV553 ) ) )
| ( SV553 = SY1276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1611,plain,
! [SV554: $i,SV265: $i] :
( ( ! [SY1281: $i] :
( ~ ( in @ SY1281 @ SV265 )
| ~ ( in @ SY1281 @ SV554 )
| ~ ( in @ SY1281 @ ( symdiff @ SV265 @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1612,plain,
! [SV555: $i,SV266: $i] :
( ( ! [SY1282: $i] :
( ~ ( in @ SY1282 @ ( cartprod @ SV266 @ SV555 ) )
| ( ( kpair @ ( kfst @ SY1282 ) @ ( ksnd @ SY1282 ) )
= SY1282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1613,plain,
! [SV556: $i,SV267: $i] :
( ( iskpair @ ( kpair @ SV267 @ SV556 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1614,plain,
! [SV268: $i,SV557: $i] :
( ( ~ ( in @ SV557 @ ( powerset @ SV268 ) )
| ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV268 )
| ~ ( in @ SY1283 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SY1283 @ SV557 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1272]) ).
thf(1615,plain,
! [SV558: $i > $o,SV269: $i] :
( ( ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SV269 )
| ~ ~ ( SV558 @ SY1284 ) )
| ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1273]) ).
thf(1616,plain,
! [SV559: $i,SV270: $i] :
( ( ! [SY1286: $i] :
( ~ ~ ( in @ SY1286 @ ( setminus @ SV270 @ SV559 ) )
| ~ ~ ( in @ SY1286 @ SV559 )
| ~ ( in @ SY1286 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1274]) ).
thf(1617,plain,
! [SV271: $i,SV560: $i] :
( ( ~ ( in @ SV560 @ ( powerset @ SV271 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ ( powerset @ SV271 ) )
| ! [SY1288: $i] :
( ~ ( in @ SY1288 @ SV271 )
| ~ ( in @ SY1288 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SY1287 ) ) )
| ( in @ SY1288 @ ( setminus @ SV271 @ SY1287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1275]) ).
thf(1618,plain,
! [SV272: $i] :
( ( ( ~ ! [SY725: $i] :
~ ( in @ SY725 @ SV272 ) )
= $true )
| ( ( SV272 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1276]) ).
thf(1619,plain,
! [SV561: $i,SV273: $i] :
( ( ~ ( subset @ SV273 @ SV561 )
| ( ( binintersect @ SV273 @ SV561 )
= SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1620,plain,
! [SV562: $i,SV274: $i] :
( ( ~ ( breln1 @ SV274 @ SV562 )
| ! [SY1289: $i] :
( ~ ( breln1 @ SV274 @ SY1289 )
| ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV274 )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV274 )
| ~ ( in @ ( kpair @ SY1290 @ SY1291 ) @ SV562 )
| ( in @ ( kpair @ SY1290 @ SY1291 ) @ ( binunion @ SV562 @ SY1289 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1621,plain,
! [SV563: $i,SV275: $i] :
( ( ! [SY1292: $i] :
( ~ ( in @ SY1292 @ ( binintersect @ SV275 @ SV563 ) )
| ( in @ SY1292 @ SV563 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1622,plain,
! [SV564: $i,SV276: $i] :
( ( ! [SY1293: $i] :
( ~ ~ ( in @ SY1293 @ SV276 )
| ~ ~ ( in @ SY1293 @ SV564 )
| ~ ( in @ SY1293 @ ( symdiff @ SV276 @ SV564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1280]) ).
thf(1623,plain,
! [SV277: $i,SV565: $i] :
( ( subset @ SV565 @ ( setadjoin @ SV277 @ SV565 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1281]) ).
thf(1624,plain,
! [SV566: $i,SV278: $i] :
( ( ! [SY1294: $i] :
( ~ ( in @ SY1294 @ SV278 )
| ! [SY1295: $i] :
( ~ ( in @ SY1295 @ SV566 )
| ( ( kfst @ ( kpair @ SY1294 @ SY1295 ) )
= SY1294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1625,plain,
! [SV279: $i,SV567: $i] :
( ( ~ ( subset @ SV567 @ SV279 )
| ( ( binintersect @ SV279 @ SV567 )
= SV567 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1283]) ).
thf(1626,plain,
! [SV280: $i,SV568: $i] :
( ( ! [SY1296: $i] :
( ~ ( in @ SY1296 @ SV568 )
| ( in @ SY1296 @ ( binunion @ SV280 @ SV568 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1627,plain,
! [SV281: $i] :
( ( ( ~ ( ( SV281 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY742: $i] :
~ ~ ( ~ ( in @ SY742 @ SV281 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1628,plain,
! [SV282: $i] :
( ( ( ~ ( iskpair @ SV282 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV282 ) @ ( ksnd @ SV282 ) )
= SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1286]) ).
thf(1629,plain,
! [SV569: $i,SV283: $i] :
( ( ( SV283 != SV569 )
| ! [SY1297: $i > $o,SY1298: $i > $o] :
( ~ ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV283 )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV569 )
| ( SY1299 != SY1300 )
| ~ ( ~ ( ~ ( SY1297 @ SY1299 )
| ( SY1298 @ SY1300 ) )
| ~ ( ~ ( SY1298 @ SY1300 )
| ( SY1297 @ SY1299 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SX4: $i] : ( SY1297 @ SX4 ) )
= ( dsetconstr @ SV569
@ ^ [SX4: $i] : ( SY1298 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1630,plain,
! [SV284: $i > $o] :
( ( ( ~ ~ ! [SY750: $i] :
~ ~ ( ~ ( SV284 @ SY750 )
| ~ ! [SY751: $i] :
( ~ ( SV284 @ SY751 )
| ( SY750 = SY751 ) ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1288]) ).
thf(1631,plain,
! [SV285: $i,SV570: $i] :
( ( ~ ( in @ SV570 @ ( powerset @ SV285 ) )
| ! [SY1303: $i] :
( ~ ( in @ SY1303 @ ( powerset @ SV285 ) )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV285 )
| ~ ( in @ SY1304 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1304 @ ( binintersect @ SV570 @ SY1303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1632,plain,
! [SV571: $i > $o,SV286: $i] :
( ( ! [SY1305: $i] :
( ~ ( in @ SY1305
@ ( dsetconstr @ SV286
@ ^ [SY1306: $i] : ( SV571 @ SY1306 ) ) )
| ( SV571 @ SY1305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1290]) ).
thf(1633,plain,
! [SV572: $i,SV287: $i] :
( ( ! [SY1307: $i,SY1308: $o] :
( ~ ( in @ SY1307 @ ( binunion @ SV287 @ SV572 ) )
| ~ ( ~ ( in @ SY1307 @ SV287 )
| SY1308 )
| ~ ( ~ ( in @ SY1307 @ SV572 )
| SY1308 )
| SY1308 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1634,plain,
! [SV573: $i,SV288: $i] :
( ( ~ ( breln1 @ SV288 @ SV573 )
| ! [SY1309: $i] :
( ~ ( breln1 @ SV288 @ SY1309 )
| ! [SY1310: $i] :
( ~ ( in @ SY1310 @ SV288 )
| ! [SY1311: $i] :
( ~ ( in @ SY1311 @ SV288 )
| ~ ( in @ ( kpair @ SY1310 @ SY1311 ) @ SY1309 )
| ( in @ ( kpair @ SY1310 @ SY1311 ) @ ( binunion @ SV573 @ SY1309 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1635,plain,
! [SV574: $i,SV289: $i] :
( ( ( SV289 != SV574 )
| ( ( powerset @ SV289 )
= ( powerset @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1293]) ).
thf(1636,plain,
! [SV575: $i,SV290: $i] :
( ( ! [SY1312: $i > $i > $o] :
( breln @ SV290 @ SV575
@ ( dpsetconstr @ SV290 @ SV575
@ ^ [SX3: $i,SX4: $i] : ( SY1312 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1294]) ).
thf(1637,plain,
! [SV576: $o,SV291: $i] :
( ( ! [SY1315: $i] :
( ~ ( in @ SY1315 @ SV291 )
| ! [SY1316: $i] :
( ~ ( in @ SY1316 @ SV291 )
| ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SY1315 @ SY1316 )
= SY1316 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1295]) ).
thf(1638,plain,
! [SV291: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV291 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV291 )
| ~ ~ $true
| ( ( if @ SV291 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1295]) ).
thf(1639,plain,
! [SV291: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV291 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV291 )
| ~ ~ $false
| ( ( if @ SV291 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1295]) ).
thf(1640,plain,
! [SV577: $i,SV292: $i] :
( ( in @ SV292 @ ( setadjoin @ SV292 @ ( setadjoin @ SV577 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1641,plain,
! [SV578: $i,SV294: $i] :
( ( ~ ( breln1 @ SV294 @ SV578 )
| ! [SY1317: $i] :
( ~ ( breln1 @ SV294 @ SY1317 )
| ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SY1317 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SY1317 ) @ ( breln1invset @ SV294 @ SV578 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1642,plain,
! [SV579: $i,SV295: $i] :
( ( subset @ SV295 @ ( binunion @ SV295 @ SV579 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1299]) ).
thf(1643,plain,
! [SV296: $i,SV580: $i] :
( ( ~ ( in @ SV580 @ ( powerset @ SV296 ) )
| ! [SY1318: $i] :
( ~ ( in @ SY1318 @ ( powerset @ SV296 ) )
| ~ ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV296 )
| ~ ( in @ SY1319 @ SV580 )
| ( in @ SY1319 @ SY1318 ) )
| ( in @ SV580 @ ( powerset @ SY1318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1644,plain,
! [SV581: $i,SV297: $i] :
( ( ~ ( breln1 @ SV297 @ SV581 )
| ! [SY1320: $i] :
( ~ ( breln1 @ SV297 @ SY1320 )
| ! [SY1321: $i] :
( ~ ( in @ SY1321 @ SV297 )
| ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1321 @ SY1322 ) @ SV581 )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ SY1320 ) )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ ( binunion @ SV581 @ SY1320 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1645,plain,
! [SV582: $i,SV298: $i] :
( ( ! [SY1323: $i] :
( ~ ( breln @ SV298 @ SV582 @ SY1323 )
| ! [SY1324: $i] :
( ~ ( breln @ SV298 @ SV582 @ SY1324 )
| ~ ! [SY1325: $i] :
( ~ ( in @ SY1325 @ SV298 )
| ! [SY1326: $i] :
( ~ ( in @ SY1326 @ SV582 )
| ~ ( in @ ( kpair @ SY1325 @ SY1326 ) @ SY1323 )
| ( in @ ( kpair @ SY1325 @ SY1326 ) @ SY1324 ) ) )
| ( subset @ SY1323 @ SY1324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1646,plain,
! [SV299: $i,SV583: $i] :
( ( ~ ( in @ SV583 @ ( powerset @ SV299 ) )
| ! [SY1327: $i] :
( ~ ( in @ SY1327 @ ( powerset @ SV299 ) )
| ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV299 )
| ~ ( in @ SY1328 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SY1327 ) ) )
| ( in @ SY1328 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SY1327 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1647,plain,
! [SV300: $i > $o] :
( ( ( ~ ~ ! [SY794: $i] :
~ ~ ( ~ ( SV300 @ SY794 )
| ~ ! [SY795: $i] :
( ~ ( SV300 @ SY795 )
| ( SY794 = SY795 ) ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1648,plain,
! [SV301: $i,SV584: $i] :
( ( ~ ( in @ SV584 @ ( powerset @ SV301 ) )
| ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( powerset @ SV301 ) )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV301 )
| ~ ( in @ SY1330 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1330 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SY1329 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1305]) ).
thf(1649,plain,
! [SV302: $i,SV585: $i] :
( ( ~ ( in @ SV585 @ ( powerset @ SV302 ) )
| ! [SY1331: $i] :
( ~ ( in @ SY1331 @ ( powerset @ SV302 ) )
| ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV302 )
| ~ ( in @ SY1332 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SY1331 ) ) )
| ( in @ SY1332 @ ( setminus @ SV302 @ SV585 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1306]) ).
thf(1650,plain,
! [SV586: $i,SV303: $i] :
( ( ( ( binintersect @ SV303 @ SV586 )
!= SV303 )
| ( subset @ SV303 @ SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1307]) ).
thf(1651,plain,
! [SV304: $i] :
( ( ( ~ ( ( SV304 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY804: $i] :
~ ( in @ SY804 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1308]) ).
thf(1652,plain,
! [SV305: $i,SV587: $i] :
( ( ~ ( in @ SV587 @ ( powerset @ SV305 ) )
| ! [SY1333: $i] :
( ~ ( in @ SY1333 @ ( powerset @ SV305 ) )
| ! [SY1334: $i] :
( ~ ( in @ SY1334 @ ( binintersect @ SV587 @ SY1333 ) )
| ( in @ SY1334 @ SV305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1653,plain,
! [SV306: $i,SV588: $i] :
( ( ! [SY1335: $i] :
( ~ ( in @ SV588 @ SY1335 )
| ~ ( in @ SY1335 @ SV306 )
| ( in @ SV588 @ ( setunion @ SV306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1654,plain,
! [SV307: $i,SV589: $i] :
( ( ~ ( in @ SV589 @ ( powerset @ SV307 ) )
| ! [SY1336: $i] :
( ~ ( in @ SY1336 @ SV307 )
| ~ ( in @ SY1336 @ SV589 )
| ~ ( in @ SY1336 @ ( setminus @ SV307 @ SV589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1655,plain,
! [SV308: $i,SV590: $i] :
( ( ~ ( in @ SV590 @ ( powerset @ SV308 ) )
| ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( powerset @ SV308 ) )
| ( ( setminus @ SV308 @ ( binunion @ SV590 @ SY1337 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SY1337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1656,plain,
! [SV591: $i,SV309: $i] :
( ( ! [SY1338: $i] :
( ~ ( in @ SY1338 @ ( setadjoin @ SV309 @ SV591 ) )
| ! [SY1339: $o] :
( ~ ( ( SY1338 != SV309 )
| SY1339 )
| ~ ( ~ ( in @ SY1338 @ SV591 )
| SY1339 )
| SY1339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1313]) ).
thf(1657,plain,
! [SV310: $i,SV592: $i] :
( ( ~ ( in @ SV592 @ ( powerset @ SV310 ) )
| ! [SY1340: $i] :
( ~ ( in @ SY1340 @ ( powerset @ SV310 ) )
| ~ ! [SY1341: $i] :
( ~ ( in @ SY1341 @ SV310 )
| ~ ( in @ SY1341 @ SV592 )
| ( in @ SY1341 @ SY1340 ) )
| ( subset @ SV592 @ SY1340 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1658,plain,
! [SV593: $i,SV311: $i] :
( ( ~ ( in @ SV311 @ ( setadjoin @ SV593 @ emptyset ) )
| ( in @ SV593 @ ( setadjoin @ SV311 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1659,plain,
! [SV594: $i,SV312: $i] :
( ( ! [SY1342: $i] :
( ~ ( in @ SY1342 @ ( binunion @ SV312 @ SV594 ) )
| ( in @ SY1342 @ SV312 )
| ( in @ SY1342 @ SV594 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1660,plain,
! [SV595: $i,SV313: $i] :
( ( ! [SY1343: $i] :
( ~ ( in @ SY1343 @ SV313 )
| ! [SY1344: $i] :
( ~ ( in @ SY1344 @ SV595 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1343 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1343 @ ( setadjoin @ SY1344 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1317]) ).
thf(1661,plain,
! [SV596: $i,SV314: $i] :
( ( ! [SY1345: $i > $i > $o,SY1346: $i] :
( ~ ( in @ SY1346 @ SV314 )
| ! [SY1347: $i] :
( ~ ( in @ SY1347 @ SV596 )
| ~ ( SY1345 @ SY1346 @ SY1347 )
| ( in @ ( kpair @ SY1346 @ SY1347 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SX5: $i,SX6: $i] : ( SY1345 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1318]) ).
thf(1662,plain,
! [SV315: $i,SV597: $i] :
( ( ~ ( in @ SV597 @ ( powerset @ SV315 ) )
| ! [SY1350: $i] :
( ~ ( in @ SY1350 @ ( powerset @ SV315 ) )
| ! [SY1351: $o,SY1352: $i] :
( ~ ( in @ SY1352 @ SV315 )
| ~ ( in @ SY1352 @ ( binunion @ SV597 @ SY1350 ) )
| ~ ( ~ ( in @ SY1352 @ SV597 )
| SY1351 )
| ~ ( ~ ( in @ SY1352 @ SY1350 )
| SY1351 )
| SY1351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1319]) ).
thf(1663,plain,
! [SV598: $i,SV316: $i] :
( ( ~ ( in @ SV316 @ ( setadjoin @ SV598 @ emptyset ) )
| ( SV316 = SV598 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1320]) ).
thf(1664,plain,
! [SV317: $i,SV599: $i] :
( ( ~ ( in @ SV599 @ ( powerset @ SV317 ) )
| ! [SY1353: $i] :
( ~ ( in @ SY1353 @ ( powerset @ SV317 ) )
| ! [SY1354: $i] :
( ~ ( in @ SY1354 @ ( powerset @ SV317 ) )
| ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SY1353 ) @ ( binunion @ SY1354 @ SY1355 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SY1353 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1354 ) @ ( setminus @ SV317 @ SY1355 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1665,plain,
! [SV318: $i,SV600: $i] :
( ( ~ ( in @ SV600 @ ( powerset @ SV318 ) )
| ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( powerset @ SV318 ) )
| ! [SY1357: $i] :
( ~ ( in @ SY1357 @ SV318 )
| ~ ( subset @ SV600 @ SY1356 )
| ~ ~ ( in @ SY1357 @ SY1356 )
| ~ ( in @ SY1357 @ SV600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1666,plain,
! [SV601: $i,SV319: $i] :
( ( ! [SY1358: $i] :
( ~ ( func @ SV319 @ SV601 @ SY1358 )
| ! [SY1359: $i] :
( ~ ( in @ SY1359 @ SV319 )
| ( in @ ( kpair @ SY1359 @ ( ap @ SV319 @ SV601 @ SY1358 @ SY1359 ) ) @ SY1358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1667,plain,
! [SV602: $i,SV320: $i] :
( ( ! [SY1360: $i] :
( ~ ( subset @ SV320 @ SV602 )
| ~ ( in @ SY1360 @ SV320 )
| ( in @ SY1360 @ SV602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1324]) ).
thf(1668,plain,
! [SV603: $i,SV321: $i] :
( ( ! [SY1361: $i] :
( ~ ( subset @ SY1361 @ SV321 )
| ~ ( subset @ SY1361 @ SV603 )
| ( subset @ SY1361 @ ( binintersect @ SV321 @ SV603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1669,plain,
! [SV322: $i,SV604: $i] :
( ( ~ ( in @ SV604 @ ( powerset @ SV322 ) )
| ! [SY1362: $i] :
( ~ ( in @ SY1362 @ ( powerset @ SV322 ) )
| ( in @ ( binintersect @ SV604 @ SY1362 ) @ ( powerset @ SV322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1670,plain,
! [SV323: $i > $o] :
( ( ( ~ ~ ! [SY853: $i] :
~ ~ ( ~ ( SV323 @ SY853 )
| ~ ! [SY854: $i] :
( ~ ( SV323 @ SY854 )
| ( SY853 = SY854 ) ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1327]) ).
thf(1671,plain,
! [SV605: $i,SV324: $i] :
( ( ! [SY1363: $i] :
( ~ ( in @ SY1363 @ SV324 )
| ! [SY1364: $i] :
( ~ ( in @ SY1364 @ SV605 )
| ( ( kpair @ SY1363 @ SY1364 )
= ( kpair @ SY1363 @ SY1364 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1672,plain,
! [SV606: $i,SV325: $i] :
( ( ( SV325 != SV606 )
| ( subset @ SV325 @ SV606 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1329]) ).
thf(1673,plain,
! [SV326: $i,SV607: $i] :
( ( ~ ( in @ SV607 @ ( powerset @ SV326 ) )
| ! [SY1365: $i] :
( ~ ( in @ SY1365 @ ( powerset @ SV326 ) )
| ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SY1365 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1674,plain,
! [SV327: $i,SV1: $i] :
( ( ( SV1 != SV327 )
= $true )
| ( ( in @ SV1 @ ( setadjoin @ SV327 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1331]) ).
thf(1675,plain,
! [SV328: $i,SV2: $i] :
( ( ( ~ ( ( SV2 != SV328 ) ) )
= $true )
| ( ( ~ ( in @ SV328 @ ( setadjoin @ SV2 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1676,plain,
! [SV3: $i] :
( ( ( ! [SY5: $i] :
( ~ ( in @ SY5 @ SV3 )
| ( subset @ SY5 @ SV3 ) ) )
= $false )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1677,plain,
! [SV329: $i,SV608: $i > $i,SV4: $i] :
( ( ~ ! [SY1366: $i] :
( ~ ( in @ SY1366 @ SV4 )
| ( in @ ( SV608 @ SY1366 ) @ SV329 ) )
| ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1678,plain,
! [SV5: $i] :
( ( ( ! [SY13: $i] :
~ ( in @ SY13 @ SV5 ) )
= $false )
| ( ( SV5 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1679,plain,
! [SV330: $i,SV6: $i,SV609: $i] :
( ( ~ ( in @ SV609 @ SV6 )
| ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV330 )
| ( ( ksnd @ ( kpair @ SV609 @ SY1368 ) )
= SY1368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1680,plain,
! [SV331: $i > $o,SV7: $i,SV610: $i] :
( ( ~ ( in @ SV610
@ ( dsetconstr @ SV7
@ ^ [SY868: $i] : ( SV331 @ SY868 ) ) )
| ( in @ SV610 @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1337]) ).
thf(1681,plain,
! [SV332: $i > $o,SV8: $i,SV611: $i] :
( ( ~ ( in @ SV611 @ SV8 )
| ~ ( SV332 @ SV611 )
| ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1682,plain,
! [SV612: $i,SV333: $i,SV9: $i] :
( ( ~ ( func @ SV9 @ SV333 @ SV612 )
| ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV9 )
| ( ( ap @ SV9 @ SV333 @ SV612 @ SY1372 )
= ( ap @ SV9 @ SV333 @ SV612 @ SY1372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1683,plain,
! [SV334: $i,SV10: $i,SV613: $i] :
( ( ~ ( in @ SV613 @ SV10 )
| ! [SY1373: $i] :
( ~ ( in @ SY1373 @ SV334 )
| ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SY1373 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1684,plain,
! [SV614: $i,SV335: $i,SV11: $i] :
( ( ~ ( func @ SV11 @ SV335 @ SV614 )
| ! [SY1374: $i] :
( ~ ( func @ SV11 @ SV335 @ SY1374 )
| ~ ! [SY1375: $i] :
( ~ ( in @ SY1375 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1375 )
= ( ap @ SV11 @ SV335 @ SY1374 @ SY1375 ) ) )
| ! [SY1376: $i] :
( ~ ( in @ SY1376 @ SV11 )
| ! [SY1377: $i] :
( ~ ( in @ SY1377 @ SV335 )
| ~ ( in @ ( kpair @ SY1376 @ SY1377 ) @ SY1374 )
| ( in @ ( kpair @ SY1376 @ SY1377 ) @ SV614 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1685,plain,
! [SV12: $i] :
( ( ( iskpair @ SV12 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV12 )
@ ^ [SY36: $i] :
( SV12
= ( kpair @ ( kfst @ SV12 ) @ SY36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1686,plain,
! [SV337: $i,SV615: $i > $i,SV14: $i] :
( ( ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ SV14 )
| ( in @ ( SV615 @ SY1378 ) @ SV337 ) )
| ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1344]) ).
thf(1687,plain,
! [SV338: $i,SV15: $i] :
( ( ( SV15 != SV338 )
= $true )
| ( ( ( setunion @ SV15 )
= ( setunion @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1688,plain,
! [SV616: $i,SV339: $i,SV16: $i] :
( ( ~ ( func @ SV16 @ SV339 @ SV616 )
| ( in @ SV616 @ ( funcSet @ SV16 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1346]) ).
thf(1689,plain,
! [SV17: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( ! [SY886: $i] :
( ~ ( in @ SY886 @ ( powerset @ SV17 ) )
| ! [SY887: $i] :
( ~ ( in @ SY887 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SY886 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY887 ) @ ( binunion @ SY886 @ SY887 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1347]) ).
thf(1690,plain,
! [SV617: $i,SV341: $i,SV18: $i] :
( ( ( binintersect @ SV18 @ ( binunion @ SV341 @ SV617 ) )
= ( binunion @ ( binintersect @ SV18 @ SV341 ) @ ( binintersect @ SV18 @ SV617 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1348]) ).
thf(1691,plain,
! [SV618: $i,SV342: $i,SV19: $i] :
( ( ~ ( breln @ SV19 @ SV342 @ SV618 )
| ! [SY1381: $i > $o] :
( ~ ! [SY1382: $i] :
( ~ ( in @ SY1382 @ SV19 )
| ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV342 )
| ~ ( in @ ( kpair @ SY1382 @ SY1383 ) @ SV618 )
| ( SY1381 @ ( kpair @ SY1382 @ SY1383 ) ) ) )
| ! [SY1384: $i] :
( ~ ( in @ SY1384 @ SV618 )
| ( SY1381 @ SY1384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1692,plain,
! [SV20: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( ! [SY894: $i] :
( ~ ( in @ SY894 @ ( powerset @ SV20 ) )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ SV20 )
| ~ ~ ( in @ SY895 @ ( binunion @ SV343 @ SY894 ) )
| ~ ( in @ SY895 @ SY894 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1693,plain,
! [SV21: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ! [SY896: $i] :
( ~ ( in @ SY896 @ ( powerset @ SV21 ) )
| ~ ( subset @ SV344 @ ( setminus @ SV21 @ SY896 ) )
| ( subset @ SY896 @ ( setminus @ SV21 @ SV344 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1351]) ).
thf(1694,plain,
! [SV22: $i] :
( ( ( in @ SV22 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV22 @ SV22 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1352]) ).
thf(1695,plain,
! [SV23: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ SV23 ) )
= $true )
| ( ( in @ ( setadjoin @ SV345 @ emptyset ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1696,plain,
! [SV346: $i,SV24: $i] :
( ( ( SV24 != SV346 )
= $true )
| ( ( ! [SY897: $i,SY898: $i] :
( ( SY897 != SY898 )
| ~ ( ~ ( ~ ( in @ SY897 @ SV24 )
| ( in @ SY898 @ SV346 ) )
| ~ ( ~ ( in @ SY898 @ SV346 )
| ( in @ SY897 @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1354]) ).
thf(1697,plain,
! [SV25: $i] :
( ( ( in @ SV25 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1698,plain,
! [SV347: $i > $o,SV26: $i] :
( ( ( ~ ~ ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV26 )
| ~ ( SV347 @ SY899 ) ) )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1699,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ~ ! [SY901: $i] :
( ~ ( in @ SY901 @ SV27 )
| ~ ( SV348 @ SY901 ) ) )
= $true )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1700,plain,
! [SV349: $i,SV28: $i,SV619: $i] :
( ( ~ ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) )
| ! [SY1385: $i] :
( ~ ( in @ SY1385 @ SV28 )
| ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SY1385 ) @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1701,plain,
! [SV350: $i,SV29: $i,SV620: $i] :
( ( ~ ( in @ SV620 @ ( funcSet @ SV29 @ SV350 ) )
| ( ( lam @ SV29 @ SV350
@ ^ [SY1386: $i] : ( ap @ SV29 @ SV350 @ SV620 @ SY1386 ) )
= SV620 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1702,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( ~ ( ~ ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
| ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ~ ( ~ ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1703,plain,
! [SV33: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ ( powerset @ SV33 ) ) )
= $true )
| ( ( subset @ SV352 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1362]) ).
thf(1704,plain,
! [SV34: $i,SV353: $i] :
( ( ( ~ ( in @ SV353 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( ! [SY908: $i] :
( ~ ( in @ SY908 @ ( powerset @ SV34 ) )
| ! [SY909: $i] :
( ~ ( in @ SY909 @ SV34 )
| ~ ~ ( in @ SY909 @ ( binunion @ SV353 @ SY908 ) )
| ~ ( in @ SY909 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1705,plain,
! [SV35: $i,SV354: $i] :
( ( ( ~ ( in @ SV354 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ! [SY910: $i] :
( ~ ( in @ SY910 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SY910 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SY910 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1364]) ).
thf(1706,plain,
! [SV36: $i] :
( ( ( in @ SV36 @ omega )
= $false )
| ( ( in @ ( omegaS @ SV36 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1707,plain,
! [SV355: $i,SV37: $i,SV622: $i] :
( ( ~ ( in @ SV622 @ ( setadjoin @ SV37 @ ( setadjoin @ SV355 @ emptyset ) ) )
| ( SV622 = SV37 )
| ( SV622 = SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1708,plain,
! [SV38: $i,SV356: $i] :
( ( ( ~ ( in @ SV356 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ ( powerset @ SV38 ) )
| ( in @ ( setminus @ SV356 @ SY912 ) @ ( powerset @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1709,plain,
! [SV357: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV357 ) )
= $true )
| ( ( ! [SY913: $i] :
( ~ ( breln1 @ SV40 @ SY913 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV40 )
| ! [SY915: $i] :
( ~ ( in @ SY915 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY915 ) @ ( breln1compset @ SV40 @ SV357 @ SY913 ) )
| ~ ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY916 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY916 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY916 @ SY915 ) @ SY913 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1710,plain,
! [SV358: $i,SV41: $i] :
( ( ( ~ ( breln1 @ SV41 @ SV358 ) )
= $true )
| ( ( ! [SY917: $i] :
( ~ ( breln1 @ SV41 @ SY917 )
| ! [SY918: $i] :
( ~ ( breln1 @ SV41 @ SY918 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SY917 ) @ SY918 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY918 ) @ ( breln1compset @ SV41 @ SY917 @ SY918 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1711,plain,
! [SV42: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV42 ) )
| ! [SY920: $i] :
( ~ ( in @ SY920 @ SV42 )
| ~ ( in @ SY920 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SY919 ) ) )
| ( in @ SY920 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SY919 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1712,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i] :
( ( ~ ~ ! [SY1387: $i] :
~ ~ ( ~ ( in @ SY1387 @ SV43 )
| ( SV623
!= ( SV360 @ SY1387 ) ) )
| ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1713,plain,
! [SV361: $i,SV44: $i,SV624: $i] :
( ( ~ ( in @ SV624 @ ( injFuncSet @ SV44 @ SV361 ) )
| ( in @ SV624 @ ( funcSet @ SV44 @ SV361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1372]) ).
thf(1714,plain,
! [SV362: $i,SV45: $i] :
( ( ( ~ ( breln1 @ SV45 @ SV362 ) )
= $true )
| ( ( ! [SY925: $i] :
( ~ ( breln1 @ SV45 @ SY925 )
| ( breln1 @ SV45 @ ( binunion @ SV362 @ SY925 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1715,plain,
! [SV625: $i,SV363: $i,SV46: $i] :
( ( ! [SY1389: $i] :
( ( ( kpair @ SV46 @ SV363 )
!= ( kpair @ SV625 @ SY1389 ) )
| ( SV46 = SV625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1374]) ).
thf(1716,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ( ~ ( in @ SV364 @ ( setunion @ SV47 ) )
| ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
| ~ ( ~ ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) )
| ( in @ SV364 @ ( setunion @ SV47 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1717,plain,
! [SV365: $i,SV48: $i,SV626: $i] :
( ( ~ ( in @ SV626 @ ( setadjoin @ SV48 @ SV365 ) )
| ( SV626 = SV48 )
| ( in @ SV626 @ SV365 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1718,plain,
! [SV366: $i,SV49: $i] :
( ( ( ~ ( breln1 @ SV49 @ SV366 ) )
= $true )
| ( ( ! [SY931: $i] :
( ~ ( breln1 @ SV49 @ SY931 )
| ( ( binunion @ SV366 @ SY931 )
= ( binunion @ SY931 @ SV366 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1719,plain,
! [SV51: $i] :
( ( ( in @ SV51 @ omega )
= $false )
| ( ( ! [SY121: $i] :
( ~ ( in @ SY121 @ omega )
| ( ( omegaS @ SV51 )
!= ( omegaS @ SY121 ) )
| ( SV51 = SY121 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1720,plain,
! [SV52: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ ( powerset @ SV52 ) )
| ! [SY933: $i] :
( ~ ( in @ SY933 @ SV52 )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SY932 ) )
| ( in @ SY933 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SY932 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1721,plain,
! [SV53: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ ( powerset @ SV53 ) ) )
= $true )
| ( ( ! [SY934: $i] :
( ~ ( in @ SY934 @ ( powerset @ SV53 ) )
| ~ ( subset @ SV368 @ SY934 )
| ( subset @ ( setminus @ SV53 @ SY934 ) @ ( setminus @ SV53 @ SV368 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1722,plain,
! [SV54: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ! [SY935: $i] :
( ~ ( in @ SY935 @ ( powerset @ SV54 ) )
| ~ ( subset @ ( setminus @ SV54 @ SY935 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SY935 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1723,plain,
! [SV55: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ ( powerset @ SV55 ) ) )
= $true )
| ( ( ! [SY936: $i] :
( ~ ( in @ SY936 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV370 @ ( setminus @ SV55 @ SY936 ) )
| ! [SY937: $i] :
( ~ ( in @ SY937 @ SV55 )
| ~ ( in @ SY937 @ SY936 )
| ( in @ SY937 @ ( setminus @ SV55 @ SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1724,plain,
! [SV56: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ ( powerset @ SV56 ) ) )
= $true )
| ( ( SV371
= ( setminus @ SV56 @ ( setminus @ SV56 @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1725,plain,
! [SV57: $i,SV372: $i] :
( ( ( ~ ( in @ SV372 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( ! [SY938: $i] :
( ~ ( in @ SY938 @ ( powerset @ SV57 ) )
| ! [SY939: $i] :
( ~ ( in @ SY939 @ SV57 )
| ~ ( in @ SY939 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SY938 ) ) )
| ~ ( in @ SY939 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1726,plain,
! [SV373: $i > $o,SV58: $i] :
( ( ( ~ ~ ~ ! [SY940: $i] :
~ ~ ( ~ ( in @ SY940 @ SV58 )
| ~ ( SV373 @ SY940 ) ) )
= $true )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1727,plain,
! [SV374: $i,SV59: $i,SV627: $i] :
( ( ~ ( in @ SV627 @ ( setminus @ SV59 @ SV374 ) )
| ~ ( in @ SV627 @ SV374 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1728,plain,
! [SV375: $i,SV60: $i,SV628: $i] :
( ( ~ ( in @ SV628 @ ( setadjoin @ SV60 @ ( setadjoin @ SV375 @ emptyset ) ) )
| ( SV628 = SV60 )
| ( SV628 = SV375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1387]) ).
thf(1729,plain,
! [SV376: $i > $o,SV61: $i] :
( ( ( ~ ~ ! [SY944: $i] :
( ~ ( in @ SY944 @ SV61 )
| ( SV376 @ SY944 ) ) )
= $true )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1730,plain,
! [SV377: $i,SV629: $i > $i,SV62: $i] :
( ( ~ ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV62 )
| ( in @ ( SV629 @ SY1390 ) @ SV377 ) )
| ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1731,plain,
! [SV378: $i,SV63: $i,SV630: $i] :
( ( ~ ~ ( in @ SV630 @ SV63 )
| ~ ( in @ SV630 @ ( setminus @ SV63 @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1390]) ).
thf(1732,plain,
! [SV65: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ ( powerset @ SV65 ) ) )
= $true )
| ( ( in @ ( setminus @ SV65 @ SV379 ) @ ( powerset @ SV65 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1733,plain,
! [SV66: $i,SV380: $i] :
( ( ( ~ ( in @ SV380 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV66 ) )
| ! [SY952: $i] :
( ~ ( in @ SY952 @ SV66 )
| ~ ~ ( in @ SY952 @ SV380 )
| ~ ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ ( binunion @ SV380 @ SY951 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1734,plain,
! [SV381: $i,SV67: $i] :
( ( ( SV67 != SV381 )
= $true )
| ( ( ! [SY953: $i,SY954: $i] :
( ( SY953 != SY954 )
| ~ ( in @ SY953 @ SV67 )
| ( in @ SY954 @ SV381 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1735,plain,
! [SV68: $i] :
( ( ( iskpair @ SV68 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV68 )
@ ^ [SY160: $i] : ( in @ ( setadjoin @ SY160 @ emptyset ) @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1394]) ).
thf(1736,plain,
! [SV69: $i,SV382: $i,SV631: $i] :
( ( ~ ( in @ SV631 @ SV382 )
| ~ ( in @ SV631 @ ( setminus @ SV69 @ SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1737,plain,
! [SV383: $o,SV70: $i,SV632: $i] :
( ( ~ ( in @ SV632 @ SV70 )
| ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV70 )
| ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1394: $i] :
( ~ ( ~ SV383
| ( SY1394 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1394 != SY1393 ) ) ) )
= ( setadjoin @ SY1393 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1738,plain,
! [SV70: $i,SV633: $i] :
( ( ~ ( in @ SV633 @ SV70 )
| ! [SY1395: $i] :
( ~ ( in @ SY1395 @ SV70 )
| ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1396: $i] :
( ~ ( ~ $true
| ( SY1396 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1396 != SY1395 ) ) ) )
= ( setadjoin @ SY1395 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1397]) ).
thf(1739,plain,
! [SV70: $i,SV634: $i] :
( ( ~ ( in @ SV634 @ SV70 )
| ! [SY1397: $i] :
( ~ ( in @ SY1397 @ SV70 )
| ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1398: $i] :
( ~ ( ~ $false
| ( SY1398 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1398 != SY1397 ) ) ) )
= ( setadjoin @ SY1397 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1398]) ).
thf(1740,plain,
! [SV71: $o] :
( ( SV71 = $false )
| ( ( set2prop @ ( prop2set @ SV71 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1741,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1742,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1743,plain,
! [SV73: $i] :
( ( ( ~ ! [SY167: $i] :
~ ( in @ SY167 @ SV73 ) )
= $false )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1744,plain,
! [SV635: $i,SV385: $i,SV75: $i] :
( ( ~ ( func @ SV75 @ SV385 @ SV635 )
| ! [SY1399: $i] :
( ~ ( in @ SY1399 @ SV75 )
| ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SY1399 ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1745,plain,
! [SV76: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( ! [SY961: $i] :
( ~ ( in @ SY961 @ ( powerset @ SV76 ) )
| ! [SY962: $i] :
( ~ ( in @ SY962 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SY961 ) )
| ~ ( in @ SY962 @ SV386 )
| ( in @ SY962 @ SY961 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1746,plain,
! [SV77: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ! [SY963: $i] :
( ~ ( in @ SY963 @ ( powerset @ SV77 ) )
| ! [SY964: $i] :
( ~ ( in @ SY964 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SY963 ) )
| ~ ( in @ SY964 @ SY963 )
| ~ ( in @ SY964 @ SV387 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1407]) ).
thf(1747,plain,
! [SV388: $i,SV78: $i,SV636: $i] :
( ( ! [SY1400: $i] :
( ~ ( in @ ( kpair @ SV636 @ SY1400 ) @ ( cartprod @ SV78 @ SV388 ) )
| ( in @ SY1400 @ SV388 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1748,plain,
! [SV389: $i,SV79: $i,SV637: $i] :
( ( ~ ( in @ SV637 @ SV79 )
| ! [SY1401: $i] :
( ~ ( in @ SY1401 @ SV389 )
| ( in @ ( kpair @ SV637 @ SY1401 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1409]) ).
thf(1749,plain,
! [SV80: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( powerset @ SV80 ) ) )
= $true )
| ( ( ! [SY969: $i] :
( ~ ( in @ SY969 @ ( powerset @ SV80 ) )
| ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SY969 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1410]) ).
thf(1750,plain,
! [SV81: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ SV81 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV391 @ emptyset ) @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1751,plain,
! [SV82: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( powerset @ SV82 ) ) )
= $true )
| ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ ( powerset @ SV82 ) )
| ! [SY971: $i] :
( ~ ( in @ SY971 @ SV82 )
| ~ ~ ( in @ SY971 @ SV392 )
| ~ ( in @ SY971 @ ( binintersect @ SV392 @ SY970 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1752,plain,
! [SV638: $i > $i > $o,SV393: $i,SV83: $i] :
( ( ! [SY1402: $i,SY1403: $i] :
( ~ ( in @ ( kpair @ SY1402 @ SY1403 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SY1404: $i,SY1405: $i] : ( SV638 @ SY1404 @ SY1405 ) ) )
| ( SV638 @ SY1402 @ SY1403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1753,plain,
! [SV639: $i,SV394: $i,SV84: $i] :
( ( ~ ( func @ SV84 @ SV394 @ SV639 )
| ! [SY1406: $i] :
( ~ ( in @ SY1406 @ SV84 )
| ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1407: $i] : ( in @ ( kpair @ SY1406 @ SY1407 ) @ SV639 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1414]) ).
thf(1754,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ~ ~ ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) )
| ~ ( in @ SV640 @ SV85 )
| ( in @ SV640 @ SV395 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1755,plain,
! [SV396: $i,SV86: $i] :
( ( ( ( setadjoin @ SV86 @ emptyset )
!= ( setadjoin @ SV396 @ emptyset ) )
= $true )
| ( ( SV86 = SV396 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1416]) ).
thf(1756,plain,
! [SV397: $i,SV87: $i,SV641: $i] :
( ( ~ ( in @ SV641 @ SV87 )
| ~ ~ ( in @ SV641 @ SV397 )
| ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1417]) ).
thf(1757,plain,
! [SV399: $i,SV642: $i > $i,SV89: $i] :
( ( ~ ! [SY1408: $i] :
( ~ ( in @ SY1408 @ SV89 )
| ( in @ ( SV642 @ SY1408 ) @ SV399 ) )
| ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1758,plain,
! [SV400: $i,SV90: $i] :
( ( ( SV90 != SV400 )
= $true )
| ( ( subset @ SV400 @ SV90 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1759,plain,
! [SV401: $i,SV91: $i,SV643: $i] :
( ( ~ ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) )
| ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SV91 )
| ( in @ ( kpair @ SY1411 @ ( ap @ SV91 @ SV401 @ SV643 @ SY1411 ) ) @ SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1760,plain,
! [SV92: $i] :
( ( ( in @ SV92 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV92 @ SV92 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1761,plain,
! [SV402: $i,SV93: $i] :
( ( ( ~ ( breln1 @ SV93 @ SV402 ) )
= $true )
| ( ( ! [SY988: $i] :
( ~ ( breln1 @ SV93 @ SY988 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV93 )
| ! [SY990: $i] :
( ~ ( in @ SY990 @ SV93 )
| ~ ( in @ ( kpair @ SY989 @ SY990 ) @ ( binunion @ SV402 @ SY988 ) )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SV402 )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SY988 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1423]) ).
thf(1762,plain,
! [SV403: $o,SV94: $i,SV644: $i] :
( ( ~ ( in @ SV644 @ SV94 )
| ! [SY1412: $i] :
( ~ ( in @ SY1412 @ SV94 )
| ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1413: $i] :
( ~ ( ~ SV403
| ( SY1413 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1413 != SY1412 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1763,plain,
! [SV94: $i,SV645: $i] :
( ( ~ ( in @ SV645 @ SV94 )
| ! [SY1414: $i] :
( ~ ( in @ SY1414 @ SV94 )
| ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1415: $i] :
( ~ ( ~ $true
| ( SY1415 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1415 != SY1414 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1425]) ).
thf(1764,plain,
! [SV94: $i,SV646: $i] :
( ( ~ ( in @ SV646 @ SV94 )
| ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV94 )
| ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1417: $i] :
( ~ ( ~ $false
| ( SY1417 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1417 != SY1416 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1426]) ).
thf(1765,plain,
! [SV95: $i,SV404: $i] :
( ( ( ~ ! [SY994: $i] :
( ~ ( in @ SY994 @ SV404 )
| ( in @ SY994 @ SV95 ) ) )
= $true )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1766,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ~ ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
| ! [SY1418: $o] :
( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SY1418 )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SY1418 )
| SY1418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1429]) ).
thf(1767,plain,
! [SV407: $i,SV98: $i,SV648: $i] :
( ( ~ ( in @ SV648 @ ( setminus @ SV98 @ SV407 ) )
| ( in @ SV648 @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1430]) ).
thf(1768,plain,
! [SV408: $i,SV99: $i] :
( ( ( ~ ( breln1 @ SV99 @ SV408 ) )
= $true )
| ( ( ! [SY998: $i] :
( ~ ( breln1 @ SV99 @ SY998 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV99 )
| ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1000 ) @ ( breln1compset @ SV99 @ SV408 @ SY998 ) )
| ! [SY1001: $o] :
( ~ ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1002 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1002 @ SY1000 ) @ SY998 )
| SY1001 )
| SY1001 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1769,plain,
! [SV100: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ ( breln1Set @ SV100 ) ) )
= $true )
| ( ( breln1 @ SV100 @ SV409 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1770,plain,
! [SV101: $i] :
( ( ( singleton @ SV101 )
= $false )
| ( ( in @ ( setunion @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1771,plain,
! [SV649: $i,SV410: $i,SV102: $i] :
( ( ! [SY1419: $i] :
( ( ( kpair @ SV102 @ SV410 )
!= ( kpair @ SV649 @ SY1419 ) )
| ( SV410 = SY1419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1772,plain,
! [SV411: $i,SV103: $i] :
( ( ( ~ ( breln1 @ SV103 @ SV411 ) )
= $true )
| ( ( breln1 @ SV103 @ ( breln1invset @ SV103 @ SV411 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1435]) ).
thf(1773,plain,
! [SV412: $i,SV104: $i] :
( ( ( ~ ( in @ SV104 @ SV412 ) )
= $true )
| ( ( ~ ( in @ SV412 @ SV104 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1774,plain,
! [SV650: $i > $i > $o,SV414: $i,SV106: $i] :
( ( subset
@ ( dpsetconstr @ SV106 @ SV414
@ ^ [SY1420: $i,SY1421: $i] : ( SV650 @ SY1420 @ SY1421 ) )
@ ( cartprod @ SV106 @ SV414 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1438]) ).
thf(1775,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY1008: $i,SY1009: $i] :
( ( SY1008 != SY1009 )
| ~ ( ~ ( ~ ( SV107 @ SY1008 )
| ( SV415 @ SY1009 ) )
| ~ ( ~ ( SV415 @ SY1009 )
| ( SV107 @ SY1008 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1776,plain,
! [SV108: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ ( powerset @ SV108 ) )
| ! [SY1019: $i] :
( ~ ( in @ SY1019 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SY1018 )
| ~ ( subset @ SV416 @ SY1019 )
| ( subset @ SV416 @ ( binintersect @ SY1018 @ SY1019 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1777,plain,
! [SV417: $i,SV109: $i,SV651: $i] :
( ( ~ ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
| ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( funcSet @ SV109 @ SV417 ) )
| ~ ! [SY1423: $i] :
( ~ ( in @ SY1423 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1423 )
= ( ap @ SV109 @ SV417 @ SY1422 @ SY1423 ) ) )
| ( SV651 = SY1422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1441]) ).
thf(1778,plain,
! [SV418: $i,SV110: $i,SV652: $i] :
( ( ~ ( in @ SV652 @ ( cartprod @ SV110 @ SV418 ) )
| ( iskpair @ SV652 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1442]) ).
thf(1779,plain,
! [SV419: $i,SV111: $i,SV653: $i] :
( ( ~ ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
| ~ ! [SY1424: $i] :
~ ~ ( ~ ( in @ SY1424 @ SV111 )
| ~ ~ ! [SY1425: $i] :
~ ~ ( ~ ( in @ SY1425 @ SV419 )
| ( SV653
!= ( kpair @ SY1424 @ SY1425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1443]) ).
thf(1780,plain,
! [SV113: $i] :
( ( ( SV113 != emptyset )
= $false )
| ( ( ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV113 )
| ( ( binintersect @ SY275 @ SV113 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1781,plain,
! [SV114: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ ( powerset @ SV114 ) ) )
= $true )
| ( ( subset @ SV421 @ ( setminus @ SV114 @ ( setminus @ SV114 @ SV421 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1782,plain,
! [SV422: $i,SV115: $i,SV654: $i] :
( ( ~ ( in @ ( setadjoin @ SV654 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) ) )
| ( SV115 = SV654 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1447]) ).
thf(1783,plain,
! [SV116: $i,SV423: $i] :
( ( ( ~ ( in @ SV423 @ ( powerset @ SV116 ) ) )
= $true )
| ( ( ! [SY1028: $i] :
( ~ ( in @ SY1028 @ ( powerset @ SV116 ) )
| ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SY1028 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1784,plain,
! [SV117: $i,SV424: $i] :
( ( ( ~ ( in @ SV424 @ ( powerset @ SV117 ) ) )
= $true )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV117 ) )
| ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( powerset @ SV117 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV117 )
| ~ ( in @ SY1031 @ ( binintersect @ SV424 @ SY1029 ) )
| ( in @ SY1031 @ ( binintersect @ ( binunion @ SV424 @ SY1030 ) @ ( binunion @ SY1029 @ SY1030 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1449]) ).
thf(1785,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV118 )
| ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV118 )
| ~ ( SV425 @ SY1032 )
| ~ ( SV425 @ SY1033 )
| ( SY1032 = SY1033 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1450]) ).
thf(1786,plain,
! [SV426: $i > $i,SV119: $i] :
( ( ! [SY1036: $i] :
~ ! [SY1037: $i] :
~ ( ~ ( ~ ( in @ SY1037 @ SY1036 )
| ~ ! [SY1038: $i] :
~ ~ ( ~ ( in @ SY1038 @ SV119 )
| ( SY1037
!= ( SV426 @ SY1038 ) ) ) )
| ~ ( ~ ~ ! [SY1039: $i] :
~ ~ ( ~ ( in @ SY1039 @ SV119 )
| ( SY1037
!= ( SV426 @ SY1039 ) ) )
| ( in @ SY1037 @ SY1036 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1451]) ).
thf(1787,plain,
! [SV655: $i,SV427: $i,SV120: $i] :
( ( ~ ( func @ SV120 @ SV427 @ SV655 )
| ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1427: $i] : ( in @ ( kpair @ SY1426 @ SY1427 ) @ SV655 ) ) )
@ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1452]) ).
thf(1788,plain,
! [SV428: $i,SV121: $i] :
( ( ( ~ ! [SY1043: $i] :
~ ( ~ ( ~ ( in @ SY1043 @ SV121 )
| ( in @ SY1043 @ SV428 ) )
| ~ ( ~ ( in @ SY1043 @ SV428 )
| ( in @ SY1043 @ SV121 ) ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1789,plain,
! [SV429: $i,SV122: $i] :
( ( ( ~ ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV122 )
| ( in @ SY1044 @ SV429 ) ) )
= $true )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1790,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_X )
| ( subset @ SX0 @ sK1_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1791,plain,
( ( ~ ( ~ ( in @ sK2_SY0 @ sK1_X )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1792,plain,
! [SV123: $i,SV430: $i] :
( ( ( ~ ( subset @ SV430 @ SV123 ) )
= $true )
| ( ( in @ SV430 @ ( powerset @ SV123 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1457]) ).
thf(1793,plain,
! [SV431: $i,SV656: $i > $i,SV124: $i] :
( ( ~ ! [SY1428: $i] :
( ~ ( in @ SY1428 @ SV124 )
| ( in @ ( SV656 @ SY1428 ) @ SV431 ) )
| ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1794,plain,
! [SV432: $o,SV125: $i,SV657: $i] :
( ( ~ ( in @ SV657 @ SV125 )
| ! [SY1430: $i] :
( ~ ( in @ SY1430 @ SV125 )
| ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1431: $i] :
( ~ ( ~ SV432
| ( SY1431 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1431 != SY1430 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1795,plain,
! [SV125: $i,SV658: $i] :
( ( ~ ( in @ SV658 @ SV125 )
| ! [SY1432: $i] :
( ~ ( in @ SY1432 @ SV125 )
| ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1433: $i] :
( ~ ( ~ $true
| ( SY1433 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1433 != SY1432 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1796,plain,
! [SV125: $i,SV659: $i] :
( ( ~ ( in @ SV659 @ SV125 )
| ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SV125 )
| ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1435: $i] :
( ~ ( ~ $false
| ( SY1435 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1435 != SY1434 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1797,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( setunion @ SV126 ) ) )
= $true )
| ( ( ! [SY1051: $o] :
( ~ ! [SY1052: $i] :
( ~ ( in @ SV433 @ SY1052 )
| ~ ( in @ SY1052 @ SV126 )
| SY1051 )
| SY1051 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1798,plain,
! [SV434: $i,SV127: $i,SV660: $i] :
( ( ~ ( in @ SV660 @ ( cartprod @ SV127 @ SV434 ) )
| ( in @ ( ksnd @ SV660 ) @ SV434 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1799,plain,
! [SV435: $i,SV128: $i] :
( ( ( ~ ( breln1 @ SV128 @ SV435 ) )
= $true )
| ( ( ! [SY1054: $i] :
( ~ ( breln1 @ SV128 @ SY1054 )
| ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SY1054 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1464]) ).
thf(1800,plain,
! [SV436: $i,SV661: $i,SV129: $i] :
( ( ~ ( subset @ SV129 @ SV661 )
| ( subset @ SV129 @ ( setadjoin @ SV436 @ SV661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1801,plain,
! [SV438: $i,SV131: $i,SV662: $i] :
( ( ~ ( in @ SV662 @ SV131 )
| ~ ~ ( in @ SV662 @ SV438 )
| ~ ( subset @ SV131 @ SV438 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1802,plain,
! [SV663: $i,SV439: $i,SV132: $i] :
( ( ! [SY1436: $i] :
( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SY1436 @ emptyset ) ) @ emptyset ) ) )
| ( SV663 != SY1436 )
| ( SV439 = SY1436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1468]) ).
thf(1803,plain,
! [SV133: $i,SV440: $i] :
( ( ( ~ ( in @ SV440 @ ( powerset @ SV133 ) ) )
= $true )
| ( ( ! [SY1059: $i] :
( ~ ( in @ SY1059 @ ( powerset @ SV133 ) )
| ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV133 )
| ~ ( in @ SY1060 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SY1059 ) ) )
| ( in @ SY1060 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SY1059 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1469]) ).
thf(1804,plain,
! [SV134: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( powerset @ SV134 ) )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( powerset @ SV134 ) )
| ! [SY1063: $i] :
( ~ ( in @ SY1063 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1062 )
| ~ ( subset @ SY1061 @ SY1063 )
| ( subset @ ( binintersect @ SV441 @ SY1061 ) @ ( binintersect @ SY1062 @ SY1063 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1470]) ).
thf(1805,plain,
! [SV136: $i > $o] :
( ( ( ~ ! [SY335: $i] :
~ ~ ( ~ ( SV136 @ SY335 )
| ~ ! [SY336: $i] :
( ~ ( SV136 @ SY336 )
| ( SY335 = SY336 ) ) ) )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1472]) ).
thf(1806,plain,
! [SV443: $i,SV137: $i] :
( ( ( ( setminus @ SV137 @ SV443 )
!= emptyset )
= $true )
| ( ( subset @ SV137 @ SV443 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1473]) ).
thf(1807,plain,
! [SV138: $i > $o] :
( ( ( ~ ! [SY340: $i] :
~ ~ ( ~ ( SV138 @ SY340 )
| ~ ! [SY341: $i] :
( ~ ( SV138 @ SY341 )
| ( SY340 = SY341 ) ) ) )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1474]) ).
thf(1808,plain,
! [SV664: $i,SV444: $i,SV139: $i] :
( ( ~ ( func @ SV139 @ SV444 @ SV664 )
| ! [SY1437: $i] :
( ~ ( func @ SV139 @ SV444 @ SY1437 )
| ~ ! [SY1438: $i] :
( ~ ( in @ SY1438 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1438 )
= ( ap @ SV139 @ SV444 @ SY1437 @ SY1438 ) ) )
| ( SV664 = SY1437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1809,plain,
! [SV445: $i > $i,SV140: $i] :
( ( ! [SY1067: $i] :
~ ~ ( ~ ! [SY1068: $i] :
~ ( ~ ( ~ ( in @ SY1068 @ SY1067 )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1068
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1068
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1068 @ SY1067 ) ) )
| ~ ! [SY1071: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1071 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1071 ) ) )
| ( SY1067 = SY1071 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1476]) ).
thf(1810,plain,
! [SV665: $i > $i > $o,SV446: $i,SV141: $i] :
( ( ! [SY1439: $i,SY1440: $i] :
( ~ ( in @ ( kpair @ SY1439 @ SY1440 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SY1441: $i,SY1442: $i] : ( SV665 @ SY1441 @ SY1442 ) ) )
| ( in @ SY1439 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1477]) ).
thf(1811,plain,
! [SV447: $i,SV142: $i,SV666: $i] :
( ( ! [SY1443: $i] :
( ~ ( in @ ( kpair @ SV666 @ SY1443 ) @ ( cartprod @ SV142 @ SV447 ) )
| ( in @ SV666 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1478]) ).
thf(1812,plain,
! [SV143: $i,SV448: $i] :
( ( ( ~ ( in @ SV448 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( ! [SY1082: $i] :
( ~ ( in @ SY1082 @ ( powerset @ SV143 ) )
| ! [SY1083: $i] :
( ~ ( in @ SY1083 @ ( powerset @ SV143 ) )
| ~ ( subset @ SY1082 @ SY1083 )
| ( subset @ ( binintersect @ SV448 @ SY1082 ) @ SY1083 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1813,plain,
! [SV449: $i > $o,SV144: $i] :
( ( ( ~ ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) ) )
= $true )
| ( ( ~ ! [SY1085: $i] :
~ ~ ( ~ ( in @ SY1085 @ SV144 )
| ~ ( SV449 @ SY1085 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1480]) ).
thf(1814,plain,
! [SV450: $i,SV145: $i] :
( ( ( ~ ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV145 )
| ( in @ SY1086 @ SV450 ) ) )
= $true )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1481]) ).
thf(1815,plain,
! [SV451: $i,SV146: $i] :
( ( ( ~ ( breln1 @ SV146 @ SV451 ) )
= $true )
| ( ( ! [SY1087: $i > $o] :
( ~ ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV146 )
| ! [SY1089: $i] :
( ~ ( in @ SY1089 @ SV146 )
| ~ ( in @ ( kpair @ SY1088 @ SY1089 ) @ SV451 )
| ( SY1087 @ ( kpair @ SY1088 @ SY1089 ) ) ) )
| ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV451 )
| ( SY1087 @ SY1090 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1482]) ).
thf(1816,plain,
! [SV452: $i,SV147: $i] :
( ( ( SV147 != SV452 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV452 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1483]) ).
thf(1817,plain,
! [SV453: $i > $i,SV148: $i,SV667: $i] :
( ( ~ ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
| ~ ! [SY1445: $i] :
~ ~ ( ~ ( in @ SY1445 @ SV148 )
| ( SV667
!= ( SV453 @ SY1445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1818,plain,
! [SV149: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( powerset @ SV149 ) ) )
= $true )
| ( ( ! [SY1094: $i] :
( ~ ( in @ SY1094 @ ( powerset @ SV149 ) )
| ~ ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV149 )
| ~ ( in @ SY1095 @ SV454 )
| ( in @ SY1095 @ SY1094 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV149 )
| ~ ( in @ SY1096 @ SY1094 )
| ( in @ SY1096 @ SV454 ) )
| ( SV454 = SY1094 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1485]) ).
thf(1819,plain,
! [SV455: $i,SV150: $i,SV668: $i] :
( ( ~ ( in @ SV668 @ ( injFuncSet @ SV150 @ SV455 ) )
| ( injective @ SV150 @ SV455 @ SV668 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1486]) ).
thf(1820,plain,
! [SV457: $i,SV152: $i] :
( ( ( ( binintersect @ SV152 @ SV457 )
!= SV457 )
= $true )
| ( ( subset @ SV457 @ SV152 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1488]) ).
thf(1821,plain,
! [SV458: $i > $o,SV153: $i] :
( ( ( ~ ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV153 )
| ~ ( SV458 @ SY1099 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1822,plain,
! [SV459: $i,SV154: $i] :
( ( ( ~ ( breln1 @ SV154 @ SV459 ) )
= $true )
| ( ( ! [SY1101: $i] :
( ~ ( breln1 @ SV154 @ SY1101 )
| ! [SY1102: $i] :
( ~ ( breln1 @ SV154 @ SY1102 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SY1101 ) @ SY1102 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SY1101 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1823,plain,
! [SV155: $i > $o] :
( ( ( ~ ! [SY399: $i] :
~ ~ ( ~ ( SV155 @ SY399 )
| ~ ! [SY400: $i] :
( ~ ( SV155 @ SY400 )
| ( SY399 = SY400 ) ) ) )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1491]) ).
thf(1824,plain,
! [SV460: $i,SV156: $i] :
( ( ( ~ ( breln1 @ SV156 @ SV460 ) )
= $true )
| ( ( ! [SY1103: $i > $o] :
( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV156 )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV156 )
| ~ ( in @ ( kpair @ SY1104 @ SY1105 ) @ SV460 )
| ( SY1103 @ ( kpair @ SY1104 @ SY1105 ) ) ) )
| ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV460 )
| ( SY1103 @ SY1106 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1492]) ).
thf(1825,plain,
! [SV461: $i,SV157: $i,SV669: $i] :
( ( ~ ( in @ SV669 @ SV157 )
| ! [SY1446: $i] :
( ~ ( in @ SY1446 @ SV461 )
| ( in @ ( kpair @ SV669 @ SY1446 ) @ ( cartprod @ SV157 @ SV461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1493]) ).
thf(1826,plain,
! [SV462: $o,SV158: $i,SV670: $i] :
( ( ~ ( in @ SV670 @ SV158 )
| ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SV158 )
| ~ ~ SV462
| ( in @ SY1447
@ ( dsetconstr @ SV158
@ ^ [SY1448: $i] :
( ~ ( ~ SV462
| ( SY1448 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1448 != SY1447 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1827,plain,
! [SV158: $i,SV671: $i] :
( ( ~ ( in @ SV671 @ SV158 )
| ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV158 )
| ~ ~ $true
| ( in @ SY1449
@ ( dsetconstr @ SV158
@ ^ [SY1450: $i] :
( ~ ( ~ $true
| ( SY1450 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1450 != SY1449 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1828,plain,
! [SV158: $i,SV672: $i] :
( ( ~ ( in @ SV672 @ SV158 )
| ! [SY1451: $i] :
( ~ ( in @ SY1451 @ SV158 )
| ~ ~ $false
| ( in @ SY1451
@ ( dsetconstr @ SV158
@ ^ [SY1452: $i] :
( ~ ( ~ $false
| ( SY1452 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1452 != SY1451 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1496]) ).
thf(1829,plain,
! [SV673: $i,SV159: $i,SV463: $i] :
( ( ~ ( in @ SV463 @ ( powerset @ SV159 ) )
| ~ ( in @ SV673 @ SV463 )
| ( in @ SV673 @ SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1830,plain,
! [SV464: $i,SV160: $i,SV674: $i] :
( ( ~ ( in @ SV674 @ SV160 )
| ~ ~ ( in @ SV674 @ SV464 )
| ( SV160 != SV464 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1831,plain,
! [SV675: $i,SV465: $i,SV161: $i] :
( ( ~ ( subset @ SV161 @ SV465 )
| ~ ( subset @ SV465 @ SV675 )
| ( subset @ SV161 @ SV675 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1499]) ).
thf(1832,plain,
! [SV162: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ ( powerset @ SV162 ) ) )
= $true )
| ( ( in @ ( powerset @ SV466 ) @ ( powerset @ ( powerset @ SV162 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1833,plain,
! [SV163: $i,SV467: $i] :
( ( ( ~ ( in @ SV467 @ ( powerset @ SV163 ) ) )
= $true )
| ( ( ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV163 )
| ~ ~ ( in @ SY1115 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SY1115 @ SV467 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1834,plain,
! [SV468: $i,SV164: $i,SV676: $i] :
( ( ~ ( in @ SV676 @ SV164 )
| ~ ~ ( in @ SV676 @ SV468 )
| ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1502]) ).
thf(1835,plain,
! [SV469: $i > $o,SV165: $i,SV677: $i] :
( ( ~ ( in @ SV677 @ SV165 )
| ~ ( SV469 @ SV677 )
| ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1503]) ).
thf(1836,plain,
! [SV166: $i > $o] :
( ( ( ~ ! [SY429: $i] :
~ ( SV166 @ SY429 ) )
= $false )
| ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1504]) ).
thf(1837,plain,
! [SV167: $i > $o] :
( ( ( ~ ! [SY434: $i] :
~ ~ ( ~ ( SV167 @ SY434 )
| ~ ! [SY435: $i] :
( ~ ( SV167 @ SY435 )
| ( SY434 = SY435 ) ) ) )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1505]) ).
thf(1838,plain,
! [SV678: $i,SV470: $i,SV168: $i] :
( ( ~ ( breln @ SV168 @ SV470 @ SV678 )
| ! [SY1454: $i] :
( ~ ( breln @ SV168 @ SV470 @ SY1454 )
| ~ ! [SY1455: $i] :
( ~ ( in @ SY1455 @ SV168 )
| ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV470 )
| ~ ( in @ ( kpair @ SY1455 @ SY1456 ) @ SV678 )
| ( in @ ( kpair @ SY1455 @ SY1456 ) @ SY1454 ) ) )
| ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV168 )
| ! [SY1458: $i] :
( ~ ( in @ SY1458 @ SV470 )
| ~ ( in @ ( kpair @ SY1457 @ SY1458 ) @ SY1454 )
| ( in @ ( kpair @ SY1457 @ SY1458 ) @ SV678 ) ) )
| ( SV678 = SY1454 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1506]) ).
thf(1839,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ~ ( ~ ( ~ ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
| ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
| ~ ( ~ ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) )
| ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1508]) ).
thf(1840,plain,
! [SV171: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ ( powerset @ SV171 ) ) )
= $true )
| ( ( ! [SY1130: $i] :
( ~ ( in @ SY1130 @ ( powerset @ SV171 ) )
| ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV171 )
| ~ ~ ( in @ SY1131 @ SY1130 )
| ~ ( in @ SY1131 @ ( binintersect @ SV473 @ SY1130 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1841,plain,
! [SV474: $i,SV680: $i > $i,SV172: $i] :
( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV172 )
| ( in @ ( SV680 @ SY1463 ) @ SV474 ) )
| ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1510]) ).
thf(1842,plain,
! [SV174: $i > $o] :
( ( ( ~ ! [SY460: $i] :
~ ! [SY461: $i] :
~ ( ~ ( ~ ( SV174 @ SY461 )
| ( SY461 = SY460 ) )
| ~ ( ( SY461 != SY460 )
| ( SV174 @ SY461 ) ) ) )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1843,plain,
! [SV475: $i,SV175: $i] :
( ( ( SV175 != SV475 )
= $true )
| ( ( ! [SY1136: $i,SY1137: $i] :
( ( SY1136 != SY1137 )
| ( ( setadjoin @ SV175 @ SY1136 )
= ( setadjoin @ SV475 @ SY1137 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1513]) ).
thf(1844,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ~ ( in @ SV681 @ SV176 )
| ~ ( ~ ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) )
| ~ ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1514]) ).
thf(1845,plain,
! [SV477: $i,SV177: $i,SV682: $i] :
( ( ~ ( in @ SV682 @ SV177 )
| ( in @ SV682 @ ( binunion @ SV177 @ SV477 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1515]) ).
thf(1846,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( setunion @ SV178 ) ) )
= $true )
| ( ( ~ ! [SY1142: $i] :
~ ~ ( ~ ( in @ SY1142 @ SV178 )
| ~ ( in @ SV478 @ SY1142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1847,plain,
! [SV179: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( powerset @ SV179 ) )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( powerset @ SV179 ) )
| ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV179 )
| ~ ( in @ SY1145 @ ( binintersect @ SV479 @ SY1143 ) )
| ( in @ SY1145 @ ( binunion @ SY1143 @ SY1144 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1517]) ).
thf(1848,plain,
! [SV480: $o,SV181: $i,SV683: $i] :
( ( ~ ( in @ SV683 @ SV181 )
| ! [SY1468: $i] :
( ~ ( in @ SY1468 @ SV181 )
| ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SY1468 )
= SV683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1849,plain,
! [SV181: $i,SV684: $i] :
( ( ~ ( in @ SV684 @ SV181 )
| ! [SY1469: $i] :
( ~ ( in @ SY1469 @ SV181 )
| ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SY1469 )
= SV684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1850,plain,
! [SV181: $i,SV685: $i] :
( ( ~ ( in @ SV685 @ SV181 )
| ! [SY1470: $i] :
( ~ ( in @ SY1470 @ SV181 )
| ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SY1470 )
= SV685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1851,plain,
! [SV481: $i,SV182: $i,SV686: $i] :
( ( ~ ~ ( in @ SV686 @ SV182 )
| ~ ( in @ SV686 @ SV481 )
| ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1521]) ).
thf(1852,plain,
! [SV687: $i,SV482: $i,SV183: $i] :
( ( ~ ( breln @ SV183 @ SV482 @ SV687 )
| ! [SY1471: $i > $o] :
( ~ ! [SY1472: $i] :
( ~ ( in @ SY1472 @ SV183 )
| ! [SY1473: $i] :
( ~ ( in @ SY1473 @ SV482 )
| ~ ( in @ ( kpair @ SY1472 @ SY1473 ) @ SV687 )
| ( SY1471 @ ( kpair @ SY1472 @ SY1473 ) ) ) )
| ! [SY1474: $i] :
( ~ ( in @ SY1474 @ SV687 )
| ( SY1471 @ SY1474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1522]) ).
thf(1853,plain,
! [SV688: $i,SV483: $i,SV184: $i] :
( ( ~ ( subset @ SV184 @ SV483 )
| ~ ~ ( in @ SV688 @ SV483 )
| ~ ( in @ SV688 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1854,plain,
! [SV484: $i,SV185: $i] :
( ( ( ~ ( subset @ SV185 @ SV484 ) )
= $true )
| ( ( ~ ( subset @ SV484 @ SV185 )
| ( SV185 = SV484 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1524]) ).
thf(1855,plain,
! [SV186: $i,SV485: $i] :
( ( ( ~ ( in @ SV485 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( ! [SY1155: $i] :
( ~ ( in @ SY1155 @ ( powerset @ SV186 ) )
| ( in @ ( binunion @ SV485 @ SY1155 ) @ ( powerset @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1856,plain,
! [SV187: $o] :
( ( SV187 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1857,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1527]) ).
thf(1858,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1528]) ).
thf(1859,plain,
! [SV188: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( powerset @ SV188 ) ) )
= $true )
| ( ( ! [SY1156: $i] :
( ~ ( in @ SY1156 @ ( powerset @ SV188 ) )
| ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV188 )
| ~ ( in @ SY1157 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SY1156 ) ) )
| ( in @ SY1157 @ ( setminus @ SV188 @ SV486 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1860,plain,
! [SV487: $i > $o,SV189: $i] :
( ( ( ~ ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) ) )
= $true )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV189 )
| ! [SY1160: $i] :
( ~ ( in @ SY1160 @ SV189 )
| ~ ( SV487 @ SY1159 )
| ~ ( SV487 @ SY1160 )
| ( SY1159 = SY1160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1861,plain,
! [SV488: $o,SV190: $i,SV689: $i] :
( ( ~ ( in @ SV689 @ SV190 )
| ! [SY1475: $i] :
( ~ ( in @ SY1475 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1476: $i] :
( ~ ( ~ SV488
| ( SY1476 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1476 != SY1475 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1531]) ).
thf(1862,plain,
! [SV190: $i,SV690: $i] :
( ( ~ ( in @ SV690 @ SV190 )
| ! [SY1477: $i] :
( ~ ( in @ SY1477 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1478: $i] :
( ~ ( ~ $true
| ( SY1478 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1478 != SY1477 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1863,plain,
! [SV190: $i,SV691: $i] :
( ( ~ ( in @ SV691 @ SV190 )
| ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1480: $i] :
( ~ ( ~ $false
| ( SY1480 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1480 != SY1479 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1864,plain,
! [SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV489 )
| ~ ! [SY508: $i] :
~ ~ ( ~ ( SV191 @ SY1164 @ SY508 )
| ~ ! [SY509: $i] :
( ~ ( SV191 @ SY1164 @ SY509 )
| ( SY508 = SY509 ) ) ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1534]) ).
thf(1865,plain,
! [SV490: $i,SV192: $i] :
( ( ( ~ ~ ( subset @ SV192 @ SV490 ) )
= $true )
| ( ( SV192 != SV490 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1535]) ).
thf(1866,plain,
! [SV491: $i,SV193: $i] :
( ( ( SV193 != SV491 )
= $true )
| ( ( ( setadjoin @ SV193 @ ( setadjoin @ SV491 @ emptyset ) )
= ( setadjoin @ SV193 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1536]) ).
thf(1867,plain,
! [SV492: $i,SV194: $i,SV692: $i] :
( ( ~ ( in @ SV692 @ ( surjFuncSet @ SV194 @ SV492 ) )
| ( surjective @ SV194 @ SV492 @ SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1537]) ).
thf(1868,plain,
! [SV494: $i,SV196: $i,SV693: $i] :
( ( ~ ( in @ SV693 @ SV196 )
| ( in @ ( setadjoin @ SV693 @ emptyset ) @ ( powerset @ ( binunion @ SV196 @ SV494 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1869,plain,
! [SV495: $i,SV197: $i] :
( ( ( ~ ( breln1 @ SV197 @ SV495 ) )
= $true )
| ( ( SV495
= ( breln1invset @ SV197 @ ( breln1invset @ SV197 @ SV495 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1540]) ).
thf(1870,plain,
! [SV198: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ ( powerset @ SV198 ) ) )
= $true )
| ( ( ! [SY1173: $i] :
( ~ ( in @ SY1173 @ ( powerset @ SV198 ) )
| ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV198 )
| ~ ( in @ SY1174 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SY1173 ) ) )
| ( in @ SY1174 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SY1173 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1871,plain,
! [SV497: $i,SV199: $i,SV694: $i] :
( ( ~ ( in @ SV694 @ ( funcSet @ SV199 @ SV497 ) )
| ~ ( injective @ SV199 @ SV497 @ SV694 )
| ( in @ SV694 @ ( injFuncSet @ SV199 @ SV497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1542]) ).
thf(1872,plain,
! [SV200: $i] :
( ( ( ! [SY527: $i] :
( ~ ( in @ SY527 @ SV200 )
| ( subset @ SY527 @ SV200 ) ) )
= $false )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1543]) ).
thf(1873,plain,
! [SV499: $i,SV695: $i > $i,SV202: $i] :
( ( ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV202 )
| ( in @ ( SV695 @ SY1481 ) @ SV499 ) )
| ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1545]) ).
thf(1874,plain,
! [SV203: $i] :
( ( ( subset @ SV203 @ emptyset )
= $false )
| ( ( SV203 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1546]) ).
thf(1875,plain,
! [SV204: $i] :
( ( ( singleton @ SV204 )
= $false )
| ( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV204 )
| ( ( setunion @ SV204 )
= SY535 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1876,plain,
! [SV205: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ ( powerset @ SV205 ) ) )
= $true )
| ( ( ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV205 )
| ~ ( in @ SY1180 @ SV500 )
| ( in @ SY1180 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1877,plain,
! [SV502: $i > $o,SV207: $i,SV696: $i] :
( ( ~ ( in @ SV696 @ SV207 )
| ~ ( SV502 @ SV696 )
| ( in @ SV696
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1550]) ).
thf(1878,plain,
! [SV697: $i > $i > $o,SV503: $i,SV208: $i] :
( ( ! [SY1485: $i,SY1486: $i] :
( ~ ( in @ ( kpair @ SY1485 @ SY1486 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SY1487: $i,SY1488: $i] : ( SV697 @ SY1487 @ SY1488 ) ) )
| ( in @ SY1486 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1879,plain,
! [SV504: $i,SV209: $i] :
( ( ( ~ ( breln1 @ SV209 @ SV504 ) )
= $true )
| ( ( ! [SY1188: $i] :
( ~ ( breln1 @ SV209 @ SY1188 )
| ~ ! [SY1189: $i] :
( ~ ( in @ SY1189 @ SV209 )
| ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV209 )
| ~ ( in @ ( kpair @ SY1189 @ SY1190 ) @ SV504 )
| ( in @ ( kpair @ SY1189 @ SY1190 ) @ SY1188 ) ) )
| ( subset @ SV504 @ SY1188 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1552]) ).
thf(1880,plain,
! [SV210: $i,SV505: $i] :
( ( ( ~ ( in @ SV505 @ SV210 ) )
= $true )
| ( ( in @ SV505 @ ( powerset @ ( setunion @ SV210 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1881,plain,
! [SV211: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ ( powerset @ SV211 ) ) )
= $true )
| ( ( ! [SY1191: $i] :
( ~ ( in @ SY1191 @ ( powerset @ SV211 ) )
| ! [SY1192: $i] :
( ~ ( in @ SY1192 @ ( powerset @ SV211 ) )
| ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV211 )
| ~ ( in @ SY1193 @ ( binintersect @ SV506 @ SY1191 ) )
| ( in @ SY1193 @ ( binunion @ SV506 @ SY1192 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1554]) ).
thf(1882,plain,
! [SV212: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
| ~ ! [SY1498: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY1498 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1498 ) )
| ~ ! [SY1501: $i] :
~ ~ ! [SY1502: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1501 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1502 @ SY1498 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1501 )
| ~ ( in @ SX5 @ SY1498 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1501 ) )
| ( in @ SY1502 @ SY1504 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1555]) ).
thf(1883,plain,
! [SV507: $i,SV213: $i,SV698: $i] :
( ( ~ ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) )
| ! [SY1506: $i] :
( ~ ( in @ SY1506 @ SV213 )
| ( ( ap @ SV213 @ SV507 @ SV698 @ SY1506 )
= ( ap @ SV213 @ SV507 @ SV698 @ SY1506 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1556]) ).
thf(1884,plain,
! [SV508: $o,SV214: $i,SV699: $i] :
( ( ~ ( in @ SV699 @ SV214 )
| ! [SY1507: $i] :
( ~ ( in @ SY1507 @ SV214 )
| ( in @ ( if @ SV214 @ SV508 @ SV699 @ SY1507 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SY1507 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1885,plain,
! [SV214: $i,SV700: $i] :
( ( ~ ( in @ SV700 @ SV214 )
| ! [SY1508: $i] :
( ~ ( in @ SY1508 @ SV214 )
| ( in @ ( if @ SV214 @ $true @ SV700 @ SY1508 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SY1508 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1886,plain,
! [SV214: $i,SV701: $i] :
( ( ~ ( in @ SV701 @ SV214 )
| ! [SY1509: $i] :
( ~ ( in @ SY1509 @ SV214 )
| ( in @ ( if @ SV214 @ $false @ SV701 @ SY1509 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SY1509 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1887,plain,
! [SV702: $i > $i > $o,SV509: $i,SV215: $i] :
( ( ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV215 )
| ~ ! [SY1511: $i] :
~ ~ ( ~ ( in @ SY1511 @ SV509 )
| ~ ( SV702 @ SY1510 @ SY1511 ) ) )
| ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1560]) ).
thf(1888,plain,
! [SV510: $i,SV216: $i] :
( ( ( ~ ( subset @ SV216 @ SV510 ) )
= $true )
| ( ( in @ SV216 @ ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1889,plain,
! [SV217: $i > $o,SV511: $i] :
( ( ( ~ ( in @ SV511 @ emptyset ) )
= $true )
| ( ( SV217 @ SV511 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1890,plain,
! [SV512: $i,SV220: $i,SV703: $i] :
( ( ~ ( in @ SV703 @ ( cartprod @ SV220 @ SV512 ) )
| ( in @ ( kfst @ SV703 ) @ SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1563]) ).
thf(1891,plain,
! [SV513: $i,SV221: $i] :
( ( ( ~ ( subset @ SV221 @ SV513 ) )
= $true )
| ( ( ( setminus @ SV221 @ SV513 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1564]) ).
thf(1892,plain,
! [SV704: $i,SV514: $i,SV222: $i] :
( ( ( ( setadjoin @ SV222 @ ( setadjoin @ SV514 @ emptyset ) )
!= ( setadjoin @ SV704 @ emptyset ) )
| ( SV222 = SV514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1565]) ).
thf(1893,plain,
! [SV705: $i,SV516: $i,SV225: $i] :
( ( ~ ( func @ SV225 @ SV516 @ SV705 )
| ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV225 )
| ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV516 )
| ~ ( in @ ( kpair @ SY1516 @ SY1517 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SY1516 )
= SY1517 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1567]) ).
thf(1894,plain,
! [SV226: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV226 )
| ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) ) )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1895,plain,
! [SV227: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ ( powerset @ SV227 ) ) )
= $true )
| ( ( ! [SY1210: $i] :
( ~ ( in @ SY1210 @ ( powerset @ SV227 ) )
| ~ ( subset @ SV517 @ ( setminus @ SV227 @ SY1210 ) )
| ( subset @ SY1210 @ ( setminus @ SV227 @ SV517 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1896,plain,
! [SV228: $i] :
( ( ( ~ ! [SY605: $i] :
~ ( in @ SY605 @ SV228 ) )
= $false )
| ( ( SV228 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1897,plain,
! [SV229: $i,SV518: $i] :
( ( ( ~ ( in @ SV518 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( ! [SY1211: $i] :
( ~ ( in @ SY1211 @ ( powerset @ SV229 ) )
| ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SY1211 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1898,plain,
! [SV519: $i,SV230: $i] :
( ( ( ~ ! [SY1212: $i] :
( ~ ( in @ SY1212 @ SV230 )
| ( in @ SY1212 @ SV519 ) ) )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1899,plain,
! [SV231: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ ( powerset @ SV231 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV231 @ ( setminus @ SV231 @ SV520 ) ) @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1900,plain,
! [SV521: $i > $o,SV232: $i] :
( ( ( ~ ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SV232 )
| ( SV521 @ SY1214 ) ) )
= $true )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1901,plain,
! [SV522: $i,SV233: $i,SV706: $i] :
( ( ~ ( in @ SV706 @ ( funcSet @ SV233 @ SV522 ) )
| ( func @ SV233 @ SV522 @ SV706 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1575]) ).
thf(1902,plain,
! [SV523: $i,SV234: $i] :
( ( ( ~ ( breln1 @ SV234 @ SV523 ) )
= $true )
| ( ( ! [SY1217: $i] :
( ~ ( breln1 @ SV234 @ SY1217 )
| ! [SY1218: $i] :
( ~ ( in @ SY1218 @ SV234 )
| ! [SY1219: $i] :
( ~ ( in @ SY1219 @ SV234 )
| ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV234 )
| ~ ( in @ ( kpair @ SY1218 @ SY1220 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1220 @ SY1219 ) @ SY1217 )
| ( in @ ( kpair @ SY1218 @ SY1219 ) @ ( breln1compset @ SV234 @ SV523 @ SY1217 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1576]) ).
thf(1903,plain,
! [SV524: $i,SV235: $i] :
( ( ( ~ ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV235 )
| ~ ( in @ SY1221 @ SV524 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1904,plain,
! [SV525: $i,SV236: $i,SV707: $i] :
( ( ~ ( in @ SV707 @ SV236 )
| ~ ( in @ SV707 @ SV525 )
| ( in @ SV707 @ ( binintersect @ SV236 @ SV525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1578]) ).
thf(1905,plain,
! [SV708: $i,SV526: $i,SV237: $i] :
( ( ! [SY1518: $i] :
( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SV526 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV708 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV708 @ ( setadjoin @ SY1518 @ emptyset ) ) @ emptyset ) ) )
| ( SV237 = SV708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1579]) ).
thf(1906,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i] :
( ( ! [SY1519: $i] :
( ~ ( in @ SY1519 @ SV238 )
| ! [SY1520: $i] :
( ~ ( in @ SY1520 @ SV527 )
| ~ ( in @ ( kpair @ SY1519 @ SY1520 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SY1519 @ SY1520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1580]) ).
thf(1907,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ~ ( in @ SV710 @ SV239 )
| ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV528 )
| ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SY1523 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1581]) ).
thf(1908,plain,
! [SV240: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( powerset @ SV240 ) ) )
= $true )
| ( ( ! [SY1232: $i] :
( ~ ( in @ SY1232 @ ( powerset @ SV240 ) )
| ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SY1232 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1909,plain,
! [SV530: $o,SV241: $i,SV711: $i] :
( ( ~ ( in @ SV711 @ SV241 )
| ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV241 )
| ( in @ ( if @ SV241 @ SV530 @ SV711 @ SY1524 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1583]) ).
thf(1910,plain,
! [SV241: $i,SV712: $i] :
( ( ~ ( in @ SV712 @ SV241 )
| ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV241 )
| ( in @ ( if @ SV241 @ $true @ SV712 @ SY1525 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1584]) ).
thf(1911,plain,
! [SV241: $i,SV713: $i] :
( ( ~ ( in @ SV713 @ SV241 )
| ! [SY1526: $i] :
( ~ ( in @ SY1526 @ SV241 )
| ( in @ ( if @ SV241 @ $false @ SV713 @ SY1526 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1912,plain,
! [SV714: $i,SV532: $i,SV243: $i] :
( ( ~ ( func @ SV243 @ SV532 @ SV714 )
| ( ( lam @ SV243 @ SV532
@ ^ [SY1527: $i] : ( ap @ SV243 @ SV532 @ SV714 @ SY1527 ) )
= SV714 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1587]) ).
thf(1913,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV245 )
| ! [SY1241: $i] :
( ~ ( in @ SY1241 @ SV245 )
| ~ ( SV534 @ SY1240 )
| ~ ( SV534 @ SY1241 )
| ( SY1240 = SY1241 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1589]) ).
thf(1914,plain,
! [SV715: $i,SV535: $i,SV246: $i] :
( ( ! [SY1528: $i] :
( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SV535 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV715 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV715 @ ( setadjoin @ SY1528 @ emptyset ) ) @ emptyset ) ) )
| ( SV535 = SY1528 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1590]) ).
thf(1915,plain,
! [SV536: $i,SV247: $i] :
( ( ( ~ ( subset @ SV247 @ SV536 ) )
= $true )
| ( ( subset @ ( powerset @ SV247 ) @ ( powerset @ SV536 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1916,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ( ~ ( in @ SV537 @ ( powerset @ SV248 ) )
| ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) )
| ~ ( ~ ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) )
| ( in @ SV537 @ ( powerset @ SV248 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1917,plain,
! [SV249: $i] :
( ( ( in @ SV249 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1918,plain,
! [SV538: $i,SV250: $i,SV716: $i] :
( ( ~ ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
| ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV250 )
| ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV538 )
| ~ ( in @ ( kpair @ SY1529 @ SY1530 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SY1529 )
= SY1530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1594]) ).
thf(1919,plain,
! [SV539: $i,SV251: $i] :
( ( ( ~ ( breln1 @ SV251 @ SV539 ) )
= $true )
| ( ( ! [SY1251: $i] :
( ~ ( in @ SY1251 @ SV251 )
| ! [SY1252: $i] :
( ~ ( in @ SY1252 @ SV251 )
| ~ ( in @ ( kpair @ SY1251 @ SY1252 ) @ SV539 )
| ( in @ ( kpair @ SY1252 @ SY1251 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1920,plain,
! [SV540: $i,SV252: $i] :
( ( ( ~ ( breln1 @ SV252 @ SV540 ) )
= $true )
| ( ( ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SV252 )
| ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV252 )
| ~ ( in @ ( kpair @ SY1254 @ SY1253 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SY1253 @ SY1254 ) @ SV540 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1596]) ).
thf(1921,plain,
! [SV253: $o,SV541: $i] :
( ( ( ~ ( in @ SV541 @ ( prop2set @ SV253 ) ) )
= $true )
| ( SV253 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1597]) ).
thf(1922,plain,
! [SV542: $i] :
( ( ( ~ ( in @ SV542 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1923,plain,
! [SV543: $i] :
( ( ( ~ ( in @ SV543 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1924,plain,
! [SV544: $i,SV254: $i,SV717: $i] :
( ( ~ ( in @ SV717 @ ( binintersect @ SV254 @ SV544 ) )
| ( in @ SV717 @ SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1600]) ).
thf(1925,plain,
! [SV545: $i,SV255: $i] :
( ( ( ~ ( breln1 @ SV255 @ SV545 ) )
= $true )
| ( ( ! [SY1256: $i] :
( ~ ( breln1 @ SV255 @ SY1256 )
| ! [SY1257: $i] :
( ~ ( in @ SY1257 @ SV255 )
| ! [SY1258: $i] :
( ~ ( in @ SY1258 @ SV255 )
| ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ ( binunion @ SV545 @ SY1256 ) )
| ! [SY1259: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SV545 )
| SY1259 )
| ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SY1256 )
| SY1259 )
| SY1259 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1926,plain,
! [SV256: $i,SV546: $i,SV718: $i] :
( ( ~ ( in @ SV718 @ SV546 )
| ( in @ SV718 @ ( setadjoin @ SV256 @ SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1602]) ).
thf(1927,plain,
! [SV547: $i,SV257: $i,SV719: $i] :
( ( ~ ( in @ SV719 @ SV257 )
| ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV547 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SY1531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1603]) ).
thf(1928,plain,
! [SV258: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ ( powerset @ SV258 ) ) )
= $true )
| ( ( ! [SY1263: $i] :
( ~ ( in @ SY1263 @ ( powerset @ SV258 ) )
| ! [SY1264: $i] :
( ~ ( in @ SY1264 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SY1263 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1264 ) @ ( binunion @ SY1263 @ SY1264 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1929,plain,
! [SV549: $i,SV259: $i,SV720: $i] :
( ( ~ ( in @ SV720 @ ( surjFuncSet @ SV259 @ SV549 ) )
| ( in @ SV720 @ ( funcSet @ SV259 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1605]) ).
thf(1930,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY1266: $i,SY1267: $i] :
( ( SY1266 != SY1267 )
| ~ ( ~ ( ~ ( SV260 @ SY1266 )
| ( SV550 @ SY1267 ) )
| ~ ( ~ ( SV550 @ SY1267 )
| ( SV260 @ SY1266 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1931,plain,
! [SV261: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ ( funcSet @ SV261 @ ( powerset @ SV261 ) ) ) )
= $true )
| ( ( ~ ( surjective @ SV261 @ ( powerset @ SV261 ) @ SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1932,plain,
! [SV262: $i] :
( ( ( in @ SV262 @ omega )
= $false )
| ( ( ( omegaS @ SV262 )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1933,plain,
! [SV263: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ ( powerset @ SV263 ) ) )
= $true )
| ( ( ! [SY1274: $i] :
( ~ ( in @ SY1274 @ ( powerset @ SV263 ) )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1275 )
| ( subset @ ( binintersect @ SV552 @ SY1274 ) @ SY1275 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1609]) ).
thf(1934,plain,
! [SV553: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV553 ) )
= $true )
| ( ( ! [SY1276: $i] :
( ~ ( breln1 @ SV264 @ SY1276 )
| ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV264 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV264 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV553 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SY1276 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV264 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV264 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SY1276 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV553 ) ) )
| ( SV553 = SY1276 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1610]) ).
thf(1935,plain,
! [SV554: $i,SV265: $i,SV721: $i] :
( ( ~ ( in @ SV721 @ SV265 )
| ~ ( in @ SV721 @ SV554 )
| ~ ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1611]) ).
thf(1936,plain,
! [SV555: $i,SV266: $i,SV722: $i] :
( ( ~ ( in @ SV722 @ ( cartprod @ SV266 @ SV555 ) )
| ( ( kpair @ ( kfst @ SV722 ) @ ( ksnd @ SV722 ) )
= SV722 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1612]) ).
thf(1937,plain,
! [SV268: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ ( powerset @ SV268 ) ) )
= $true )
| ( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV268 )
| ~ ( in @ SY1283 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SY1283 @ SV557 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1938,plain,
! [SV558: $i > $o,SV269: $i] :
( ( ( ~ ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SV269 )
| ~ ~ ( SV558 @ SY1284 ) ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1939,plain,
! [SV559: $i,SV270: $i,SV723: $i] :
( ( ~ ~ ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
| ~ ~ ( in @ SV723 @ SV559 )
| ~ ( in @ SV723 @ SV270 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1616]) ).
thf(1940,plain,
! [SV271: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ ( powerset @ SV271 ) ) )
= $true )
| ( ( ! [SY1287: $i] :
( ~ ( in @ SY1287 @ ( powerset @ SV271 ) )
| ! [SY1288: $i] :
( ~ ( in @ SY1288 @ SV271 )
| ~ ( in @ SY1288 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SY1287 ) ) )
| ( in @ SY1288 @ ( setminus @ SV271 @ SY1287 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1941,plain,
! [SV272: $i] :
( ( ( ! [SY725: $i] :
~ ( in @ SY725 @ SV272 ) )
= $false )
| ( ( SV272 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1618]) ).
thf(1942,plain,
! [SV561: $i,SV273: $i] :
( ( ( ~ ( subset @ SV273 @ SV561 ) )
= $true )
| ( ( ( binintersect @ SV273 @ SV561 )
= SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1619]) ).
thf(1943,plain,
! [SV562: $i,SV274: $i] :
( ( ( ~ ( breln1 @ SV274 @ SV562 ) )
= $true )
| ( ( ! [SY1289: $i] :
( ~ ( breln1 @ SV274 @ SY1289 )
| ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV274 )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV274 )
| ~ ( in @ ( kpair @ SY1290 @ SY1291 ) @ SV562 )
| ( in @ ( kpair @ SY1290 @ SY1291 ) @ ( binunion @ SV562 @ SY1289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1944,plain,
! [SV563: $i,SV275: $i,SV724: $i] :
( ( ~ ( in @ SV724 @ ( binintersect @ SV275 @ SV563 ) )
| ( in @ SV724 @ SV563 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1621]) ).
thf(1945,plain,
! [SV564: $i,SV276: $i,SV725: $i] :
( ( ~ ~ ( in @ SV725 @ SV276 )
| ~ ~ ( in @ SV725 @ SV564 )
| ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1622]) ).
thf(1946,plain,
! [SV566: $i,SV278: $i,SV726: $i] :
( ( ~ ( in @ SV726 @ SV278 )
| ! [SY1532: $i] :
( ~ ( in @ SY1532 @ SV566 )
| ( ( kfst @ ( kpair @ SV726 @ SY1532 ) )
= SV726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1624]) ).
thf(1947,plain,
! [SV279: $i,SV567: $i] :
( ( ( ~ ( subset @ SV567 @ SV279 ) )
= $true )
| ( ( ( binintersect @ SV279 @ SV567 )
= SV567 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1625]) ).
thf(1948,plain,
! [SV280: $i,SV568: $i,SV727: $i] :
( ( ~ ( in @ SV727 @ SV568 )
| ( in @ SV727 @ ( binunion @ SV280 @ SV568 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1626]) ).
thf(1949,plain,
! [SV281: $i] :
( ( ( SV281 != emptyset )
= $false )
| ( ( ~ ! [SY742: $i] :
~ ~ ( ~ ( in @ SY742 @ SV281 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1950,plain,
! [SV282: $i] :
( ( ( iskpair @ SV282 )
= $false )
| ( ( ( kpair @ ( kfst @ SV282 ) @ ( ksnd @ SV282 ) )
= SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1628]) ).
thf(1951,plain,
! [SV569: $i,SV283: $i] :
( ( ( SV283 != SV569 )
= $true )
| ( ( ! [SY1297: $i > $o,SY1298: $i > $o] :
( ~ ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV283 )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV569 )
| ( SY1299 != SY1300 )
| ~ ( ~ ( ~ ( SY1297 @ SY1299 )
| ( SY1298 @ SY1300 ) )
| ~ ( ~ ( SY1298 @ SY1300 )
| ( SY1297 @ SY1299 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SX4: $i] : ( SY1297 @ SX4 ) )
= ( dsetconstr @ SV569
@ ^ [SX4: $i] : ( SY1298 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1952,plain,
! [SV284: $i > $o] :
( ( ( ~ ! [SY750: $i] :
~ ~ ( ~ ( SV284 @ SY750 )
| ~ ! [SY751: $i] :
( ~ ( SV284 @ SY751 )
| ( SY750 = SY751 ) ) ) )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1953,plain,
! [SV285: $i,SV570: $i] :
( ( ( ~ ( in @ SV570 @ ( powerset @ SV285 ) ) )
= $true )
| ( ( ! [SY1303: $i] :
( ~ ( in @ SY1303 @ ( powerset @ SV285 ) )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV285 )
| ~ ( in @ SY1304 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1304 @ ( binintersect @ SV570 @ SY1303 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1631]) ).
thf(1954,plain,
! [SV571: $i > $o,SV286: $i,SV728: $i] :
( ( ~ ( in @ SV728
@ ( dsetconstr @ SV286
@ ^ [SY1306: $i] : ( SV571 @ SY1306 ) ) )
| ( SV571 @ SV728 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1632]) ).
thf(1955,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ! [SY1534: $o] :
( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
| ~ ( ~ ( in @ SV729 @ SV287 )
| SY1534 )
| ~ ( ~ ( in @ SV729 @ SV572 )
| SY1534 )
| SY1534 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1956,plain,
! [SV573: $i,SV288: $i] :
( ( ( ~ ( breln1 @ SV288 @ SV573 ) )
= $true )
| ( ( ! [SY1309: $i] :
( ~ ( breln1 @ SV288 @ SY1309 )
| ! [SY1310: $i] :
( ~ ( in @ SY1310 @ SV288 )
| ! [SY1311: $i] :
( ~ ( in @ SY1311 @ SV288 )
| ~ ( in @ ( kpair @ SY1310 @ SY1311 ) @ SY1309 )
| ( in @ ( kpair @ SY1310 @ SY1311 ) @ ( binunion @ SV573 @ SY1309 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1957,plain,
! [SV574: $i,SV289: $i] :
( ( ( SV289 != SV574 )
= $true )
| ( ( ( powerset @ SV289 )
= ( powerset @ SV574 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1958,plain,
! [SV730: $i > $i > $o,SV575: $i,SV290: $i] :
( ( breln @ SV290 @ SV575
@ ( dpsetconstr @ SV290 @ SV575
@ ^ [SY1535: $i,SY1536: $i] : ( SV730 @ SY1535 @ SY1536 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1636]) ).
thf(1959,plain,
! [SV576: $o,SV291: $i,SV731: $i] :
( ( ~ ( in @ SV731 @ SV291 )
| ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV291 )
| ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SY1537 )
= SY1537 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1637]) ).
thf(1960,plain,
! [SV291: $i,SV732: $i] :
( ( ~ ( in @ SV732 @ SV291 )
| ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV291 )
| ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SY1538 )
= SY1538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1638]) ).
thf(1961,plain,
! [SV291: $i,SV733: $i] :
( ( ~ ( in @ SV733 @ SV291 )
| ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV291 )
| ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SY1539 )
= SY1539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1639]) ).
thf(1962,plain,
! [SV578: $i,SV294: $i] :
( ( ( ~ ( breln1 @ SV294 @ SV578 ) )
= $true )
| ( ( ! [SY1317: $i] :
( ~ ( breln1 @ SV294 @ SY1317 )
| ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SY1317 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SY1317 ) @ ( breln1invset @ SV294 @ SV578 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1963,plain,
! [SV296: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ ( powerset @ SV296 ) ) )
= $true )
| ( ( ! [SY1318: $i] :
( ~ ( in @ SY1318 @ ( powerset @ SV296 ) )
| ~ ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV296 )
| ~ ( in @ SY1319 @ SV580 )
| ( in @ SY1319 @ SY1318 ) )
| ( in @ SV580 @ ( powerset @ SY1318 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1964,plain,
! [SV581: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV581 ) )
= $true )
| ( ( ! [SY1320: $i] :
( ~ ( breln1 @ SV297 @ SY1320 )
| ! [SY1321: $i] :
( ~ ( in @ SY1321 @ SV297 )
| ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1321 @ SY1322 ) @ SV581 )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ SY1320 ) )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ ( binunion @ SV581 @ SY1320 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1644]) ).
thf(1965,plain,
! [SV734: $i,SV582: $i,SV298: $i] :
( ( ~ ( breln @ SV298 @ SV582 @ SV734 )
| ! [SY1540: $i] :
( ~ ( breln @ SV298 @ SV582 @ SY1540 )
| ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV298 )
| ! [SY1542: $i] :
( ~ ( in @ SY1542 @ SV582 )
| ~ ( in @ ( kpair @ SY1541 @ SY1542 ) @ SV734 )
| ( in @ ( kpair @ SY1541 @ SY1542 ) @ SY1540 ) ) )
| ( subset @ SV734 @ SY1540 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1645]) ).
thf(1966,plain,
! [SV299: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ ( powerset @ SV299 ) ) )
= $true )
| ( ( ! [SY1327: $i] :
( ~ ( in @ SY1327 @ ( powerset @ SV299 ) )
| ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV299 )
| ~ ( in @ SY1328 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SY1327 ) ) )
| ( in @ SY1328 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SY1327 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1646]) ).
thf(1967,plain,
! [SV300: $i > $o] :
( ( ( ~ ! [SY794: $i] :
~ ~ ( ~ ( SV300 @ SY794 )
| ~ ! [SY795: $i] :
( ~ ( SV300 @ SY795 )
| ( SY794 = SY795 ) ) ) )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1968,plain,
! [SV301: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ ( powerset @ SV301 ) ) )
= $true )
| ( ( ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( powerset @ SV301 ) )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV301 )
| ~ ( in @ SY1330 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1330 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SY1329 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1969,plain,
! [SV302: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ ( powerset @ SV302 ) ) )
= $true )
| ( ( ! [SY1331: $i] :
( ~ ( in @ SY1331 @ ( powerset @ SV302 ) )
| ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV302 )
| ~ ( in @ SY1332 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SY1331 ) ) )
| ( in @ SY1332 @ ( setminus @ SV302 @ SV585 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1970,plain,
! [SV586: $i,SV303: $i] :
( ( ( ( binintersect @ SV303 @ SV586 )
!= SV303 )
= $true )
| ( ( subset @ SV303 @ SV586 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1971,plain,
! [SV304: $i] :
( ( ( SV304 != emptyset )
= $false )
| ( ( ~ ! [SY804: $i] :
~ ( in @ SY804 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1651]) ).
thf(1972,plain,
! [SV305: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ ( powerset @ SV305 ) ) )
= $true )
| ( ( ! [SY1333: $i] :
( ~ ( in @ SY1333 @ ( powerset @ SV305 ) )
| ! [SY1334: $i] :
( ~ ( in @ SY1334 @ ( binintersect @ SV587 @ SY1333 ) )
| ( in @ SY1334 @ SV305 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1652]) ).
thf(1973,plain,
! [SV306: $i,SV735: $i,SV588: $i] :
( ( ~ ( in @ SV588 @ SV735 )
| ~ ( in @ SV735 @ SV306 )
| ( in @ SV588 @ ( setunion @ SV306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1653]) ).
thf(1974,plain,
! [SV307: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ ( powerset @ SV307 ) ) )
= $true )
| ( ( ! [SY1336: $i] :
( ~ ( in @ SY1336 @ SV307 )
| ~ ( in @ SY1336 @ SV589 )
| ~ ( in @ SY1336 @ ( setminus @ SV307 @ SV589 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1654]) ).
thf(1975,plain,
! [SV308: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ ( powerset @ SV308 ) ) )
= $true )
| ( ( ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( powerset @ SV308 ) )
| ( ( setminus @ SV308 @ ( binunion @ SV590 @ SY1337 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SY1337 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1655]) ).
thf(1976,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ~ ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
| ! [SY1543: $o] :
( ~ ( ( SV736 != SV309 )
| SY1543 )
| ~ ( ~ ( in @ SV736 @ SV591 )
| SY1543 )
| SY1543 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1656]) ).
thf(1977,plain,
! [SV310: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ ( powerset @ SV310 ) ) )
= $true )
| ( ( ! [SY1340: $i] :
( ~ ( in @ SY1340 @ ( powerset @ SV310 ) )
| ~ ! [SY1341: $i] :
( ~ ( in @ SY1341 @ SV310 )
| ~ ( in @ SY1341 @ SV592 )
| ( in @ SY1341 @ SY1340 ) )
| ( subset @ SV592 @ SY1340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1978,plain,
! [SV593: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ ( setadjoin @ SV593 @ emptyset ) ) )
= $true )
| ( ( in @ SV593 @ ( setadjoin @ SV311 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1979,plain,
! [SV594: $i,SV312: $i,SV737: $i] :
( ( ~ ( in @ SV737 @ ( binunion @ SV312 @ SV594 ) )
| ( in @ SV737 @ SV312 )
| ( in @ SV737 @ SV594 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1659]) ).
thf(1980,plain,
! [SV595: $i,SV313: $i,SV738: $i] :
( ( ~ ( in @ SV738 @ SV313 )
| ! [SY1544: $i] :
( ~ ( in @ SY1544 @ SV595 )
| ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SY1544 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(1981,plain,
! [SV739: $i > $i > $o,SV596: $i,SV314: $i] :
( ( ! [SY1545: $i] :
( ~ ( in @ SY1545 @ SV314 )
| ! [SY1546: $i] :
( ~ ( in @ SY1546 @ SV596 )
| ~ ( SV739 @ SY1545 @ SY1546 )
| ( in @ ( kpair @ SY1545 @ SY1546 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(1982,plain,
! [SV315: $i,SV597: $i] :
( ( ( ~ ( in @ SV597 @ ( powerset @ SV315 ) ) )
= $true )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ ( powerset @ SV315 ) )
| ! [SY1351: $o,SY1352: $i] :
( ~ ( in @ SY1352 @ SV315 )
| ~ ( in @ SY1352 @ ( binunion @ SV597 @ SY1350 ) )
| ~ ( ~ ( in @ SY1352 @ SV597 )
| SY1351 )
| ~ ( ~ ( in @ SY1352 @ SY1350 )
| SY1351 )
| SY1351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1662]) ).
thf(1983,plain,
! [SV598: $i,SV316: $i] :
( ( ( ~ ( in @ SV316 @ ( setadjoin @ SV598 @ emptyset ) ) )
= $true )
| ( ( SV316 = SV598 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1663]) ).
thf(1984,plain,
! [SV317: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY1353: $i] :
( ~ ( in @ SY1353 @ ( powerset @ SV317 ) )
| ! [SY1354: $i] :
( ~ ( in @ SY1354 @ ( powerset @ SV317 ) )
| ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SY1353 ) @ ( binunion @ SY1354 @ SY1355 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SY1353 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1354 ) @ ( setminus @ SV317 @ SY1355 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1664]) ).
thf(1985,plain,
! [SV318: $i,SV600: $i] :
( ( ( ~ ( in @ SV600 @ ( powerset @ SV318 ) ) )
= $true )
| ( ( ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( powerset @ SV318 ) )
| ! [SY1357: $i] :
( ~ ( in @ SY1357 @ SV318 )
| ~ ( subset @ SV600 @ SY1356 )
| ~ ~ ( in @ SY1357 @ SY1356 )
| ~ ( in @ SY1357 @ SV600 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1986,plain,
! [SV740: $i,SV601: $i,SV319: $i] :
( ( ~ ( func @ SV319 @ SV601 @ SV740 )
| ! [SY1549: $i] :
( ~ ( in @ SY1549 @ SV319 )
| ( in @ ( kpair @ SY1549 @ ( ap @ SV319 @ SV601 @ SV740 @ SY1549 ) ) @ SV740 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1666]) ).
thf(1987,plain,
! [SV741: $i,SV602: $i,SV320: $i] :
( ( ~ ( subset @ SV320 @ SV602 )
| ~ ( in @ SV741 @ SV320 )
| ( in @ SV741 @ SV602 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1667]) ).
thf(1988,plain,
! [SV603: $i,SV321: $i,SV742: $i] :
( ( ~ ( subset @ SV742 @ SV321 )
| ~ ( subset @ SV742 @ SV603 )
| ( subset @ SV742 @ ( binintersect @ SV321 @ SV603 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1668]) ).
thf(1989,plain,
! [SV322: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ ( powerset @ SV322 ) ) )
= $true )
| ( ( ! [SY1362: $i] :
( ~ ( in @ SY1362 @ ( powerset @ SV322 ) )
| ( in @ ( binintersect @ SV604 @ SY1362 ) @ ( powerset @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1990,plain,
! [SV323: $i > $o] :
( ( ( ~ ! [SY853: $i] :
~ ~ ( ~ ( SV323 @ SY853 )
| ~ ! [SY854: $i] :
( ~ ( SV323 @ SY854 )
| ( SY853 = SY854 ) ) ) )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1991,plain,
! [SV605: $i,SV324: $i,SV743: $i] :
( ( ~ ( in @ SV743 @ SV324 )
| ! [SY1550: $i] :
( ~ ( in @ SY1550 @ SV605 )
| ( ( kpair @ SV743 @ SY1550 )
= ( kpair @ SV743 @ SY1550 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1671]) ).
thf(1992,plain,
! [SV606: $i,SV325: $i] :
( ( ( SV325 != SV606 )
= $true )
| ( ( subset @ SV325 @ SV606 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1993,plain,
! [SV326: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ ( powerset @ SV326 ) ) )
= $true )
| ( ( ! [SY1365: $i] :
( ~ ( in @ SY1365 @ ( powerset @ SV326 ) )
| ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SY1365 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1994,plain,
! [SV327: $i,SV1: $i] :
( ( ( SV1 = SV327 )
= $false )
| ( ( in @ SV1 @ ( setadjoin @ SV327 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1995,plain,
! [SV328: $i,SV2: $i] :
( ( ( SV2 != SV328 )
= $false )
| ( ( ~ ( in @ SV328 @ ( setadjoin @ SV2 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1675]) ).
thf(1996,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
| ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1676]) ).
thf(1997,plain,
! [SV329: $i,SV608: $i > $i,SV4: $i] :
( ( ( ~ ! [SY1366: $i] :
( ~ ( in @ SY1366 @ SV4 )
| ( in @ ( SV608 @ SY1366 ) @ SV329 ) ) )
= $true )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1677]) ).
thf(1998,plain,
! [SV5: $i] :
( ( ( ~ ( in @ ( sK6_SY13 @ SV5 ) @ SV5 ) )
= $false )
| ( ( SV5 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1678]) ).
thf(1999,plain,
! [SV330: $i,SV6: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV6 ) )
= $true )
| ( ( ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV330 )
| ( ( ksnd @ ( kpair @ SV609 @ SY1368 ) )
= SY1368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1679]) ).
thf(2000,plain,
! [SV331: $i > $o,SV7: $i,SV610: $i] :
( ( ( ~ ( in @ SV610
@ ( dsetconstr @ SV7
@ ^ [SY868: $i] : ( SV331 @ SY868 ) ) ) )
= $true )
| ( ( in @ SV610 @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(2001,plain,
! [SV332: $i > $o,SV8: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV8 ) )
= $true )
| ( ( ~ ( SV332 @ SV611 )
| ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(2002,plain,
! [SV612: $i,SV333: $i,SV9: $i] :
( ( ( ~ ( func @ SV9 @ SV333 @ SV612 ) )
= $true )
| ( ( ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV9 )
| ( ( ap @ SV9 @ SV333 @ SV612 @ SY1372 )
= ( ap @ SV9 @ SV333 @ SV612 @ SY1372 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1682]) ).
thf(2003,plain,
! [SV334: $i,SV10: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV10 ) )
= $true )
| ( ( ! [SY1373: $i] :
( ~ ( in @ SY1373 @ SV334 )
| ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SY1373 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(2004,plain,
! [SV614: $i,SV335: $i,SV11: $i] :
( ( ( ~ ( func @ SV11 @ SV335 @ SV614 ) )
= $true )
| ( ( ! [SY1374: $i] :
( ~ ( func @ SV11 @ SV335 @ SY1374 )
| ~ ! [SY1375: $i] :
( ~ ( in @ SY1375 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1375 )
= ( ap @ SV11 @ SV335 @ SY1374 @ SY1375 ) ) )
| ! [SY1376: $i] :
( ~ ( in @ SY1376 @ SV11 )
| ! [SY1377: $i] :
( ~ ( in @ SY1377 @ SV335 )
| ~ ( in @ ( kpair @ SY1376 @ SY1377 ) @ SY1374 )
| ( in @ ( kpair @ SY1376 @ SY1377 ) @ SV614 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(2005,plain,
! [SV337: $i,SV615: $i > $i,SV14: $i] :
( ( ( ~ ! [SY1378: $i] :
( ~ ( in @ SY1378 @ SV14 )
| ( in @ ( SV615 @ SY1378 ) @ SV337 ) ) )
= $true )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(2006,plain,
! [SV338: $i,SV15: $i] :
( ( ( SV15 = SV338 )
= $false )
| ( ( ( setunion @ SV15 )
= ( setunion @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(2007,plain,
! [SV616: $i,SV339: $i,SV16: $i] :
( ( ( ~ ( func @ SV16 @ SV339 @ SV616 ) )
= $true )
| ( ( in @ SV616 @ ( funcSet @ SV16 @ SV339 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1688]) ).
thf(2008,plain,
! [SV17: $i,SV340: $i] :
( ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false )
| ( ( ! [SY886: $i] :
( ~ ( in @ SY886 @ ( powerset @ SV17 ) )
| ! [SY887: $i] :
( ~ ( in @ SY887 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SY886 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY887 ) @ ( binunion @ SY886 @ SY887 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(2009,plain,
! [SV618: $i,SV342: $i,SV19: $i] :
( ( ( ~ ( breln @ SV19 @ SV342 @ SV618 ) )
= $true )
| ( ( ! [SY1381: $i > $o] :
( ~ ! [SY1382: $i] :
( ~ ( in @ SY1382 @ SV19 )
| ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV342 )
| ~ ( in @ ( kpair @ SY1382 @ SY1383 ) @ SV618 )
| ( SY1381 @ ( kpair @ SY1382 @ SY1383 ) ) ) )
| ! [SY1384: $i] :
( ~ ( in @ SY1384 @ SV618 )
| ( SY1381 @ SY1384 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(2010,plain,
! [SV20: $i,SV343: $i] :
( ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false )
| ( ( ! [SY894: $i] :
( ~ ( in @ SY894 @ ( powerset @ SV20 ) )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ SV20 )
| ~ ~ ( in @ SY895 @ ( binunion @ SV343 @ SY894 ) )
| ~ ( in @ SY895 @ SY894 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(2011,plain,
! [SV21: $i,SV344: $i] :
( ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false )
| ( ( ! [SY896: $i] :
( ~ ( in @ SY896 @ ( powerset @ SV21 ) )
| ~ ( subset @ SV344 @ ( setminus @ SV21 @ SY896 ) )
| ( subset @ SY896 @ ( setminus @ SV21 @ SV344 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(2012,plain,
! [SV23: $i,SV345: $i] :
( ( ( in @ SV345 @ SV23 )
= $false )
| ( ( in @ ( setadjoin @ SV345 @ emptyset ) @ ( powerset @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(2013,plain,
! [SV346: $i,SV24: $i] :
( ( ( SV24 = SV346 )
= $false )
| ( ( ! [SY897: $i,SY898: $i] :
( ( SY897 != SY898 )
| ~ ( ~ ( ~ ( in @ SY897 @ SV24 )
| ( in @ SY898 @ SV346 ) )
| ~ ( ~ ( in @ SY898 @ SV346 )
| ( in @ SY897 @ SV24 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1696]) ).
thf(2014,plain,
! [SV25: $i,SV744: $o] :
( ( SV744 = $true )
| ( ( in @ SV25 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1697]) ).
thf(2015,plain,
! [SV25: $i] :
( ( $true = $true )
| ( ( in @ SV25 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1697]) ).
thf(2016,plain,
! [SV25: $i] :
( ( $false = $true )
| ( ( in @ SV25 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1697]) ).
thf(2017,plain,
! [SV347: $i > $o,SV26: $i] :
( ( ( ~ ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV26 )
| ~ ( SV347 @ SY899 ) ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1698]) ).
thf(2018,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ! [SY901: $i] :
( ~ ( in @ SY901 @ SV27 )
| ~ ( SV348 @ SY901 ) ) )
= $false )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(2019,plain,
! [SV349: $i,SV28: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) ) )
= $true )
| ( ( ! [SY1385: $i] :
( ~ ( in @ SY1385 @ SV28 )
| ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SY1385 ) @ SV349 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(2020,plain,
! [SV350: $i,SV29: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ ( funcSet @ SV29 @ SV350 ) ) )
= $true )
| ( ( ( lam @ SV29 @ SV350
@ ^ [SY1386: $i] : ( ap @ SV29 @ SV350 @ SV620 @ SY1386 ) )
= SV620 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(2021,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( ~ ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
| ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ~ ( ~ ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(2022,plain,
! [SV33: $i,SV352: $i] :
( ( ( in @ SV352 @ ( powerset @ SV33 ) )
= $false )
| ( ( subset @ SV352 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(2023,plain,
! [SV34: $i,SV353: $i] :
( ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false )
| ( ( ! [SY908: $i] :
( ~ ( in @ SY908 @ ( powerset @ SV34 ) )
| ! [SY909: $i] :
( ~ ( in @ SY909 @ SV34 )
| ~ ~ ( in @ SY909 @ ( binunion @ SV353 @ SY908 ) )
| ~ ( in @ SY909 @ SV353 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(2024,plain,
! [SV35: $i,SV354: $i] :
( ( ( in @ SV354 @ ( powerset @ SV35 ) )
= $false )
| ( ( ! [SY910: $i] :
( ~ ( in @ SY910 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SY910 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SY910 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(2025,plain,
! [SV355: $i,SV37: $i,SV622: $i] :
( ( ( ~ ( in @ SV622 @ ( setadjoin @ SV37 @ ( setadjoin @ SV355 @ emptyset ) ) ) )
= $true )
| ( ( ( SV622 = SV37 )
| ( SV622 = SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1707]) ).
thf(2026,plain,
! [SV38: $i,SV356: $i] :
( ( ( in @ SV356 @ ( powerset @ SV38 ) )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ ( powerset @ SV38 ) )
| ( in @ ( setminus @ SV356 @ SY912 ) @ ( powerset @ SV38 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(2027,plain,
! [SV357: $i,SV40: $i] :
( ( ( breln1 @ SV40 @ SV357 )
= $false )
| ( ( ! [SY913: $i] :
( ~ ( breln1 @ SV40 @ SY913 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV40 )
| ! [SY915: $i] :
( ~ ( in @ SY915 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY915 ) @ ( breln1compset @ SV40 @ SV357 @ SY913 ) )
| ~ ! [SY916: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY916 @ SV40 )
| ~ ( in @ ( kpair @ SY914 @ SY916 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY916 @ SY915 ) @ SY913 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(2028,plain,
! [SV358: $i,SV41: $i] :
( ( ( breln1 @ SV41 @ SV358 )
= $false )
| ( ( ! [SY917: $i] :
( ~ ( breln1 @ SV41 @ SY917 )
| ! [SY918: $i] :
( ~ ( breln1 @ SV41 @ SY918 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SY917 ) @ SY918 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY918 ) @ ( breln1compset @ SV41 @ SY917 @ SY918 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1710]) ).
thf(2029,plain,
! [SV42: $i,SV359: $i] :
( ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false )
| ( ( ! [SY919: $i] :
( ~ ( in @ SY919 @ ( powerset @ SV42 ) )
| ! [SY920: $i] :
( ~ ( in @ SY920 @ SV42 )
| ~ ( in @ SY920 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SY919 ) ) )
| ( in @ SY920 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SY919 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(2030,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i] :
( ( ( ~ ~ ! [SY1387: $i] :
~ ~ ( ~ ( in @ SY1387 @ SV43 )
| ( SV623
!= ( SV360 @ SY1387 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1712]) ).
thf(2031,plain,
! [SV361: $i,SV44: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ ( injFuncSet @ SV44 @ SV361 ) ) )
= $true )
| ( ( in @ SV624 @ ( funcSet @ SV44 @ SV361 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(2032,plain,
! [SV362: $i,SV45: $i] :
( ( ( breln1 @ SV45 @ SV362 )
= $false )
| ( ( ! [SY925: $i] :
( ~ ( breln1 @ SV45 @ SY925 )
| ( breln1 @ SV45 @ ( binunion @ SV362 @ SY925 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(2033,plain,
! [SV745: $i,SV625: $i,SV363: $i,SV46: $i] :
( ( ( ( kpair @ SV46 @ SV363 )
!= ( kpair @ SV625 @ SV745 ) )
| ( SV46 = SV625 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1715]) ).
thf(2034,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ( ~ ( in @ SV364 @ ( setunion @ SV47 ) )
| ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(2035,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ( ~ ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) )
| ( in @ SV364 @ ( setunion @ SV47 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1716]) ).
thf(2036,plain,
! [SV365: $i,SV48: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ ( setadjoin @ SV48 @ SV365 ) ) )
= $true )
| ( ( ( SV626 = SV48 )
| ( in @ SV626 @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1717]) ).
thf(2037,plain,
! [SV366: $i,SV49: $i] :
( ( ( breln1 @ SV49 @ SV366 )
= $false )
| ( ( ! [SY931: $i] :
( ~ ( breln1 @ SV49 @ SY931 )
| ( ( binunion @ SV366 @ SY931 )
= ( binunion @ SY931 @ SV366 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1718]) ).
thf(2038,plain,
! [SV51: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ omega )
| ( ( omegaS @ SV51 )
!= ( omegaS @ SV746 ) )
| ( SV51 = SV746 ) )
= $true )
| ( ( in @ SV51 @ omega )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1719]) ).
thf(2039,plain,
! [SV52: $i,SV367: $i] :
( ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ ( powerset @ SV52 ) )
| ! [SY933: $i] :
( ~ ( in @ SY933 @ SV52 )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY933 @ ( setminus @ SV52 @ SY932 ) )
| ( in @ SY933 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SY932 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(2040,plain,
! [SV53: $i,SV368: $i] :
( ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false )
| ( ( ! [SY934: $i] :
( ~ ( in @ SY934 @ ( powerset @ SV53 ) )
| ~ ( subset @ SV368 @ SY934 )
| ( subset @ ( setminus @ SV53 @ SY934 ) @ ( setminus @ SV53 @ SV368 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(2041,plain,
! [SV54: $i,SV369: $i] :
( ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false )
| ( ( ! [SY935: $i] :
( ~ ( in @ SY935 @ ( powerset @ SV54 ) )
| ~ ( subset @ ( setminus @ SV54 @ SY935 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SY935 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(2042,plain,
! [SV55: $i,SV370: $i] :
( ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false )
| ( ( ! [SY936: $i] :
( ~ ( in @ SY936 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV370 @ ( setminus @ SV55 @ SY936 ) )
| ! [SY937: $i] :
( ~ ( in @ SY937 @ SV55 )
| ~ ( in @ SY937 @ SY936 )
| ( in @ SY937 @ ( setminus @ SV55 @ SV370 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1723]) ).
thf(2043,plain,
! [SV56: $i,SV371: $i] :
( ( ( in @ SV371 @ ( powerset @ SV56 ) )
= $false )
| ( ( SV371
= ( setminus @ SV56 @ ( setminus @ SV56 @ SV371 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(2044,plain,
! [SV57: $i,SV372: $i] :
( ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false )
| ( ( ! [SY938: $i] :
( ~ ( in @ SY938 @ ( powerset @ SV57 ) )
| ! [SY939: $i] :
( ~ ( in @ SY939 @ SV57 )
| ~ ( in @ SY939 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SY938 ) ) )
| ~ ( in @ SY939 @ SV372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1725]) ).
thf(2045,plain,
! [SV373: $i > $o,SV58: $i] :
( ( ( ~ ~ ! [SY940: $i] :
~ ~ ( ~ ( in @ SY940 @ SV58 )
| ~ ( SV373 @ SY940 ) ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(2046,plain,
! [SV374: $i,SV59: $i,SV627: $i] :
( ( ( ~ ( in @ SV627 @ ( setminus @ SV59 @ SV374 ) ) )
= $true )
| ( ( ~ ( in @ SV627 @ SV374 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1727]) ).
thf(2047,plain,
! [SV375: $i,SV60: $i,SV628: $i] :
( ( ( ~ ( in @ SV628 @ ( setadjoin @ SV60 @ ( setadjoin @ SV375 @ emptyset ) ) ) )
= $true )
| ( ( ( SV628 = SV60 )
| ( SV628 = SV375 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1728]) ).
thf(2048,plain,
! [SV376: $i > $o,SV61: $i] :
( ( ( ~ ! [SY944: $i] :
( ~ ( in @ SY944 @ SV61 )
| ( SV376 @ SY944 ) ) )
= $false )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1729]) ).
thf(2049,plain,
! [SV377: $i,SV629: $i > $i,SV62: $i] :
( ( ( ~ ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV62 )
| ( in @ ( SV629 @ SY1390 ) @ SV377 ) ) )
= $true )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1730]) ).
thf(2050,plain,
! [SV378: $i,SV63: $i,SV630: $i] :
( ( ( ~ ~ ( in @ SV630 @ SV63 ) )
= $true )
| ( ( ~ ( in @ SV630 @ ( setminus @ SV63 @ SV378 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1731]) ).
thf(2051,plain,
! [SV65: $i,SV379: $i] :
( ( ( in @ SV379 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ ( setminus @ SV65 @ SV379 ) @ ( powerset @ SV65 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(2052,plain,
! [SV66: $i,SV380: $i] :
( ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false )
| ( ( ! [SY951: $i] :
( ~ ( in @ SY951 @ ( powerset @ SV66 ) )
| ! [SY952: $i] :
( ~ ( in @ SY952 @ SV66 )
| ~ ~ ( in @ SY952 @ SV380 )
| ~ ~ ( in @ SY952 @ SY951 )
| ~ ( in @ SY952 @ ( binunion @ SV380 @ SY951 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(2053,plain,
! [SV381: $i,SV67: $i] :
( ( ( SV67 = SV381 )
= $false )
| ( ( ! [SY953: $i,SY954: $i] :
( ( SY953 != SY954 )
| ~ ( in @ SY953 @ SV67 )
| ( in @ SY954 @ SV381 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(2054,plain,
! [SV69: $i,SV382: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV382 ) )
= $true )
| ( ( ~ ( in @ SV631 @ ( setminus @ SV69 @ SV382 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2055,plain,
! [SV383: $o,SV70: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV70 ) )
= $true )
| ( ( ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV70 )
| ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1394: $i] :
( ~ ( ~ SV383
| ( SY1394 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1394 != SY1393 ) ) ) )
= ( setadjoin @ SY1393 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1737]) ).
thf(2056,plain,
! [SV70: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV70 ) )
= $true )
| ( ( ! [SY1395: $i] :
( ~ ( in @ SY1395 @ SV70 )
| ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1396: $i] :
( ~ ( ~ $true
| ( SY1396 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1396 != SY1395 ) ) ) )
= ( setadjoin @ SY1395 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1738]) ).
thf(2057,plain,
! [SV70: $i,SV634: $i] :
( ( ( ~ ( in @ SV634 @ SV70 ) )
= $true )
| ( ( ! [SY1397: $i] :
( ~ ( in @ SY1397 @ SV70 )
| ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1398: $i] :
( ~ ( ~ $false
| ( SY1398 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1398 != SY1397 ) ) ) )
= ( setadjoin @ SY1397 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1739]) ).
thf(2058,plain,
! [SV73: $i] :
( ( ( ! [SY167: $i] :
~ ( in @ SY167 @ SV73 ) )
= $true )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1743]) ).
thf(2059,plain,
! [SV635: $i,SV385: $i,SV75: $i] :
( ( ( ~ ( func @ SV75 @ SV385 @ SV635 ) )
= $true )
| ( ( ! [SY1399: $i] :
( ~ ( in @ SY1399 @ SV75 )
| ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SY1399 ) @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1744]) ).
thf(2060,plain,
! [SV76: $i,SV386: $i] :
( ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false )
| ( ( ! [SY961: $i] :
( ~ ( in @ SY961 @ ( powerset @ SV76 ) )
| ! [SY962: $i] :
( ~ ( in @ SY962 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SY961 ) )
| ~ ( in @ SY962 @ SV386 )
| ( in @ SY962 @ SY961 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(2061,plain,
! [SV77: $i,SV387: $i] :
( ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false )
| ( ( ! [SY963: $i] :
( ~ ( in @ SY963 @ ( powerset @ SV77 ) )
| ! [SY964: $i] :
( ~ ( in @ SY964 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SY963 ) )
| ~ ( in @ SY964 @ SY963 )
| ~ ( in @ SY964 @ SV387 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(2062,plain,
! [SV388: $i,SV78: $i,SV747: $i,SV636: $i] :
( ( ~ ( in @ ( kpair @ SV636 @ SV747 ) @ ( cartprod @ SV78 @ SV388 ) )
| ( in @ SV747 @ SV388 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2063,plain,
! [SV389: $i,SV79: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ SV79 ) )
= $true )
| ( ( ! [SY1401: $i] :
( ~ ( in @ SY1401 @ SV389 )
| ( in @ ( kpair @ SV637 @ SY1401 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(2064,plain,
! [SV80: $i,SV390: $i] :
( ( ( in @ SV390 @ ( powerset @ SV80 ) )
= $false )
| ( ( ! [SY969: $i] :
( ~ ( in @ SY969 @ ( powerset @ SV80 ) )
| ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SY969 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(2065,plain,
! [SV81: $i,SV391: $i] :
( ( ( in @ SV391 @ SV81 )
= $false )
| ( ( subset @ ( setadjoin @ SV391 @ emptyset ) @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(2066,plain,
! [SV82: $i,SV392: $i] :
( ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false )
| ( ( ! [SY970: $i] :
( ~ ( in @ SY970 @ ( powerset @ SV82 ) )
| ! [SY971: $i] :
( ~ ( in @ SY971 @ SV82 )
| ~ ~ ( in @ SY971 @ SV392 )
| ~ ( in @ SY971 @ ( binintersect @ SV392 @ SY970 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1751]) ).
thf(2067,plain,
! [SV638: $i > $i > $o,SV393: $i,SV83: $i,SV748: $i] :
( ( ! [SY1551: $i] :
( ~ ( in @ ( kpair @ SV748 @ SY1551 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SY1404: $i,SY1405: $i] : ( SV638 @ SY1404 @ SY1405 ) ) )
| ( SV638 @ SV748 @ SY1551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1752]) ).
thf(2068,plain,
! [SV639: $i,SV394: $i,SV84: $i] :
( ( ( ~ ( func @ SV84 @ SV394 @ SV639 ) )
= $true )
| ( ( ! [SY1406: $i] :
( ~ ( in @ SY1406 @ SV84 )
| ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1407: $i] : ( in @ ( kpair @ SY1406 @ SY1407 ) @ SV639 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1753]) ).
thf(2069,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ( ~ ~ ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) ) )
= $true )
| ( ( ~ ( in @ SV640 @ SV85 )
| ( in @ SV640 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(2070,plain,
! [SV396: $i,SV86: $i] :
( ( ( ( setadjoin @ SV86 @ emptyset )
= ( setadjoin @ SV396 @ emptyset ) )
= $false )
| ( ( SV86 = SV396 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1755]) ).
thf(2071,plain,
! [SV397: $i,SV87: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV87 ) )
= $true )
| ( ( ~ ~ ( in @ SV641 @ SV397 )
| ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2072,plain,
! [SV399: $i,SV642: $i > $i,SV89: $i] :
( ( ( ~ ! [SY1408: $i] :
( ~ ( in @ SY1408 @ SV89 )
| ( in @ ( SV642 @ SY1408 ) @ SV399 ) ) )
= $true )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1757]) ).
thf(2073,plain,
! [SV400: $i,SV90: $i] :
( ( ( SV90 = SV400 )
= $false )
| ( ( subset @ SV400 @ SV90 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(2074,plain,
! [SV401: $i,SV91: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) ) )
= $true )
| ( ( ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SV91 )
| ( in @ ( kpair @ SY1411 @ ( ap @ SV91 @ SV401 @ SV643 @ SY1411 ) ) @ SV643 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2075,plain,
! [SV402: $i,SV93: $i] :
( ( ( breln1 @ SV93 @ SV402 )
= $false )
| ( ( ! [SY988: $i] :
( ~ ( breln1 @ SV93 @ SY988 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV93 )
| ! [SY990: $i] :
( ~ ( in @ SY990 @ SV93 )
| ~ ( in @ ( kpair @ SY989 @ SY990 ) @ ( binunion @ SV402 @ SY988 ) )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SV402 )
| ( in @ ( kpair @ SY989 @ SY990 ) @ SY988 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1761]) ).
thf(2076,plain,
! [SV403: $o,SV94: $i,SV644: $i] :
( ( ( ~ ( in @ SV644 @ SV94 ) )
= $true )
| ( ( ! [SY1412: $i] :
( ~ ( in @ SY1412 @ SV94 )
| ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1413: $i] :
( ~ ( ~ SV403
| ( SY1413 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1413 != SY1412 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2077,plain,
! [SV94: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV94 ) )
= $true )
| ( ( ! [SY1414: $i] :
( ~ ( in @ SY1414 @ SV94 )
| ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1415: $i] :
( ~ ( ~ $true
| ( SY1415 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1415 != SY1414 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2078,plain,
! [SV94: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV94 ) )
= $true )
| ( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV94 )
| ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1417: $i] :
( ~ ( ~ $false
| ( SY1417 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1417 != SY1416 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2079,plain,
! [SV95: $i,SV404: $i] :
( ( ( ! [SY994: $i] :
( ~ ( in @ SY994 @ SV404 )
| ( in @ SY994 @ SV95 ) ) )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(2080,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) ) )
= $true )
| ( ( ! [SY1418: $o] :
( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SY1418 )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SY1418 )
| SY1418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(2081,plain,
! [SV407: $i,SV98: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ ( setminus @ SV98 @ SV407 ) ) )
= $true )
| ( ( in @ SV648 @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1767]) ).
thf(2082,plain,
! [SV408: $i,SV99: $i] :
( ( ( breln1 @ SV99 @ SV408 )
= $false )
| ( ( ! [SY998: $i] :
( ~ ( breln1 @ SV99 @ SY998 )
| ! [SY999: $i] :
( ~ ( in @ SY999 @ SV99 )
| ! [SY1000: $i] :
( ~ ( in @ SY1000 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1000 ) @ ( breln1compset @ SV99 @ SV408 @ SY998 ) )
| ! [SY1001: $o] :
( ~ ! [SY1002: $i] :
( ~ ( in @ SY1002 @ SV99 )
| ~ ( in @ ( kpair @ SY999 @ SY1002 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1002 @ SY1000 ) @ SY998 )
| SY1001 )
| SY1001 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(2083,plain,
! [SV100: $i,SV409: $i] :
( ( ( in @ SV409 @ ( breln1Set @ SV100 ) )
= $false )
| ( ( breln1 @ SV100 @ SV409 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(2084,plain,
! [SV749: $i,SV649: $i,SV410: $i,SV102: $i] :
( ( ( ( kpair @ SV102 @ SV410 )
!= ( kpair @ SV649 @ SV749 ) )
| ( SV410 = SV749 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1771]) ).
thf(2085,plain,
! [SV411: $i,SV103: $i] :
( ( ( breln1 @ SV103 @ SV411 )
= $false )
| ( ( breln1 @ SV103 @ ( breln1invset @ SV103 @ SV411 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1772]) ).
thf(2086,plain,
! [SV412: $i,SV104: $i] :
( ( ( in @ SV104 @ SV412 )
= $false )
| ( ( ~ ( in @ SV412 @ SV104 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1773]) ).
thf(2087,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY1008: $i,SY1009: $i] :
( ( SY1008 != SY1009 )
| ~ ( ~ ( ~ ( SV107 @ SY1008 )
| ( SV415 @ SY1009 ) )
| ~ ( ~ ( SV415 @ SY1009 )
| ( SV107 @ SY1008 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1775]) ).
thf(2088,plain,
! [SV108: $i,SV416: $i] :
( ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false )
| ( ( ! [SY1018: $i] :
( ~ ( in @ SY1018 @ ( powerset @ SV108 ) )
| ! [SY1019: $i] :
( ~ ( in @ SY1019 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SY1018 )
| ~ ( subset @ SV416 @ SY1019 )
| ( subset @ SV416 @ ( binintersect @ SY1018 @ SY1019 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(2089,plain,
! [SV417: $i,SV109: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) ) )
= $true )
| ( ( ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( funcSet @ SV109 @ SV417 ) )
| ~ ! [SY1423: $i] :
( ~ ( in @ SY1423 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1423 )
= ( ap @ SV109 @ SV417 @ SY1422 @ SY1423 ) ) )
| ( SV651 = SY1422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1777]) ).
thf(2090,plain,
! [SV418: $i,SV110: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( cartprod @ SV110 @ SV418 ) ) )
= $true )
| ( ( iskpair @ SV652 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1778]) ).
thf(2091,plain,
! [SV419: $i,SV111: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) ) )
= $true )
| ( ( ~ ! [SY1424: $i] :
~ ~ ( ~ ( in @ SY1424 @ SV111 )
| ~ ~ ! [SY1425: $i] :
~ ~ ( ~ ( in @ SY1425 @ SV419 )
| ( SV653
!= ( kpair @ SY1424 @ SY1425 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1779]) ).
thf(2092,plain,
! [SV113: $i] :
( ( ( SV113 = emptyset )
= $true )
| ( ( ~ ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV113 )
| ( ( binintersect @ SY275 @ SV113 )
!= emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1780]) ).
thf(2093,plain,
! [SV114: $i,SV421: $i] :
( ( ( in @ SV421 @ ( powerset @ SV114 ) )
= $false )
| ( ( subset @ SV421 @ ( setminus @ SV114 @ ( setminus @ SV114 @ SV421 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(2094,plain,
! [SV422: $i,SV115: $i,SV654: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV654 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV115 = SV654 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(2095,plain,
! [SV116: $i,SV423: $i] :
( ( ( in @ SV423 @ ( powerset @ SV116 ) )
= $false )
| ( ( ! [SY1028: $i] :
( ~ ( in @ SY1028 @ ( powerset @ SV116 ) )
| ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SY1028 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(2096,plain,
! [SV117: $i,SV424: $i] :
( ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false )
| ( ( ! [SY1029: $i] :
( ~ ( in @ SY1029 @ ( powerset @ SV117 ) )
| ! [SY1030: $i] :
( ~ ( in @ SY1030 @ ( powerset @ SV117 ) )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV117 )
| ~ ( in @ SY1031 @ ( binintersect @ SV424 @ SY1029 ) )
| ( in @ SY1031 @ ( binintersect @ ( binunion @ SV424 @ SY1030 ) @ ( binunion @ SY1029 @ SY1030 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1784]) ).
thf(2097,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1032: $i] :
( ~ ( in @ SY1032 @ SV118 )
| ! [SY1033: $i] :
( ~ ( in @ SY1033 @ SV118 )
| ~ ( SV425 @ SY1032 )
| ~ ( SV425 @ SY1033 )
| ( SY1032 = SY1033 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(2098,plain,
! [SV119: $i,SV426: $i > $i] :
( ( ~ ! [SY1554: $i] :
~ ( ~ ( ~ ( in @ SY1554 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1038: $i] :
~ ~ ( ~ ( in @ SY1038 @ SV119 )
| ( SY1554
!= ( SV426 @ SY1038 ) ) ) )
| ~ ( ~ ~ ! [SY1039: $i] :
~ ~ ( ~ ( in @ SY1039 @ SV119 )
| ( SY1554
!= ( SV426 @ SY1039 ) ) )
| ( in @ SY1554 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1786]) ).
thf(2099,plain,
! [SV655: $i,SV427: $i,SV120: $i] :
( ( ( ~ ( func @ SV120 @ SV427 @ SV655 ) )
= $true )
| ( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1427: $i] : ( in @ ( kpair @ SY1426 @ SY1427 ) @ SV655 ) ) )
@ SV427 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(2100,plain,
! [SV428: $i,SV121: $i] :
( ( ( ! [SY1043: $i] :
~ ( ~ ( ~ ( in @ SY1043 @ SV121 )
| ( in @ SY1043 @ SV428 ) )
| ~ ( ~ ( in @ SY1043 @ SV428 )
| ( in @ SY1043 @ SV121 ) ) ) )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2101,plain,
! [SV429: $i,SV122: $i] :
( ( ( ! [SY1044: $i] :
( ~ ( in @ SY1044 @ SV122 )
| ( in @ SY1044 @ SV429 ) ) )
= $false )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(2102,plain,
! [SV750: $i] :
( ( ~ ( in @ SV750 @ sK1_X )
| ( subset @ SV750 @ sK1_X ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2103,plain,
( ( ~ ( in @ sK2_SY0 @ sK1_X )
| ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(2104,plain,
! [SV123: $i,SV430: $i] :
( ( ( subset @ SV430 @ SV123 )
= $false )
| ( ( in @ SV430 @ ( powerset @ SV123 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(2105,plain,
! [SV431: $i,SV656: $i > $i,SV124: $i] :
( ( ( ~ ! [SY1428: $i] :
( ~ ( in @ SY1428 @ SV124 )
| ( in @ ( SV656 @ SY1428 ) @ SV431 ) ) )
= $true )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1793]) ).
thf(2106,plain,
! [SV432: $o,SV125: $i,SV657: $i] :
( ( ( ~ ( in @ SV657 @ SV125 ) )
= $true )
| ( ( ! [SY1430: $i] :
( ~ ( in @ SY1430 @ SV125 )
| ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1431: $i] :
( ~ ( ~ SV432
| ( SY1431 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1431 != SY1430 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1794]) ).
thf(2107,plain,
! [SV125: $i,SV658: $i] :
( ( ( ~ ( in @ SV658 @ SV125 ) )
= $true )
| ( ( ! [SY1432: $i] :
( ~ ( in @ SY1432 @ SV125 )
| ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1433: $i] :
( ~ ( ~ $true
| ( SY1433 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1433 != SY1432 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1795]) ).
thf(2108,plain,
! [SV125: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ SV125 ) )
= $true )
| ( ( ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SV125 )
| ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1435: $i] :
( ~ ( ~ $false
| ( SY1435 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1435 != SY1434 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1796]) ).
thf(2109,plain,
! [SV126: $i,SV433: $i] :
( ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false )
| ( ( ! [SY1051: $o] :
( ~ ! [SY1052: $i] :
( ~ ( in @ SV433 @ SY1052 )
| ~ ( in @ SY1052 @ SV126 )
| SY1051 )
| SY1051 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1797]) ).
thf(2110,plain,
! [SV434: $i,SV127: $i,SV660: $i] :
( ( ( ~ ( in @ SV660 @ ( cartprod @ SV127 @ SV434 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV660 ) @ SV434 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2111,plain,
! [SV435: $i,SV128: $i] :
( ( ( breln1 @ SV128 @ SV435 )
= $false )
| ( ( ! [SY1054: $i] :
( ~ ( breln1 @ SV128 @ SY1054 )
| ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SY1054 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(2112,plain,
! [SV436: $i,SV661: $i,SV129: $i] :
( ( ( ~ ( subset @ SV129 @ SV661 ) )
= $true )
| ( ( subset @ SV129 @ ( setadjoin @ SV436 @ SV661 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1800]) ).
thf(2113,plain,
! [SV438: $i,SV131: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV131 ) )
= $true )
| ( ( ~ ~ ( in @ SV662 @ SV438 )
| ~ ( subset @ SV131 @ SV438 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1801]) ).
thf(2114,plain,
! [SV751: $i,SV663: $i,SV439: $i,SV132: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SV751 @ emptyset ) ) @ emptyset ) ) )
| ( SV663 != SV751 )
| ( SV439 = SV751 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2115,plain,
! [SV133: $i,SV440: $i] :
( ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false )
| ( ( ! [SY1059: $i] :
( ~ ( in @ SY1059 @ ( powerset @ SV133 ) )
| ! [SY1060: $i] :
( ~ ( in @ SY1060 @ SV133 )
| ~ ( in @ SY1060 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SY1059 ) ) )
| ( in @ SY1060 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SY1059 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(2116,plain,
! [SV134: $i,SV441: $i] :
( ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false )
| ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( powerset @ SV134 ) )
| ! [SY1062: $i] :
( ~ ( in @ SY1062 @ ( powerset @ SV134 ) )
| ! [SY1063: $i] :
( ~ ( in @ SY1063 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1062 )
| ~ ( subset @ SY1061 @ SY1063 )
| ( subset @ ( binintersect @ SV441 @ SY1061 ) @ ( binintersect @ SY1062 @ SY1063 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(2117,plain,
! [SV136: $i > $o] :
( ( ( ! [SY335: $i] :
~ ~ ( ~ ( SV136 @ SY335 )
| ~ ! [SY336: $i] :
( ~ ( SV136 @ SY336 )
| ( SY335 = SY336 ) ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(2118,plain,
! [SV443: $i,SV137: $i] :
( ( ( ( setminus @ SV137 @ SV443 )
= emptyset )
= $false )
| ( ( subset @ SV137 @ SV443 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1806]) ).
thf(2119,plain,
! [SV138: $i > $o] :
( ( ( ! [SY340: $i] :
~ ~ ( ~ ( SV138 @ SY340 )
| ~ ! [SY341: $i] :
( ~ ( SV138 @ SY341 )
| ( SY340 = SY341 ) ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1807]) ).
thf(2120,plain,
! [SV664: $i,SV444: $i,SV139: $i] :
( ( ( ~ ( func @ SV139 @ SV444 @ SV664 ) )
= $true )
| ( ( ! [SY1437: $i] :
( ~ ( func @ SV139 @ SV444 @ SY1437 )
| ~ ! [SY1438: $i] :
( ~ ( in @ SY1438 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1438 )
= ( ap @ SV139 @ SV444 @ SY1437 @ SY1438 ) ) )
| ( SV664 = SY1437 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1808]) ).
thf(2121,plain,
! [SV140: $i,SV445: $i > $i] :
( ( ~ ~ ( ~ ! [SY1557: $i] :
~ ( ~ ( ~ ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) )
| ~ ! [SY1560: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1560 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1560 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SY1560 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1809]) ).
thf(2122,plain,
! [SV665: $i > $i > $o,SV446: $i,SV141: $i,SV752: $i] :
( ( ! [SY1564: $i] :
( ~ ( in @ ( kpair @ SV752 @ SY1564 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SY1441: $i,SY1442: $i] : ( SV665 @ SY1441 @ SY1442 ) ) )
| ( in @ SV752 @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1810]) ).
thf(2123,plain,
! [SV447: $i,SV142: $i,SV753: $i,SV666: $i] :
( ( ~ ( in @ ( kpair @ SV666 @ SV753 ) @ ( cartprod @ SV142 @ SV447 ) )
| ( in @ SV666 @ SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1811]) ).
thf(2124,plain,
! [SV143: $i,SV448: $i] :
( ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false )
| ( ( ! [SY1082: $i] :
( ~ ( in @ SY1082 @ ( powerset @ SV143 ) )
| ! [SY1083: $i] :
( ~ ( in @ SY1083 @ ( powerset @ SV143 ) )
| ~ ( subset @ SY1082 @ SY1083 )
| ( subset @ ( binintersect @ SV448 @ SY1082 ) @ SY1083 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(2125,plain,
! [SV449: $i > $o,SV144: $i] :
( ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false )
| ( ( ~ ! [SY1085: $i] :
~ ~ ( ~ ( in @ SY1085 @ SV144 )
| ~ ( SV449 @ SY1085 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(2126,plain,
! [SV450: $i,SV145: $i] :
( ( ( ! [SY1086: $i] :
( ~ ( in @ SY1086 @ SV145 )
| ( in @ SY1086 @ SV450 ) ) )
= $false )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2127,plain,
! [SV451: $i,SV146: $i] :
( ( ( breln1 @ SV146 @ SV451 )
= $false )
| ( ( ! [SY1087: $i > $o] :
( ~ ! [SY1088: $i] :
( ~ ( in @ SY1088 @ SV146 )
| ! [SY1089: $i] :
( ~ ( in @ SY1089 @ SV146 )
| ~ ( in @ ( kpair @ SY1088 @ SY1089 ) @ SV451 )
| ( SY1087 @ ( kpair @ SY1088 @ SY1089 ) ) ) )
| ! [SY1090: $i] :
( ~ ( in @ SY1090 @ SV451 )
| ( SY1087 @ SY1090 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(2128,plain,
! [SV452: $i,SV147: $i] :
( ( ( SV147 = SV452 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV452 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(2129,plain,
! [SV453: $i > $i,SV148: $i,SV667: $i] :
( ( ( ~ ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) ) )
= $true )
| ( ( ~ ! [SY1445: $i] :
~ ~ ( ~ ( in @ SY1445 @ SV148 )
| ( SV667
!= ( SV453 @ SY1445 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1817]) ).
thf(2130,plain,
! [SV149: $i,SV454: $i] :
( ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false )
| ( ( ! [SY1094: $i] :
( ~ ( in @ SY1094 @ ( powerset @ SV149 ) )
| ~ ! [SY1095: $i] :
( ~ ( in @ SY1095 @ SV149 )
| ~ ( in @ SY1095 @ SV454 )
| ( in @ SY1095 @ SY1094 ) )
| ~ ! [SY1096: $i] :
( ~ ( in @ SY1096 @ SV149 )
| ~ ( in @ SY1096 @ SY1094 )
| ( in @ SY1096 @ SV454 ) )
| ( SV454 = SY1094 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1818]) ).
thf(2131,plain,
! [SV455: $i,SV150: $i,SV668: $i] :
( ( ( ~ ( in @ SV668 @ ( injFuncSet @ SV150 @ SV455 ) ) )
= $true )
| ( ( injective @ SV150 @ SV455 @ SV668 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1819]) ).
thf(2132,plain,
! [SV457: $i,SV152: $i] :
( ( ( ( binintersect @ SV152 @ SV457 )
= SV457 )
= $false )
| ( ( subset @ SV457 @ SV152 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1820]) ).
thf(2133,plain,
! [SV458: $i > $o,SV153: $i] :
( ( ( ~ ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV153 )
| ~ ( SV458 @ SY1099 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1821]) ).
thf(2134,plain,
! [SV459: $i,SV154: $i] :
( ( ( breln1 @ SV154 @ SV459 )
= $false )
| ( ( ! [SY1101: $i] :
( ~ ( breln1 @ SV154 @ SY1101 )
| ! [SY1102: $i] :
( ~ ( breln1 @ SV154 @ SY1102 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SY1101 ) @ SY1102 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SY1101 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1102 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(2135,plain,
! [SV155: $i > $o] :
( ( ( ! [SY399: $i] :
~ ~ ( ~ ( SV155 @ SY399 )
| ~ ! [SY400: $i] :
( ~ ( SV155 @ SY400 )
| ( SY399 = SY400 ) ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(2136,plain,
! [SV460: $i,SV156: $i] :
( ( ( breln1 @ SV156 @ SV460 )
= $false )
| ( ( ! [SY1103: $i > $o] :
( ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ SV156 )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SV156 )
| ~ ( in @ ( kpair @ SY1104 @ SY1105 ) @ SV460 )
| ( SY1103 @ ( kpair @ SY1104 @ SY1105 ) ) ) )
| ! [SY1106: $i] :
( ~ ( in @ SY1106 @ SV460 )
| ( SY1103 @ SY1106 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(2137,plain,
! [SV461: $i,SV157: $i,SV669: $i] :
( ( ( ~ ( in @ SV669 @ SV157 ) )
= $true )
| ( ( ! [SY1446: $i] :
( ~ ( in @ SY1446 @ SV461 )
| ( in @ ( kpair @ SV669 @ SY1446 ) @ ( cartprod @ SV157 @ SV461 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1825]) ).
thf(2138,plain,
! [SV462: $o,SV158: $i,SV670: $i] :
( ( ( ~ ( in @ SV670 @ SV158 ) )
= $true )
| ( ( ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SV158 )
| ~ ~ SV462
| ( in @ SY1447
@ ( dsetconstr @ SV158
@ ^ [SY1448: $i] :
( ~ ( ~ SV462
| ( SY1448 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1448 != SY1447 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(2139,plain,
! [SV158: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV158 ) )
= $true )
| ( ( ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV158 )
| ~ ~ $true
| ( in @ SY1449
@ ( dsetconstr @ SV158
@ ^ [SY1450: $i] :
( ~ ( ~ $true
| ( SY1450 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1450 != SY1449 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(2140,plain,
! [SV158: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV158 ) )
= $true )
| ( ( ! [SY1451: $i] :
( ~ ( in @ SY1451 @ SV158 )
| ~ ~ $false
| ( in @ SY1451
@ ( dsetconstr @ SV158
@ ^ [SY1452: $i] :
( ~ ( ~ $false
| ( SY1452 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1452 != SY1451 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1828]) ).
thf(2141,plain,
! [SV673: $i,SV159: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ ( powerset @ SV159 ) ) )
= $true )
| ( ( ~ ( in @ SV673 @ SV463 )
| ( in @ SV673 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2142,plain,
! [SV464: $i,SV160: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV160 ) )
= $true )
| ( ( ~ ~ ( in @ SV674 @ SV464 )
| ( SV160 != SV464 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2143,plain,
! [SV675: $i,SV465: $i,SV161: $i] :
( ( ( ~ ( subset @ SV161 @ SV465 ) )
= $true )
| ( ( ~ ( subset @ SV465 @ SV675 )
| ( subset @ SV161 @ SV675 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2144,plain,
! [SV162: $i,SV466: $i] :
( ( ( in @ SV466 @ ( powerset @ SV162 ) )
= $false )
| ( ( in @ ( powerset @ SV466 ) @ ( powerset @ ( powerset @ SV162 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2145,plain,
! [SV163: $i,SV467: $i] :
( ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false )
| ( ( ! [SY1115: $i] :
( ~ ( in @ SY1115 @ SV163 )
| ~ ~ ( in @ SY1115 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SY1115 @ SV467 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2146,plain,
! [SV468: $i,SV164: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ SV164 ) )
= $true )
| ( ( ~ ~ ( in @ SV676 @ SV468 )
| ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1834]) ).
thf(2147,plain,
! [SV469: $i > $o,SV165: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ SV165 ) )
= $true )
| ( ( ~ ( SV469 @ SV677 )
| ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1835]) ).
thf(2148,plain,
! [SV166: $i > $o] :
( ( ( ! [SY429: $i] :
~ ( SV166 @ SY429 ) )
= $true )
| ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1836]) ).
thf(2149,plain,
! [SV167: $i > $o] :
( ( ( ! [SY434: $i] :
~ ~ ( ~ ( SV167 @ SY434 )
| ~ ! [SY435: $i] :
( ~ ( SV167 @ SY435 )
| ( SY434 = SY435 ) ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1837]) ).
thf(2150,plain,
! [SV678: $i,SV470: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV470 @ SV678 ) )
= $true )
| ( ( ! [SY1454: $i] :
( ~ ( breln @ SV168 @ SV470 @ SY1454 )
| ~ ! [SY1455: $i] :
( ~ ( in @ SY1455 @ SV168 )
| ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV470 )
| ~ ( in @ ( kpair @ SY1455 @ SY1456 ) @ SV678 )
| ( in @ ( kpair @ SY1455 @ SY1456 ) @ SY1454 ) ) )
| ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV168 )
| ! [SY1458: $i] :
( ~ ( in @ SY1458 @ SV470 )
| ~ ( in @ ( kpair @ SY1457 @ SY1458 ) @ SY1454 )
| ( in @ ( kpair @ SY1457 @ SY1458 ) @ SV678 ) ) )
| ( SV678 = SY1454 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1838]) ).
thf(2151,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ~ ( ~ ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
| ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
| ~ ( ~ ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) )
| ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2152,plain,
! [SV171: $i,SV473: $i] :
( ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false )
| ( ( ! [SY1130: $i] :
( ~ ( in @ SY1130 @ ( powerset @ SV171 ) )
| ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SV171 )
| ~ ~ ( in @ SY1131 @ SY1130 )
| ~ ( in @ SY1131 @ ( binintersect @ SV473 @ SY1130 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1840]) ).
thf(2153,plain,
! [SV474: $i,SV680: $i > $i,SV172: $i] :
( ( ( ~ ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV172 )
| ( in @ ( SV680 @ SY1463 ) @ SV474 ) ) )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1841]) ).
thf(2154,plain,
! [SV174: $i > $o] :
( ( ( ! [SY460: $i] :
~ ! [SY461: $i] :
~ ( ~ ( ~ ( SV174 @ SY461 )
| ( SY461 = SY460 ) )
| ~ ( ( SY461 != SY460 )
| ( SV174 @ SY461 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1842]) ).
thf(2155,plain,
! [SV475: $i,SV175: $i] :
( ( ( SV175 = SV475 )
= $false )
| ( ( ! [SY1136: $i,SY1137: $i] :
( ( SY1136 != SY1137 )
| ( ( setadjoin @ SV175 @ SY1136 )
= ( setadjoin @ SV475 @ SY1137 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1843]) ).
thf(2156,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV176 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) )
| ~ ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1844]) ).
thf(2157,plain,
! [SV477: $i,SV177: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV177 ) )
= $true )
| ( ( in @ SV682 @ ( binunion @ SV177 @ SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1845]) ).
thf(2158,plain,
! [SV178: $i,SV478: $i] :
( ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false )
| ( ( ~ ! [SY1142: $i] :
~ ~ ( ~ ( in @ SY1142 @ SV178 )
| ~ ( in @ SV478 @ SY1142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(2159,plain,
! [SV179: $i,SV479: $i] :
( ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false )
| ( ( ! [SY1143: $i] :
( ~ ( in @ SY1143 @ ( powerset @ SV179 ) )
| ! [SY1144: $i] :
( ~ ( in @ SY1144 @ ( powerset @ SV179 ) )
| ! [SY1145: $i] :
( ~ ( in @ SY1145 @ SV179 )
| ~ ( in @ SY1145 @ ( binintersect @ SV479 @ SY1143 ) )
| ( in @ SY1145 @ ( binunion @ SY1143 @ SY1144 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2160,plain,
! [SV480: $o,SV181: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV181 ) )
= $true )
| ( ( ! [SY1468: $i] :
( ~ ( in @ SY1468 @ SV181 )
| ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SY1468 )
= SV683 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1848]) ).
thf(2161,plain,
! [SV181: $i,SV684: $i] :
( ( ( ~ ( in @ SV684 @ SV181 ) )
= $true )
| ( ( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ SV181 )
| ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SY1469 )
= SV684 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(2162,plain,
! [SV181: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV181 ) )
= $true )
| ( ( ! [SY1470: $i] :
( ~ ( in @ SY1470 @ SV181 )
| ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SY1470 )
= SV685 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(2163,plain,
! [SV481: $i,SV182: $i,SV686: $i] :
( ( ( ~ ~ ( in @ SV686 @ SV182 ) )
= $true )
| ( ( ~ ( in @ SV686 @ SV481 )
| ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(2164,plain,
! [SV687: $i,SV482: $i,SV183: $i] :
( ( ( ~ ( breln @ SV183 @ SV482 @ SV687 ) )
= $true )
| ( ( ! [SY1471: $i > $o] :
( ~ ! [SY1472: $i] :
( ~ ( in @ SY1472 @ SV183 )
| ! [SY1473: $i] :
( ~ ( in @ SY1473 @ SV482 )
| ~ ( in @ ( kpair @ SY1472 @ SY1473 ) @ SV687 )
| ( SY1471 @ ( kpair @ SY1472 @ SY1473 ) ) ) )
| ! [SY1474: $i] :
( ~ ( in @ SY1474 @ SV687 )
| ( SY1471 @ SY1474 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1852]) ).
thf(2165,plain,
! [SV688: $i,SV483: $i,SV184: $i] :
( ( ( ~ ( subset @ SV184 @ SV483 ) )
= $true )
| ( ( ~ ~ ( in @ SV688 @ SV483 )
| ~ ( in @ SV688 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1853]) ).
thf(2166,plain,
! [SV484: $i,SV185: $i] :
( ( ( subset @ SV185 @ SV484 )
= $false )
| ( ( ~ ( subset @ SV484 @ SV185 )
| ( SV185 = SV484 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(2167,plain,
! [SV186: $i,SV485: $i] :
( ( ( in @ SV485 @ ( powerset @ SV186 ) )
= $false )
| ( ( ! [SY1155: $i] :
( ~ ( in @ SY1155 @ ( powerset @ SV186 ) )
| ( in @ ( binunion @ SV485 @ SY1155 ) @ ( powerset @ SV186 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(2168,plain,
! [SV188: $i,SV486: $i] :
( ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false )
| ( ( ! [SY1156: $i] :
( ~ ( in @ SY1156 @ ( powerset @ SV188 ) )
| ! [SY1157: $i] :
( ~ ( in @ SY1157 @ SV188 )
| ~ ( in @ SY1157 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SY1156 ) ) )
| ( in @ SY1157 @ ( setminus @ SV188 @ SV486 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(2169,plain,
! [SV487: $i > $o,SV189: $i] :
( ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false )
| ( ( ! [SY1159: $i] :
( ~ ( in @ SY1159 @ SV189 )
| ! [SY1160: $i] :
( ~ ( in @ SY1160 @ SV189 )
| ~ ( SV487 @ SY1159 )
| ~ ( SV487 @ SY1160 )
| ( SY1159 = SY1160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1860]) ).
thf(2170,plain,
! [SV488: $o,SV190: $i,SV689: $i] :
( ( ( ~ ( in @ SV689 @ SV190 ) )
= $true )
| ( ( ! [SY1475: $i] :
( ~ ( in @ SY1475 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1476: $i] :
( ~ ( ~ SV488
| ( SY1476 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1476 != SY1475 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1861]) ).
thf(2171,plain,
! [SV190: $i,SV690: $i] :
( ( ( ~ ( in @ SV690 @ SV190 ) )
= $true )
| ( ( ! [SY1477: $i] :
( ~ ( in @ SY1477 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1478: $i] :
( ~ ( ~ $true
| ( SY1478 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1478 != SY1477 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(2172,plain,
! [SV190: $i,SV691: $i] :
( ( ( ~ ( in @ SV691 @ SV190 ) )
= $true )
| ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1480: $i] :
( ~ ( ~ $false
| ( SY1480 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1480 != SY1479 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1863]) ).
thf(2173,plain,
! [SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1164: $i] :
( ~ ( in @ SY1164 @ SV489 )
| ~ ! [SY508: $i] :
~ ~ ( ~ ( SV191 @ SY1164 @ SY508 )
| ~ ! [SY509: $i] :
( ~ ( SV191 @ SY1164 @ SY509 )
| ( SY508 = SY509 ) ) ) ) )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1864]) ).
thf(2174,plain,
! [SV490: $i,SV192: $i] :
( ( ( ~ ( subset @ SV192 @ SV490 ) )
= $false )
| ( ( SV192 != SV490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2175,plain,
! [SV491: $i,SV193: $i] :
( ( ( SV193 = SV491 )
= $false )
| ( ( ( setadjoin @ SV193 @ ( setadjoin @ SV491 @ emptyset ) )
= ( setadjoin @ SV193 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2176,plain,
! [SV492: $i,SV194: $i,SV692: $i] :
( ( ( ~ ( in @ SV692 @ ( surjFuncSet @ SV194 @ SV492 ) ) )
= $true )
| ( ( surjective @ SV194 @ SV492 @ SV692 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1867]) ).
thf(2177,plain,
! [SV494: $i,SV196: $i,SV693: $i] :
( ( ( ~ ( in @ SV693 @ SV196 ) )
= $true )
| ( ( in @ ( setadjoin @ SV693 @ emptyset ) @ ( powerset @ ( binunion @ SV196 @ SV494 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1868]) ).
thf(2178,plain,
! [SV495: $i,SV197: $i] :
( ( ( breln1 @ SV197 @ SV495 )
= $false )
| ( ( SV495
= ( breln1invset @ SV197 @ ( breln1invset @ SV197 @ SV495 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2179,plain,
! [SV198: $i,SV496: $i] :
( ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false )
| ( ( ! [SY1173: $i] :
( ~ ( in @ SY1173 @ ( powerset @ SV198 ) )
| ! [SY1174: $i] :
( ~ ( in @ SY1174 @ SV198 )
| ~ ( in @ SY1174 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SY1173 ) ) )
| ( in @ SY1174 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SY1173 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2180,plain,
! [SV497: $i,SV199: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ ( funcSet @ SV199 @ SV497 ) ) )
= $true )
| ( ( ~ ( injective @ SV199 @ SV497 @ SV694 )
| ( in @ SV694 @ ( injFuncSet @ SV199 @ SV497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(2181,plain,
! [SV200: $i] :
( ( ( ~ ( in @ ( sK9_SY527 @ SV200 ) @ SV200 )
| ( subset @ ( sK9_SY527 @ SV200 ) @ SV200 ) )
= $false )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1872]) ).
thf(2182,plain,
! [SV499: $i,SV695: $i > $i,SV202: $i] :
( ( ( ~ ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV202 )
| ( in @ ( SV695 @ SY1481 ) @ SV499 ) ) )
= $true )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1873]) ).
thf(2183,plain,
! [SV204: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV204 )
| ( ( setunion @ SV204 )
= SV754 ) )
= $true )
| ( ( singleton @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2184,plain,
! [SV205: $i,SV500: $i] :
( ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false )
| ( ( ! [SY1180: $i] :
( ~ ( in @ SY1180 @ SV205 )
| ~ ( in @ SY1180 @ SV500 )
| ( in @ SY1180 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2185,plain,
! [SV502: $i > $o,SV207: $i,SV696: $i] :
( ( ( ~ ( in @ SV696 @ SV207 ) )
= $true )
| ( ( ~ ( SV502 @ SV696 )
| ( in @ SV696
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1877]) ).
thf(2186,plain,
! [SV697: $i > $i > $o,SV503: $i,SV208: $i,SV755: $i] :
( ( ! [SY1567: $i] :
( ~ ( in @ ( kpair @ SV755 @ SY1567 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SY1487: $i,SY1488: $i] : ( SV697 @ SY1487 @ SY1488 ) ) )
| ( in @ SY1567 @ SV503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2187,plain,
! [SV504: $i,SV209: $i] :
( ( ( breln1 @ SV209 @ SV504 )
= $false )
| ( ( ! [SY1188: $i] :
( ~ ( breln1 @ SV209 @ SY1188 )
| ~ ! [SY1189: $i] :
( ~ ( in @ SY1189 @ SV209 )
| ! [SY1190: $i] :
( ~ ( in @ SY1190 @ SV209 )
| ~ ( in @ ( kpair @ SY1189 @ SY1190 ) @ SV504 )
| ( in @ ( kpair @ SY1189 @ SY1190 ) @ SY1188 ) ) )
| ( subset @ SV504 @ SY1188 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(2188,plain,
! [SV210: $i,SV505: $i] :
( ( ( in @ SV505 @ SV210 )
= $false )
| ( ( in @ SV505 @ ( powerset @ ( setunion @ SV210 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2189,plain,
! [SV211: $i,SV506: $i] :
( ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false )
| ( ( ! [SY1191: $i] :
( ~ ( in @ SY1191 @ ( powerset @ SV211 ) )
| ! [SY1192: $i] :
( ~ ( in @ SY1192 @ ( powerset @ SV211 ) )
| ! [SY1193: $i] :
( ~ ( in @ SY1193 @ SV211 )
| ~ ( in @ SY1193 @ ( binintersect @ SV506 @ SY1191 ) )
| ( in @ SY1193 @ ( binunion @ SV506 @ SY1192 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1881]) ).
thf(2190,plain,
! [SV212: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
| ~ ! [SY1498: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY1498 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1498 ) )
| ~ ! [SY1501: $i] :
~ ~ ! [SY1502: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1501 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1502 @ SY1498 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1501 )
| ~ ( in @ SX5 @ SY1498 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1501 ) )
| ( in @ SY1502 @ SY1504 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(2191,plain,
! [SV507: $i,SV213: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) ) )
= $true )
| ( ( ! [SY1506: $i] :
( ~ ( in @ SY1506 @ SV213 )
| ( ( ap @ SV213 @ SV507 @ SV698 @ SY1506 )
= ( ap @ SV213 @ SV507 @ SV698 @ SY1506 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(2192,plain,
! [SV508: $o,SV214: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ SV214 ) )
= $true )
| ( ( ! [SY1507: $i] :
( ~ ( in @ SY1507 @ SV214 )
| ( in @ ( if @ SV214 @ SV508 @ SV699 @ SY1507 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SY1507 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(2193,plain,
! [SV214: $i,SV700: $i] :
( ( ( ~ ( in @ SV700 @ SV214 ) )
= $true )
| ( ( ! [SY1508: $i] :
( ~ ( in @ SY1508 @ SV214 )
| ( in @ ( if @ SV214 @ $true @ SV700 @ SY1508 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SY1508 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(2194,plain,
! [SV214: $i,SV701: $i] :
( ( ( ~ ( in @ SV701 @ SV214 ) )
= $true )
| ( ( ! [SY1509: $i] :
( ~ ( in @ SY1509 @ SV214 )
| ( in @ ( if @ SV214 @ $false @ SV701 @ SY1509 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SY1509 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1886]) ).
thf(2195,plain,
! [SV702: $i > $i > $o,SV509: $i,SV215: $i] :
( ( ( ~ ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV215 )
| ~ ! [SY1511: $i] :
~ ~ ( ~ ( in @ SY1511 @ SV509 )
| ~ ( SV702 @ SY1510 @ SY1511 ) ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1887]) ).
thf(2196,plain,
! [SV510: $i,SV216: $i] :
( ( ( subset @ SV216 @ SV510 )
= $false )
| ( ( in @ SV216 @ ( powerset @ SV510 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2197,plain,
! [SV217: $i > $o,SV511: $i] :
( ( ( in @ SV511 @ emptyset )
= $false )
| ( ( SV217 @ SV511 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2198,plain,
! [SV512: $i,SV220: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ ( cartprod @ SV220 @ SV512 ) ) )
= $true )
| ( ( in @ ( kfst @ SV703 ) @ SV220 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(2199,plain,
! [SV513: $i,SV221: $i] :
( ( ( subset @ SV221 @ SV513 )
= $false )
| ( ( ( setminus @ SV221 @ SV513 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2200,plain,
! [SV704: $i,SV514: $i,SV222: $i] :
( ( ( ( setadjoin @ SV222 @ ( setadjoin @ SV514 @ emptyset ) )
!= ( setadjoin @ SV704 @ emptyset ) )
= $true )
| ( ( SV222 = SV514 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1892]) ).
thf(2201,plain,
! [SV705: $i,SV516: $i,SV225: $i] :
( ( ( ~ ( func @ SV225 @ SV516 @ SV705 ) )
= $true )
| ( ( ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV225 )
| ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV516 )
| ~ ( in @ ( kpair @ SY1516 @ SY1517 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SY1516 )
= SY1517 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(2202,plain,
! [SV226: $i] :
( ( ( ~ ( in @ emptyset @ SV226 )
| ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) )
= $true )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1894]) ).
thf(2203,plain,
! [SV227: $i,SV517: $i] :
( ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false )
| ( ( ! [SY1210: $i] :
( ~ ( in @ SY1210 @ ( powerset @ SV227 ) )
| ~ ( subset @ SV517 @ ( setminus @ SV227 @ SY1210 ) )
| ( subset @ SY1210 @ ( setminus @ SV227 @ SV517 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(2204,plain,
! [SV228: $i] :
( ( ( ! [SY605: $i] :
~ ( in @ SY605 @ SV228 ) )
= $true )
| ( ( SV228 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1896]) ).
thf(2205,plain,
! [SV229: $i,SV518: $i] :
( ( ( in @ SV518 @ ( powerset @ SV229 ) )
= $false )
| ( ( ! [SY1211: $i] :
( ~ ( in @ SY1211 @ ( powerset @ SV229 ) )
| ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SY1211 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(2206,plain,
! [SV519: $i,SV230: $i] :
( ( ( ! [SY1212: $i] :
( ~ ( in @ SY1212 @ SV230 )
| ( in @ SY1212 @ SV519 ) ) )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2207,plain,
! [SV231: $i,SV520: $i] :
( ( ( in @ SV520 @ ( powerset @ SV231 ) )
= $false )
| ( ( subset @ ( setminus @ SV231 @ ( setminus @ SV231 @ SV520 ) ) @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2208,plain,
! [SV521: $i > $o,SV232: $i] :
( ( ( ~ ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SV232 )
| ( SV521 @ SY1214 ) ) )
= $false )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2209,plain,
! [SV522: $i,SV233: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ ( funcSet @ SV233 @ SV522 ) ) )
= $true )
| ( ( func @ SV233 @ SV522 @ SV706 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(2210,plain,
! [SV523: $i,SV234: $i] :
( ( ( breln1 @ SV234 @ SV523 )
= $false )
| ( ( ! [SY1217: $i] :
( ~ ( breln1 @ SV234 @ SY1217 )
| ! [SY1218: $i] :
( ~ ( in @ SY1218 @ SV234 )
| ! [SY1219: $i] :
( ~ ( in @ SY1219 @ SV234 )
| ! [SY1220: $i] :
( ~ ( in @ SY1220 @ SV234 )
| ~ ( in @ ( kpair @ SY1218 @ SY1220 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1220 @ SY1219 ) @ SY1217 )
| ( in @ ( kpair @ SY1218 @ SY1219 ) @ ( breln1compset @ SV234 @ SV523 @ SY1217 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2211,plain,
! [SV524: $i,SV235: $i] :
( ( ( ~ ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV235 )
| ~ ( in @ SY1221 @ SV524 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2212,plain,
! [SV525: $i,SV236: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV236 ) )
= $true )
| ( ( ~ ( in @ SV707 @ SV525 )
| ( in @ SV707 @ ( binintersect @ SV236 @ SV525 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1904]) ).
thf(2213,plain,
! [SV756: $i,SV708: $i,SV526: $i,SV237: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SV526 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV708 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV708 @ ( setadjoin @ SV756 @ emptyset ) ) @ emptyset ) ) )
| ( SV237 = SV708 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2214,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i,SV757: $i] :
( ( ~ ( in @ SV757 @ SV238 )
| ! [SY1570: $i] :
( ~ ( in @ SY1570 @ SV527 )
| ~ ( in @ ( kpair @ SV757 @ SY1570 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SY1570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2215,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV239 ) )
= $true )
| ( ( ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV528 )
| ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SY1523 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2216,plain,
! [SV240: $i,SV529: $i] :
( ( ( in @ SV529 @ ( powerset @ SV240 ) )
= $false )
| ( ( ! [SY1232: $i] :
( ~ ( in @ SY1232 @ ( powerset @ SV240 ) )
| ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SY1232 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1908]) ).
thf(2217,plain,
! [SV530: $o,SV241: $i,SV711: $i] :
( ( ( ~ ( in @ SV711 @ SV241 ) )
= $true )
| ( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV241 )
| ( in @ ( if @ SV241 @ SV530 @ SV711 @ SY1524 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(2218,plain,
! [SV241: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ SV241 ) )
= $true )
| ( ( ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV241 )
| ( in @ ( if @ SV241 @ $true @ SV712 @ SY1525 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(2219,plain,
! [SV241: $i,SV713: $i] :
( ( ( ~ ( in @ SV713 @ SV241 ) )
= $true )
| ( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ SV241 )
| ( in @ ( if @ SV241 @ $false @ SV713 @ SY1526 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2220,plain,
! [SV714: $i,SV532: $i,SV243: $i] :
( ( ( ~ ( func @ SV243 @ SV532 @ SV714 ) )
= $true )
| ( ( ( lam @ SV243 @ SV532
@ ^ [SY1527: $i] : ( ap @ SV243 @ SV532 @ SV714 @ SY1527 ) )
= SV714 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(2221,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1240: $i] :
( ~ ( in @ SY1240 @ SV245 )
| ! [SY1241: $i] :
( ~ ( in @ SY1241 @ SV245 )
| ~ ( SV534 @ SY1240 )
| ~ ( SV534 @ SY1241 )
| ( SY1240 = SY1241 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2222,plain,
! [SV758: $i,SV715: $i,SV535: $i,SV246: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SV535 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV715 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV715 @ ( setadjoin @ SV758 @ emptyset ) ) @ emptyset ) ) )
| ( SV535 = SV758 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2223,plain,
! [SV536: $i,SV247: $i] :
( ( ( subset @ SV247 @ SV536 )
= $false )
| ( ( subset @ ( powerset @ SV247 ) @ ( powerset @ SV536 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(2224,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ( ~ ( in @ SV537 @ ( powerset @ SV248 ) )
| ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(2225,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ( ~ ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) )
| ( in @ SV537 @ ( powerset @ SV248 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(2226,plain,
! [SV538: $i,SV250: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) ) )
= $true )
| ( ( ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV250 )
| ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV538 )
| ~ ( in @ ( kpair @ SY1529 @ SY1530 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SY1529 )
= SY1530 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2227,plain,
! [SV539: $i,SV251: $i] :
( ( ( breln1 @ SV251 @ SV539 )
= $false )
| ( ( ! [SY1251: $i] :
( ~ ( in @ SY1251 @ SV251 )
| ! [SY1252: $i] :
( ~ ( in @ SY1252 @ SV251 )
| ~ ( in @ ( kpair @ SY1251 @ SY1252 ) @ SV539 )
| ( in @ ( kpair @ SY1252 @ SY1251 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2228,plain,
! [SV540: $i,SV252: $i] :
( ( ( breln1 @ SV252 @ SV540 )
= $false )
| ( ( ! [SY1253: $i] :
( ~ ( in @ SY1253 @ SV252 )
| ! [SY1254: $i] :
( ~ ( in @ SY1254 @ SV252 )
| ~ ( in @ ( kpair @ SY1254 @ SY1253 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SY1253 @ SY1254 ) @ SV540 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2229,plain,
! [SV253: $o,SV541: $i] :
( ( ( in @ SV541 @ ( prop2set @ SV253 ) )
= $false )
| ( SV253 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1921]) ).
thf(2230,plain,
! [SV542: $i] :
( ( ( in @ SV542 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1922]) ).
thf(2231,plain,
! [SV543: $i] :
( ( ( in @ SV543 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2232,plain,
! [SV544: $i,SV254: $i,SV717: $i] :
( ( ( ~ ( in @ SV717 @ ( binintersect @ SV254 @ SV544 ) ) )
= $true )
| ( ( in @ SV717 @ SV254 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2233,plain,
! [SV545: $i,SV255: $i] :
( ( ( breln1 @ SV255 @ SV545 )
= $false )
| ( ( ! [SY1256: $i] :
( ~ ( breln1 @ SV255 @ SY1256 )
| ! [SY1257: $i] :
( ~ ( in @ SY1257 @ SV255 )
| ! [SY1258: $i] :
( ~ ( in @ SY1258 @ SV255 )
| ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ ( binunion @ SV545 @ SY1256 ) )
| ! [SY1259: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SV545 )
| SY1259 )
| ~ ( ~ ( in @ ( kpair @ SY1257 @ SY1258 ) @ SY1256 )
| SY1259 )
| SY1259 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2234,plain,
! [SV256: $i,SV546: $i,SV718: $i] :
( ( ( ~ ( in @ SV718 @ SV546 ) )
= $true )
| ( ( in @ SV718 @ ( setadjoin @ SV256 @ SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2235,plain,
! [SV547: $i,SV257: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ SV257 ) )
= $true )
| ( ( ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV547 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SY1531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1927]) ).
thf(2236,plain,
! [SV258: $i,SV548: $i] :
( ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false )
| ( ( ! [SY1263: $i] :
( ~ ( in @ SY1263 @ ( powerset @ SV258 ) )
| ! [SY1264: $i] :
( ~ ( in @ SY1264 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SY1263 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1264 ) @ ( binunion @ SY1263 @ SY1264 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2237,plain,
! [SV549: $i,SV259: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( surjFuncSet @ SV259 @ SV549 ) ) )
= $true )
| ( ( in @ SV720 @ ( funcSet @ SV259 @ SV549 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1929]) ).
thf(2238,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY1266: $i,SY1267: $i] :
( ( SY1266 != SY1267 )
| ~ ( ~ ( ~ ( SV260 @ SY1266 )
| ( SV550 @ SY1267 ) )
| ~ ( ~ ( SV550 @ SY1267 )
| ( SV260 @ SY1266 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2239,plain,
! [SV261: $i,SV551: $i] :
( ( ( in @ SV551 @ ( funcSet @ SV261 @ ( powerset @ SV261 ) ) )
= $false )
| ( ( ~ ( surjective @ SV261 @ ( powerset @ SV261 ) @ SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2240,plain,
! [SV262: $i] :
( ( ( ( omegaS @ SV262 )
= emptyset )
= $false )
| ( ( in @ SV262 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2241,plain,
! [SV263: $i,SV552: $i] :
( ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false )
| ( ( ! [SY1274: $i] :
( ~ ( in @ SY1274 @ ( powerset @ SV263 ) )
| ! [SY1275: $i] :
( ~ ( in @ SY1275 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1275 )
| ( subset @ ( binintersect @ SV552 @ SY1274 ) @ SY1275 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2242,plain,
! [SV553: $i,SV264: $i] :
( ( ( breln1 @ SV264 @ SV553 )
= $false )
| ( ( ! [SY1276: $i] :
( ~ ( breln1 @ SV264 @ SY1276 )
| ~ ! [SY1277: $i] :
( ~ ( in @ SY1277 @ SV264 )
| ! [SY1278: $i] :
( ~ ( in @ SY1278 @ SV264 )
| ~ ( in @ ( kpair @ SY1277 @ SY1278 ) @ SV553 )
| ( in @ ( kpair @ SY1277 @ SY1278 ) @ SY1276 ) ) )
| ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ SV264 )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SV264 )
| ~ ( in @ ( kpair @ SY1279 @ SY1280 ) @ SY1276 )
| ( in @ ( kpair @ SY1279 @ SY1280 ) @ SV553 ) ) )
| ( SV553 = SY1276 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2243,plain,
! [SV554: $i,SV265: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV265 ) )
= $true )
| ( ( ~ ( in @ SV721 @ SV554 )
| ~ ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1935]) ).
thf(2244,plain,
! [SV555: $i,SV266: $i,SV722: $i] :
( ( ( ~ ( in @ SV722 @ ( cartprod @ SV266 @ SV555 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV722 ) @ ( ksnd @ SV722 ) )
= SV722 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1936]) ).
thf(2245,plain,
! [SV268: $i,SV557: $i] :
( ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false )
| ( ( ! [SY1283: $i] :
( ~ ( in @ SY1283 @ SV268 )
| ~ ( in @ SY1283 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SY1283 @ SV557 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2246,plain,
! [SV558: $i > $o,SV269: $i] :
( ( ( ~ ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SV269 )
| ~ ~ ( SV558 @ SY1284 ) ) )
= $false )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2247,plain,
! [SV559: $i,SV270: $i,SV723: $i] :
( ( ( ~ ~ ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV723 @ SV559 )
| ~ ( in @ SV723 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2248,plain,
! [SV271: $i,SV560: $i] :
( ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false )
| ( ( ! [SY1287: $i] :
( ~ ( in @ SY1287 @ ( powerset @ SV271 ) )
| ! [SY1288: $i] :
( ~ ( in @ SY1288 @ SV271 )
| ~ ( in @ SY1288 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SY1287 ) ) )
| ( in @ SY1288 @ ( setminus @ SV271 @ SY1287 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1940]) ).
thf(2249,plain,
! [SV272: $i] :
( ( ( ~ ( in @ ( sK10_SY725 @ SV272 ) @ SV272 ) )
= $false )
| ( ( SV272 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1941]) ).
thf(2250,plain,
! [SV561: $i,SV273: $i] :
( ( ( subset @ SV273 @ SV561 )
= $false )
| ( ( ( binintersect @ SV273 @ SV561 )
= SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2251,plain,
! [SV562: $i,SV274: $i] :
( ( ( breln1 @ SV274 @ SV562 )
= $false )
| ( ( ! [SY1289: $i] :
( ~ ( breln1 @ SV274 @ SY1289 )
| ! [SY1290: $i] :
( ~ ( in @ SY1290 @ SV274 )
| ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV274 )
| ~ ( in @ ( kpair @ SY1290 @ SY1291 ) @ SV562 )
| ( in @ ( kpair @ SY1290 @ SY1291 ) @ ( binunion @ SV562 @ SY1289 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2252,plain,
! [SV563: $i,SV275: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( binintersect @ SV275 @ SV563 ) ) )
= $true )
| ( ( in @ SV724 @ SV563 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1944]) ).
thf(2253,plain,
! [SV564: $i,SV276: $i,SV725: $i] :
( ( ( ~ ~ ( in @ SV725 @ SV276 ) )
= $true )
| ( ( ~ ~ ( in @ SV725 @ SV564 )
| ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1945]) ).
thf(2254,plain,
! [SV566: $i,SV278: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ SV278 ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( in @ SY1532 @ SV566 )
| ( ( kfst @ ( kpair @ SV726 @ SY1532 ) )
= SV726 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2255,plain,
! [SV279: $i,SV567: $i] :
( ( ( subset @ SV567 @ SV279 )
= $false )
| ( ( ( binintersect @ SV279 @ SV567 )
= SV567 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2256,plain,
! [SV280: $i,SV568: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ SV568 ) )
= $true )
| ( ( in @ SV727 @ ( binunion @ SV280 @ SV568 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2257,plain,
! [SV281: $i] :
( ( ( SV281 = emptyset )
= $true )
| ( ( ~ ! [SY742: $i] :
~ ~ ( ~ ( in @ SY742 @ SV281 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1949]) ).
thf(2258,plain,
! [SV569: $i,SV283: $i] :
( ( ( SV283 = SV569 )
= $false )
| ( ( ! [SY1297: $i > $o,SY1298: $i > $o] :
( ~ ! [SY1299: $i] :
( ~ ( in @ SY1299 @ SV283 )
| ! [SY1300: $i] :
( ~ ( in @ SY1300 @ SV569 )
| ( SY1299 != SY1300 )
| ~ ( ~ ( ~ ( SY1297 @ SY1299 )
| ( SY1298 @ SY1300 ) )
| ~ ( ~ ( SY1298 @ SY1300 )
| ( SY1297 @ SY1299 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SX4: $i] : ( SY1297 @ SX4 ) )
= ( dsetconstr @ SV569
@ ^ [SX4: $i] : ( SY1298 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2259,plain,
! [SV284: $i > $o] :
( ( ( ! [SY750: $i] :
~ ~ ( ~ ( SV284 @ SY750 )
| ~ ! [SY751: $i] :
( ~ ( SV284 @ SY751 )
| ( SY750 = SY751 ) ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2260,plain,
! [SV285: $i,SV570: $i] :
( ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false )
| ( ( ! [SY1303: $i] :
( ~ ( in @ SY1303 @ ( powerset @ SV285 ) )
| ! [SY1304: $i] :
( ~ ( in @ SY1304 @ SV285 )
| ~ ( in @ SY1304 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1304 @ ( binintersect @ SV570 @ SY1303 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2261,plain,
! [SV571: $i > $o,SV286: $i,SV728: $i] :
( ( ( ~ ( in @ SV728
@ ( dsetconstr @ SV286
@ ^ [SY1306: $i] : ( SV571 @ SY1306 ) ) ) )
= $true )
| ( ( SV571 @ SV728 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1954]) ).
thf(2262,plain,
! [SV759: $o,SV572: $i,SV287: $i,SV729: $i] :
( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
| ~ ( ~ ( in @ SV729 @ SV287 )
| SV759 )
| ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1955]) ).
thf(2263,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
| ~ ( ~ ( in @ SV729 @ SV287 )
| $true )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1955]) ).
thf(2264,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
| ~ ( ~ ( in @ SV729 @ SV287 )
| $false )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1955]) ).
thf(2265,plain,
! [SV573: $i,SV288: $i] :
( ( ( breln1 @ SV288 @ SV573 )
= $false )
| ( ( ! [SY1309: $i] :
( ~ ( breln1 @ SV288 @ SY1309 )
| ! [SY1310: $i] :
( ~ ( in @ SY1310 @ SV288 )
| ! [SY1311: $i] :
( ~ ( in @ SY1311 @ SV288 )
| ~ ( in @ ( kpair @ SY1310 @ SY1311 ) @ SY1309 )
| ( in @ ( kpair @ SY1310 @ SY1311 ) @ ( binunion @ SV573 @ SY1309 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2266,plain,
! [SV574: $i,SV289: $i] :
( ( ( SV289 = SV574 )
= $false )
| ( ( ( powerset @ SV289 )
= ( powerset @ SV574 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2267,plain,
! [SV576: $o,SV291: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ SV291 ) )
= $true )
| ( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV291 )
| ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SY1537 )
= SY1537 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1959]) ).
thf(2268,plain,
! [SV291: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ SV291 ) )
= $true )
| ( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV291 )
| ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SY1538 )
= SY1538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1960]) ).
thf(2269,plain,
! [SV291: $i,SV733: $i] :
( ( ( ~ ( in @ SV733 @ SV291 ) )
= $true )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV291 )
| ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SY1539 )
= SY1539 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1961]) ).
thf(2270,plain,
! [SV578: $i,SV294: $i] :
( ( ( breln1 @ SV294 @ SV578 )
= $false )
| ( ( ! [SY1317: $i] :
( ~ ( breln1 @ SV294 @ SY1317 )
| ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SY1317 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SY1317 ) @ ( breln1invset @ SV294 @ SV578 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2271,plain,
! [SV296: $i,SV580: $i] :
( ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false )
| ( ( ! [SY1318: $i] :
( ~ ( in @ SY1318 @ ( powerset @ SV296 ) )
| ~ ! [SY1319: $i] :
( ~ ( in @ SY1319 @ SV296 )
| ~ ( in @ SY1319 @ SV580 )
| ( in @ SY1319 @ SY1318 ) )
| ( in @ SV580 @ ( powerset @ SY1318 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2272,plain,
! [SV581: $i,SV297: $i] :
( ( ( breln1 @ SV297 @ SV581 )
= $false )
| ( ( ! [SY1320: $i] :
( ~ ( breln1 @ SV297 @ SY1320 )
| ! [SY1321: $i] :
( ~ ( in @ SY1321 @ SV297 )
| ! [SY1322: $i] :
( ~ ( in @ SY1322 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1321 @ SY1322 ) @ SV581 )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ SY1320 ) )
| ( in @ ( kpair @ SY1321 @ SY1322 ) @ ( binunion @ SV581 @ SY1320 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2273,plain,
! [SV734: $i,SV582: $i,SV298: $i] :
( ( ( ~ ( breln @ SV298 @ SV582 @ SV734 ) )
= $true )
| ( ( ! [SY1540: $i] :
( ~ ( breln @ SV298 @ SV582 @ SY1540 )
| ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV298 )
| ! [SY1542: $i] :
( ~ ( in @ SY1542 @ SV582 )
| ~ ( in @ ( kpair @ SY1541 @ SY1542 ) @ SV734 )
| ( in @ ( kpair @ SY1541 @ SY1542 ) @ SY1540 ) ) )
| ( subset @ SV734 @ SY1540 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2274,plain,
! [SV299: $i,SV583: $i] :
( ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false )
| ( ( ! [SY1327: $i] :
( ~ ( in @ SY1327 @ ( powerset @ SV299 ) )
| ! [SY1328: $i] :
( ~ ( in @ SY1328 @ SV299 )
| ~ ( in @ SY1328 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SY1327 ) ) )
| ( in @ SY1328 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SY1327 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2275,plain,
! [SV300: $i > $o] :
( ( ( ! [SY794: $i] :
~ ~ ( ~ ( SV300 @ SY794 )
| ~ ! [SY795: $i] :
( ~ ( SV300 @ SY795 )
| ( SY794 = SY795 ) ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2276,plain,
! [SV301: $i,SV584: $i] :
( ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false )
| ( ( ! [SY1329: $i] :
( ~ ( in @ SY1329 @ ( powerset @ SV301 ) )
| ! [SY1330: $i] :
( ~ ( in @ SY1330 @ SV301 )
| ~ ( in @ SY1330 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1330 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SY1329 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1968]) ).
thf(2277,plain,
! [SV302: $i,SV585: $i] :
( ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false )
| ( ( ! [SY1331: $i] :
( ~ ( in @ SY1331 @ ( powerset @ SV302 ) )
| ! [SY1332: $i] :
( ~ ( in @ SY1332 @ SV302 )
| ~ ( in @ SY1332 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SY1331 ) ) )
| ( in @ SY1332 @ ( setminus @ SV302 @ SV585 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2278,plain,
! [SV586: $i,SV303: $i] :
( ( ( ( binintersect @ SV303 @ SV586 )
= SV303 )
= $false )
| ( ( subset @ SV303 @ SV586 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1970]) ).
thf(2279,plain,
! [SV304: $i] :
( ( ( SV304 = emptyset )
= $true )
| ( ( ~ ! [SY804: $i] :
~ ( in @ SY804 @ SV304 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2280,plain,
! [SV305: $i,SV587: $i] :
( ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false )
| ( ( ! [SY1333: $i] :
( ~ ( in @ SY1333 @ ( powerset @ SV305 ) )
| ! [SY1334: $i] :
( ~ ( in @ SY1334 @ ( binintersect @ SV587 @ SY1333 ) )
| ( in @ SY1334 @ SV305 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2281,plain,
! [SV306: $i,SV735: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV735 ) )
= $true )
| ( ( ~ ( in @ SV735 @ SV306 )
| ( in @ SV588 @ ( setunion @ SV306 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2282,plain,
! [SV307: $i,SV589: $i] :
( ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false )
| ( ( ! [SY1336: $i] :
( ~ ( in @ SY1336 @ SV307 )
| ~ ( in @ SY1336 @ SV589 )
| ~ ( in @ SY1336 @ ( setminus @ SV307 @ SV589 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2283,plain,
! [SV308: $i,SV590: $i] :
( ( ( in @ SV590 @ ( powerset @ SV308 ) )
= $false )
| ( ( ! [SY1337: $i] :
( ~ ( in @ SY1337 @ ( powerset @ SV308 ) )
| ( ( setminus @ SV308 @ ( binunion @ SV590 @ SY1337 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SY1337 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1975]) ).
thf(2284,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) ) )
= $true )
| ( ( ! [SY1543: $o] :
( ~ ( ( SV736 != SV309 )
| SY1543 )
| ~ ( ~ ( in @ SV736 @ SV591 )
| SY1543 )
| SY1543 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1976]) ).
thf(2285,plain,
! [SV310: $i,SV592: $i] :
( ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false )
| ( ( ! [SY1340: $i] :
( ~ ( in @ SY1340 @ ( powerset @ SV310 ) )
| ~ ! [SY1341: $i] :
( ~ ( in @ SY1341 @ SV310 )
| ~ ( in @ SY1341 @ SV592 )
| ( in @ SY1341 @ SY1340 ) )
| ( subset @ SV592 @ SY1340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2286,plain,
! [SV593: $i,SV311: $i] :
( ( ( in @ SV311 @ ( setadjoin @ SV593 @ emptyset ) )
= $false )
| ( ( in @ SV593 @ ( setadjoin @ SV311 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2287,plain,
! [SV594: $i,SV312: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( binunion @ SV312 @ SV594 ) ) )
= $true )
| ( ( ( in @ SV737 @ SV312 )
| ( in @ SV737 @ SV594 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1979]) ).
thf(2288,plain,
! [SV595: $i,SV313: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ SV313 ) )
= $true )
| ( ( ! [SY1544: $i] :
( ~ ( in @ SY1544 @ SV595 )
| ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SY1544 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2289,plain,
! [SV739: $i > $i > $o,SV596: $i,SV314: $i,SV760: $i] :
( ( ~ ( in @ SV760 @ SV314 )
| ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV596 )
| ~ ( SV739 @ SV760 @ SY1573 )
| ( in @ ( kpair @ SV760 @ SY1573 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2290,plain,
! [SV315: $i,SV597: $i] :
( ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false )
| ( ( ! [SY1350: $i] :
( ~ ( in @ SY1350 @ ( powerset @ SV315 ) )
| ! [SY1351: $o,SY1352: $i] :
( ~ ( in @ SY1352 @ SV315 )
| ~ ( in @ SY1352 @ ( binunion @ SV597 @ SY1350 ) )
| ~ ( ~ ( in @ SY1352 @ SV597 )
| SY1351 )
| ~ ( ~ ( in @ SY1352 @ SY1350 )
| SY1351 )
| SY1351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2291,plain,
! [SV598: $i,SV316: $i] :
( ( ( in @ SV316 @ ( setadjoin @ SV598 @ emptyset ) )
= $false )
| ( ( SV316 = SV598 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2292,plain,
! [SV317: $i,SV599: $i] :
( ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY1353: $i] :
( ~ ( in @ SY1353 @ ( powerset @ SV317 ) )
| ! [SY1354: $i] :
( ~ ( in @ SY1354 @ ( powerset @ SV317 ) )
| ! [SY1355: $i] :
( ~ ( in @ SY1355 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SY1353 ) @ ( binunion @ SY1354 @ SY1355 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SY1353 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1354 ) @ ( setminus @ SV317 @ SY1355 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1984]) ).
thf(2293,plain,
! [SV318: $i,SV600: $i] :
( ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false )
| ( ( ! [SY1356: $i] :
( ~ ( in @ SY1356 @ ( powerset @ SV318 ) )
| ! [SY1357: $i] :
( ~ ( in @ SY1357 @ SV318 )
| ~ ( subset @ SV600 @ SY1356 )
| ~ ~ ( in @ SY1357 @ SY1356 )
| ~ ( in @ SY1357 @ SV600 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2294,plain,
! [SV740: $i,SV601: $i,SV319: $i] :
( ( ( ~ ( func @ SV319 @ SV601 @ SV740 ) )
= $true )
| ( ( ! [SY1549: $i] :
( ~ ( in @ SY1549 @ SV319 )
| ( in @ ( kpair @ SY1549 @ ( ap @ SV319 @ SV601 @ SV740 @ SY1549 ) ) @ SV740 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1986]) ).
thf(2295,plain,
! [SV741: $i,SV602: $i,SV320: $i] :
( ( ( ~ ( subset @ SV320 @ SV602 ) )
= $true )
| ( ( ~ ( in @ SV741 @ SV320 )
| ( in @ SV741 @ SV602 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1987]) ).
thf(2296,plain,
! [SV603: $i,SV321: $i,SV742: $i] :
( ( ( ~ ( subset @ SV742 @ SV321 ) )
= $true )
| ( ( ~ ( subset @ SV742 @ SV603 )
| ( subset @ SV742 @ ( binintersect @ SV321 @ SV603 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1988]) ).
thf(2297,plain,
! [SV322: $i,SV604: $i] :
( ( ( in @ SV604 @ ( powerset @ SV322 ) )
= $false )
| ( ( ! [SY1362: $i] :
( ~ ( in @ SY1362 @ ( powerset @ SV322 ) )
| ( in @ ( binintersect @ SV604 @ SY1362 ) @ ( powerset @ SV322 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2298,plain,
! [SV323: $i > $o] :
( ( ( ! [SY853: $i] :
~ ~ ( ~ ( SV323 @ SY853 )
| ~ ! [SY854: $i] :
( ~ ( SV323 @ SY854 )
| ( SY853 = SY854 ) ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1990]) ).
thf(2299,plain,
! [SV605: $i,SV324: $i,SV743: $i] :
( ( ( ~ ( in @ SV743 @ SV324 ) )
= $true )
| ( ( ! [SY1550: $i] :
( ~ ( in @ SY1550 @ SV605 )
| ( ( kpair @ SV743 @ SY1550 )
= ( kpair @ SV743 @ SY1550 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2300,plain,
! [SV606: $i,SV325: $i] :
( ( ( SV325 = SV606 )
= $false )
| ( ( subset @ SV325 @ SV606 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2301,plain,
! [SV326: $i,SV607: $i] :
( ( ( in @ SV607 @ ( powerset @ SV326 ) )
= $false )
| ( ( ! [SY1365: $i] :
( ~ ( in @ SY1365 @ ( powerset @ SV326 ) )
| ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SY1365 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2302,plain,
! [SV328: $i,SV2: $i] :
( ( ( SV2 = SV328 )
= $true )
| ( ( ~ ( in @ SV328 @ ( setadjoin @ SV2 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1995]) ).
thf(2303,plain,
! [SV3: $i] :
( ( ( ~ ( in @ ( sK5_SY5 @ SV3 ) @ SV3 ) )
= $false )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2304,plain,
! [SV3: $i] :
( ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1996]) ).
thf(2305,plain,
! [SV329: $i,SV608: $i > $i,SV4: $i] :
( ( ( ! [SY1366: $i] :
( ~ ( in @ SY1366 @ SV4 )
| ( in @ ( SV608 @ SY1366 ) @ SV329 ) ) )
= $false )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2306,plain,
! [SV5: $i] :
( ( ( in @ ( sK6_SY13 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1998]) ).
thf(2307,plain,
! [SV330: $i,SV6: $i,SV609: $i] :
( ( ( in @ SV609 @ SV6 )
= $false )
| ( ( ! [SY1368: $i] :
( ~ ( in @ SY1368 @ SV330 )
| ( ( ksnd @ ( kpair @ SV609 @ SY1368 ) )
= SY1368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2308,plain,
! [SV331: $i > $o,SV7: $i,SV610: $i] :
( ( ( in @ SV610
@ ( dsetconstr @ SV7
@ ^ [SY868: $i] : ( SV331 @ SY868 ) ) )
= $false )
| ( ( in @ SV610 @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2309,plain,
! [SV332: $i > $o,SV8: $i,SV611: $i] :
( ( ( in @ SV611 @ SV8 )
= $false )
| ( ( ~ ( SV332 @ SV611 )
| ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2001]) ).
thf(2310,plain,
! [SV612: $i,SV333: $i,SV9: $i] :
( ( ( func @ SV9 @ SV333 @ SV612 )
= $false )
| ( ( ! [SY1372: $i] :
( ~ ( in @ SY1372 @ SV9 )
| ( ( ap @ SV9 @ SV333 @ SV612 @ SY1372 )
= ( ap @ SV9 @ SV333 @ SV612 @ SY1372 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2002]) ).
thf(2311,plain,
! [SV334: $i,SV10: $i,SV613: $i] :
( ( ( in @ SV613 @ SV10 )
= $false )
| ( ( ! [SY1373: $i] :
( ~ ( in @ SY1373 @ SV334 )
| ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SY1373 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2003]) ).
thf(2312,plain,
! [SV614: $i,SV335: $i,SV11: $i] :
( ( ( func @ SV11 @ SV335 @ SV614 )
= $false )
| ( ( ! [SY1374: $i] :
( ~ ( func @ SV11 @ SV335 @ SY1374 )
| ~ ! [SY1375: $i] :
( ~ ( in @ SY1375 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1375 )
= ( ap @ SV11 @ SV335 @ SY1374 @ SY1375 ) ) )
| ! [SY1376: $i] :
( ~ ( in @ SY1376 @ SV11 )
| ! [SY1377: $i] :
( ~ ( in @ SY1377 @ SV335 )
| ~ ( in @ ( kpair @ SY1376 @ SY1377 ) @ SY1374 )
| ( in @ ( kpair @ SY1376 @ SY1377 ) @ SV614 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2004]) ).
thf(2313,plain,
! [SV337: $i,SV615: $i > $i,SV14: $i] :
( ( ( ! [SY1378: $i] :
( ~ ( in @ SY1378 @ SV14 )
| ( in @ ( SV615 @ SY1378 ) @ SV337 ) ) )
= $false )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2314,plain,
! [SV616: $i,SV339: $i,SV16: $i] :
( ( ( func @ SV16 @ SV339 @ SV616 )
= $false )
| ( ( in @ SV616 @ ( funcSet @ SV16 @ SV339 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2315,plain,
! [SV340: $i,SV17: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( powerset @ SV17 ) )
| ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY1576 ) @ ( binunion @ SV761 @ SY1576 ) ) ) ) ) )
= $true )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2316,plain,
! [SV618: $i,SV342: $i,SV19: $i] :
( ( ( breln @ SV19 @ SV342 @ SV618 )
= $false )
| ( ( ! [SY1381: $i > $o] :
( ~ ! [SY1382: $i] :
( ~ ( in @ SY1382 @ SV19 )
| ! [SY1383: $i] :
( ~ ( in @ SY1383 @ SV342 )
| ~ ( in @ ( kpair @ SY1382 @ SY1383 ) @ SV618 )
| ( SY1381 @ ( kpair @ SY1382 @ SY1383 ) ) ) )
| ! [SY1384: $i] :
( ~ ( in @ SY1384 @ SV618 )
| ( SY1381 @ SY1384 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2317,plain,
! [SV343: $i,SV20: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV20 ) )
| ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV20 )
| ~ ~ ( in @ SY1577 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SY1577 @ SV762 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2318,plain,
! [SV344: $i,SV21: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV21 ) )
| ~ ( subset @ SV344 @ ( setminus @ SV21 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV21 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2319,plain,
! [SV346: $i,SV24: $i,SV764: $i] :
( ( ( ! [SY1578: $i] :
( ( SV764 != SY1578 )
| ~ ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SY1578 @ SV346 ) )
| ~ ( ~ ( in @ SY1578 @ SV346 )
| ( in @ SV764 @ SV24 ) ) ) ) )
= $true )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2320,plain,
! [SV347: $i > $o,SV26: $i] :
( ( ( ~ ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV26 )
| ~ ( SV347 @ SY899 ) ) )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2321,plain,
! [SV27: $i,SV348: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
| ~ ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) ) )
= $false )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2018]) ).
thf(2322,plain,
! [SV349: $i,SV28: $i,SV619: $i] :
( ( ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) )
= $false )
| ( ( ! [SY1385: $i] :
( ~ ( in @ SY1385 @ SV28 )
| ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SY1385 ) @ SV349 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2323,plain,
! [SV350: $i,SV29: $i,SV620: $i] :
( ( ( in @ SV620 @ ( funcSet @ SV29 @ SV350 ) )
= $false )
| ( ( ( lam @ SV29 @ SV350
@ ^ [SY1386: $i] : ( ap @ SV29 @ SV350 @ SV620 @ SY1386 ) )
= SV620 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2324,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( ~ ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
| ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2325,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( ~ ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2021]) ).
thf(2326,plain,
! [SV353: $i,SV34: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ ( powerset @ SV34 ) )
| ! [SY1579: $i] :
( ~ ( in @ SY1579 @ SV34 )
| ~ ~ ( in @ SY1579 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SY1579 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2023]) ).
thf(2327,plain,
! [SV354: $i,SV35: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SV766 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SV766 ) ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2024]) ).
thf(2328,plain,
! [SV355: $i,SV37: $i,SV622: $i] :
( ( ( in @ SV622 @ ( setadjoin @ SV37 @ ( setadjoin @ SV355 @ emptyset ) ) )
= $false )
| ( ( ( SV622 = SV37 )
| ( SV622 = SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2329,plain,
! [SV356: $i,SV38: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ ( powerset @ SV38 ) )
| ( in @ ( setminus @ SV356 @ SV767 ) @ ( powerset @ SV38 ) ) )
= $true )
| ( ( in @ SV356 @ ( powerset @ SV38 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2330,plain,
! [SV357: $i,SV768: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV768 )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SV40 )
| ! [SY1581: $i] :
( ~ ( in @ SY1581 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1581 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1582: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1582 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1582 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1582 @ SY1581 ) @ SV768 ) ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2331,plain,
! [SV358: $i,SV769: $i,SV41: $i] :
( ( ( ~ ( breln1 @ SV41 @ SV769 )
| ! [SY1583: $i] :
( ~ ( breln1 @ SV41 @ SY1583 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SY1583 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY1583 ) @ ( breln1compset @ SV41 @ SV769 @ SY1583 ) ) ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2332,plain,
! [SV359: $i,SV42: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ ( powerset @ SV42 ) )
| ! [SY1584: $i] :
( ~ ( in @ SY1584 @ SV42 )
| ~ ( in @ SY1584 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SY1584 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) ) )
= $true )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2333,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i] :
( ( ( ~ ! [SY1387: $i] :
~ ~ ( ~ ( in @ SY1387 @ SV43 )
| ( SV623
!= ( SV360 @ SY1387 ) ) ) )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2334,plain,
! [SV361: $i,SV44: $i,SV624: $i] :
( ( ( in @ SV624 @ ( injFuncSet @ SV44 @ SV361 ) )
= $false )
| ( ( in @ SV624 @ ( funcSet @ SV44 @ SV361 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2031]) ).
thf(2335,plain,
! [SV362: $i,SV771: $i,SV45: $i] :
( ( ( ~ ( breln1 @ SV45 @ SV771 )
| ( breln1 @ SV45 @ ( binunion @ SV362 @ SV771 ) ) )
= $true )
| ( ( breln1 @ SV45 @ SV362 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2336,plain,
! [SV745: $i,SV625: $i,SV363: $i,SV46: $i] :
( ( ( ( kpair @ SV46 @ SV363 )
!= ( kpair @ SV625 @ SV745 ) )
= $true )
| ( ( SV46 = SV625 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2033]) ).
thf(2337,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ( in @ SV364 @ ( setunion @ SV47 ) )
| ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2034]) ).
thf(2338,plain,
! [SV47: $i,SV364: $i] :
( ( ~ ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) )
| ( in @ SV364 @ ( setunion @ SV47 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2035]) ).
thf(2339,plain,
! [SV365: $i,SV48: $i,SV626: $i] :
( ( ( in @ SV626 @ ( setadjoin @ SV48 @ SV365 ) )
= $false )
| ( ( ( SV626 = SV48 )
| ( in @ SV626 @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2340,plain,
! [SV366: $i,SV772: $i,SV49: $i] :
( ( ( ~ ( breln1 @ SV49 @ SV772 )
| ( ( binunion @ SV366 @ SV772 )
= ( binunion @ SV772 @ SV366 ) ) )
= $true )
| ( ( breln1 @ SV49 @ SV366 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2037]) ).
thf(2341,plain,
! [SV51: $i,SV746: $i] :
( ( ( ~ ( in @ SV746 @ omega ) )
= $true )
| ( ( ( ( omegaS @ SV51 )
!= ( omegaS @ SV746 ) )
| ( SV51 = SV746 ) )
= $true )
| ( ( in @ SV51 @ omega )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2038]) ).
thf(2342,plain,
! [SV367: $i,SV52: $i,SV773: $i] :
( ( ( ~ ( in @ SV773 @ ( powerset @ SV52 ) )
| ! [SY1585: $i] :
( ~ ( in @ SY1585 @ SV52 )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SY1585 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) ) )
= $true )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2039]) ).
thf(2343,plain,
! [SV368: $i,SV53: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ ( powerset @ SV53 ) )
| ~ ( subset @ SV368 @ SV774 )
| ( subset @ ( setminus @ SV53 @ SV774 ) @ ( setminus @ SV53 @ SV368 ) ) )
= $true )
| ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2040]) ).
thf(2344,plain,
! [SV369: $i,SV54: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ ( powerset @ SV54 ) )
| ~ ( subset @ ( setminus @ SV54 @ SV775 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SV775 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2345,plain,
! [SV370: $i,SV55: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV55 ) )
| ~ ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
| ! [SY1586: $i] :
( ~ ( in @ SY1586 @ SV55 )
| ~ ( in @ SY1586 @ SV776 )
| ( in @ SY1586 @ ( setminus @ SV55 @ SV370 ) ) ) )
= $true )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2346,plain,
! [SV372: $i,SV57: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ ( powerset @ SV57 ) )
| ! [SY1587: $i] :
( ~ ( in @ SY1587 @ SV57 )
| ~ ( in @ SY1587 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SY1587 @ SV372 ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2347,plain,
! [SV373: $i > $o,SV58: $i] :
( ( ( ~ ! [SY940: $i] :
~ ~ ( ~ ( in @ SY940 @ SV58 )
| ~ ( SV373 @ SY940 ) ) )
= $true )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2045]) ).
thf(2348,plain,
! [SV374: $i,SV59: $i,SV627: $i] :
( ( ( in @ SV627 @ ( setminus @ SV59 @ SV374 ) )
= $false )
| ( ( ~ ( in @ SV627 @ SV374 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2046]) ).
thf(2349,plain,
! [SV375: $i,SV60: $i,SV628: $i] :
( ( ( in @ SV628 @ ( setadjoin @ SV60 @ ( setadjoin @ SV375 @ emptyset ) ) )
= $false )
| ( ( ( SV628 = SV60 )
| ( SV628 = SV375 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2350,plain,
! [SV376: $i > $o,SV61: $i] :
( ( ( ! [SY944: $i] :
( ~ ( in @ SY944 @ SV61 )
| ( SV376 @ SY944 ) ) )
= $true )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2048]) ).
thf(2351,plain,
! [SV377: $i,SV629: $i > $i,SV62: $i] :
( ( ( ! [SY1390: $i] :
( ~ ( in @ SY1390 @ SV62 )
| ( in @ ( SV629 @ SY1390 ) @ SV377 ) ) )
= $false )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2352,plain,
! [SV378: $i,SV63: $i,SV630: $i] :
( ( ( ~ ( in @ SV630 @ SV63 ) )
= $false )
| ( ( ~ ( in @ SV630 @ ( setminus @ SV63 @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2353,plain,
! [SV380: $i,SV66: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV66 ) )
| ! [SY1588: $i] :
( ~ ( in @ SY1588 @ SV66 )
| ~ ~ ( in @ SY1588 @ SV380 )
| ~ ~ ( in @ SY1588 @ SV778 )
| ~ ( in @ SY1588 @ ( binunion @ SV380 @ SV778 ) ) ) )
= $true )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2052]) ).
thf(2354,plain,
! [SV381: $i,SV67: $i,SV779: $i] :
( ( ( ! [SY1589: $i] :
( ( SV779 != SY1589 )
| ~ ( in @ SV779 @ SV67 )
| ( in @ SY1589 @ SV381 ) ) )
= $true )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2053]) ).
thf(2355,plain,
! [SV69: $i,SV382: $i,SV631: $i] :
( ( ( in @ SV631 @ SV382 )
= $false )
| ( ( ~ ( in @ SV631 @ ( setminus @ SV69 @ SV382 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2356,plain,
! [SV383: $o,SV70: $i,SV632: $i] :
( ( ( in @ SV632 @ SV70 )
= $false )
| ( ( ! [SY1393: $i] :
( ~ ( in @ SY1393 @ SV70 )
| ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1394: $i] :
( ~ ( ~ SV383
| ( SY1394 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1394 != SY1393 ) ) ) )
= ( setadjoin @ SY1393 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2357,plain,
! [SV70: $i,SV633: $i] :
( ( ( in @ SV633 @ SV70 )
= $false )
| ( ( ! [SY1395: $i] :
( ~ ( in @ SY1395 @ SV70 )
| ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1396: $i] :
( ~ ( ~ $true
| ( SY1396 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1396 != SY1395 ) ) ) )
= ( setadjoin @ SY1395 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2358,plain,
! [SV70: $i,SV634: $i] :
( ( ( in @ SV634 @ SV70 )
= $false )
| ( ( ! [SY1397: $i] :
( ~ ( in @ SY1397 @ SV70 )
| ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1398: $i] :
( ~ ( ~ $false
| ( SY1398 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1398 != SY1397 ) ) ) )
= ( setadjoin @ SY1397 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2359,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV73 ) )
= $true )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2360,plain,
! [SV635: $i,SV385: $i,SV75: $i] :
( ( ( func @ SV75 @ SV385 @ SV635 )
= $false )
| ( ( ! [SY1399: $i] :
( ~ ( in @ SY1399 @ SV75 )
| ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SY1399 ) @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2361,plain,
! [SV386: $i,SV76: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ ( powerset @ SV76 ) )
| ! [SY1590: $i] :
( ~ ( in @ SY1590 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SY1590 @ SV386 )
| ( in @ SY1590 @ SV781 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2362,plain,
! [SV387: $i,SV77: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( powerset @ SV77 ) )
| ! [SY1591: $i] :
( ~ ( in @ SY1591 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SY1591 @ SV782 )
| ~ ( in @ SY1591 @ SV387 ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2363,plain,
! [SV388: $i,SV78: $i,SV747: $i,SV636: $i] :
( ( ( ~ ( in @ ( kpair @ SV636 @ SV747 ) @ ( cartprod @ SV78 @ SV388 ) ) )
= $true )
| ( ( in @ SV747 @ SV388 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2062]) ).
thf(2364,plain,
! [SV389: $i,SV79: $i,SV637: $i] :
( ( ( in @ SV637 @ SV79 )
= $false )
| ( ( ! [SY1401: $i] :
( ~ ( in @ SY1401 @ SV389 )
| ( in @ ( kpair @ SV637 @ SY1401 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2063]) ).
thf(2365,plain,
! [SV390: $i,SV80: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ ( powerset @ SV80 ) )
| ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SV783 ) ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2366,plain,
! [SV392: $i,SV82: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( powerset @ SV82 ) )
| ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV82 )
| ~ ~ ( in @ SY1592 @ SV392 )
| ~ ( in @ SY1592 @ ( binintersect @ SV392 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2367,plain,
! [SV638: $i > $i > $o,SV393: $i,SV83: $i,SV785: $i,SV748: $i] :
( ( ~ ( in @ ( kpair @ SV748 @ SV785 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SY1404: $i,SY1405: $i] : ( SV638 @ SY1404 @ SY1405 ) ) )
| ( SV638 @ SV748 @ SV785 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2368,plain,
! [SV639: $i,SV394: $i,SV84: $i] :
( ( ( func @ SV84 @ SV394 @ SV639 )
= $false )
| ( ( ! [SY1406: $i] :
( ~ ( in @ SY1406 @ SV84 )
| ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1407: $i] : ( in @ ( kpair @ SY1406 @ SY1407 ) @ SV639 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2369,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) ) )
= $false )
| ( ( ~ ( in @ SV640 @ SV85 )
| ( in @ SV640 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2069]) ).
thf(2370,plain,
! [SV397: $i,SV87: $i,SV641: $i] :
( ( ( in @ SV641 @ SV87 )
= $false )
| ( ( ~ ~ ( in @ SV641 @ SV397 )
| ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2371,plain,
! [SV399: $i,SV642: $i > $i,SV89: $i] :
( ( ( ! [SY1408: $i] :
( ~ ( in @ SY1408 @ SV89 )
| ( in @ ( SV642 @ SY1408 ) @ SV399 ) ) )
= $false )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2072]) ).
thf(2372,plain,
! [SV401: $i,SV91: $i,SV643: $i] :
( ( ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) )
= $false )
| ( ( ! [SY1411: $i] :
( ~ ( in @ SY1411 @ SV91 )
| ( in @ ( kpair @ SY1411 @ ( ap @ SV91 @ SV401 @ SV643 @ SY1411 ) ) @ SV643 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2074]) ).
thf(2373,plain,
! [SV402: $i,SV786: $i,SV93: $i] :
( ( ( ~ ( breln1 @ SV93 @ SV786 )
| ! [SY1595: $i] :
( ~ ( in @ SY1595 @ SV93 )
| ! [SY1596: $i] :
( ~ ( in @ SY1596 @ SV93 )
| ~ ( in @ ( kpair @ SY1595 @ SY1596 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV402 )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV786 ) ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2374,plain,
! [SV403: $o,SV94: $i,SV644: $i] :
( ( ( in @ SV644 @ SV94 )
= $false )
| ( ( ! [SY1412: $i] :
( ~ ( in @ SY1412 @ SV94 )
| ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1413: $i] :
( ~ ( ~ SV403
| ( SY1413 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1413 != SY1412 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2375,plain,
! [SV94: $i,SV645: $i] :
( ( ( in @ SV645 @ SV94 )
= $false )
| ( ( ! [SY1414: $i] :
( ~ ( in @ SY1414 @ SV94 )
| ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1415: $i] :
( ~ ( ~ $true
| ( SY1415 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1415 != SY1414 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2376,plain,
! [SV94: $i,SV646: $i] :
( ( ( in @ SV646 @ SV94 )
= $false )
| ( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV94 )
| ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1417: $i] :
( ~ ( ~ $false
| ( SY1417 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1417 != SY1416 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2377,plain,
! [SV404: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK12_SY994 @ SV95 @ SV404 ) @ SV404 )
| ( in @ ( sK12_SY994 @ SV95 @ SV404 ) @ SV95 ) )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2079]) ).
thf(2378,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false )
| ( ( ! [SY1418: $o] :
( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SY1418 )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SY1418 )
| SY1418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2379,plain,
! [SV407: $i,SV98: $i,SV648: $i] :
( ( ( in @ SV648 @ ( setminus @ SV98 @ SV407 ) )
= $false )
| ( ( in @ SV648 @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2380,plain,
! [SV408: $i,SV787: $i,SV99: $i] :
( ( ( ~ ( breln1 @ SV99 @ SV787 )
| ! [SY1597: $i] :
( ~ ( in @ SY1597 @ SV99 )
| ! [SY1598: $i] :
( ~ ( in @ SY1598 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1598 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1599: $o] :
( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1600 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1600 @ SY1598 ) @ SV787 )
| SY1599 )
| SY1599 ) ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2381,plain,
! [SV749: $i,SV649: $i,SV410: $i,SV102: $i] :
( ( ( ( kpair @ SV102 @ SV410 )
!= ( kpair @ SV649 @ SV749 ) )
= $true )
| ( ( SV410 = SV749 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2382,plain,
! [SV104: $i,SV412: $i] :
( ( ( in @ SV412 @ SV104 )
= $false )
| ( ( in @ SV104 @ SV412 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2086]) ).
thf(2383,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1601: $i] :
( ( ( sK13_SY1008 @ SV415 @ SV107 )
!= SY1601 )
| ~ ( ~ ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ SY1601 ) )
| ~ ( ~ ( SV415 @ SY1601 )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2087]) ).
thf(2384,plain,
! [SV416: $i,SV108: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ ( powerset @ SV108 ) )
| ! [SY1602: $i] :
( ~ ( in @ SY1602 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SY1602 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SY1602 ) ) ) )
= $true )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2088]) ).
thf(2385,plain,
! [SV417: $i,SV109: $i,SV651: $i] :
( ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( ! [SY1422: $i] :
( ~ ( in @ SY1422 @ ( funcSet @ SV109 @ SV417 ) )
| ~ ! [SY1423: $i] :
( ~ ( in @ SY1423 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1423 )
= ( ap @ SV109 @ SV417 @ SY1422 @ SY1423 ) ) )
| ( SV651 = SY1422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2386,plain,
! [SV418: $i,SV110: $i,SV652: $i] :
( ( ( in @ SV652 @ ( cartprod @ SV110 @ SV418 ) )
= $false )
| ( ( iskpair @ SV652 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2090]) ).
thf(2387,plain,
! [SV419: $i,SV111: $i,SV653: $i] :
( ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false )
| ( ( ~ ! [SY1424: $i] :
~ ~ ( ~ ( in @ SY1424 @ SV111 )
| ~ ~ ! [SY1425: $i] :
~ ~ ( ~ ( in @ SY1425 @ SV419 )
| ( SV653
!= ( kpair @ SY1424 @ SY1425 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2091]) ).
thf(2388,plain,
! [SV113: $i] :
( ( ( ! [SY275: $i] :
~ ~ ( ~ ( in @ SY275 @ SV113 )
| ( ( binintersect @ SY275 @ SV113 )
!= emptyset ) ) )
= $false )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2092]) ).
thf(2389,plain,
! [SV422: $i,SV115: $i,SV654: $i] :
( ( ( in @ ( setadjoin @ SV654 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV422 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV115 = SV654 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2094]) ).
thf(2390,plain,
! [SV423: $i,SV116: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ ( powerset @ SV116 ) )
| ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SV789 ) ) ) )
= $true )
| ( ( in @ SV423 @ ( powerset @ SV116 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2391,plain,
! [SV424: $i,SV117: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ ( powerset @ SV117 ) )
| ! [SY1603: $i] :
( ~ ( in @ SY1603 @ ( powerset @ SV117 ) )
| ! [SY1604: $i] :
( ~ ( in @ SY1604 @ SV117 )
| ~ ( in @ SY1604 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1604 @ ( binintersect @ ( binunion @ SV424 @ SY1603 ) @ ( binunion @ SV790 @ SY1603 ) ) ) ) ) )
= $true )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2392,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
| ! [SY1605: $i] :
( ~ ( in @ SY1605 @ SV118 )
| ~ ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
| ~ ( SV425 @ SY1605 )
| ( ( sK14_SY1032 @ SV425 @ SV118 )
= SY1605 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2097]) ).
thf(2393,plain,
! [SV119: $i,SV426: $i > $i] :
( ( ! [SY1554: $i] :
~ ( ~ ( ~ ( in @ SY1554 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1038: $i] :
~ ~ ( ~ ( in @ SY1038 @ SV119 )
| ( SY1554
!= ( SV426 @ SY1038 ) ) ) )
| ~ ( ~ ~ ! [SY1039: $i] :
~ ~ ( ~ ( in @ SY1039 @ SV119 )
| ( SY1554
!= ( SV426 @ SY1039 ) ) )
| ( in @ SY1554 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2098]) ).
thf(2394,plain,
! [SV655: $i,SV427: $i,SV120: $i] :
( ( ( func @ SV120 @ SV427 @ SV655 )
= $false )
| ( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1427: $i] : ( in @ ( kpair @ SY1426 @ SY1427 ) @ SV655 ) ) )
@ SV427 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2395,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) )
| ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) ) )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2100]) ).
thf(2396,plain,
! [SV122: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK16_SY1044 @ SV429 @ SV122 ) @ SV122 )
| ( in @ ( sK16_SY1044 @ SV429 @ SV122 ) @ SV429 ) )
= $false )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2101]) ).
thf(2397,plain,
! [SV750: $i] :
( ( ( ~ ( in @ SV750 @ sK1_X ) )
= $true )
| ( ( subset @ SV750 @ sK1_X )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2398,plain,
( ( ~ ( in @ sK2_SY0 @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2399,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2103]) ).
thf(2400,plain,
! [SV431: $i,SV656: $i > $i,SV124: $i] :
( ( ( ! [SY1428: $i] :
( ~ ( in @ SY1428 @ SV124 )
| ( in @ ( SV656 @ SY1428 ) @ SV431 ) ) )
= $false )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2105]) ).
thf(2401,plain,
! [SV432: $o,SV125: $i,SV657: $i] :
( ( ( in @ SV657 @ SV125 )
= $false )
| ( ( ! [SY1430: $i] :
( ~ ( in @ SY1430 @ SV125 )
| ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1431: $i] :
( ~ ( ~ SV432
| ( SY1431 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1431 != SY1430 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2402,plain,
! [SV125: $i,SV658: $i] :
( ( ( in @ SV658 @ SV125 )
= $false )
| ( ( ! [SY1432: $i] :
( ~ ( in @ SY1432 @ SV125 )
| ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1433: $i] :
( ~ ( ~ $true
| ( SY1433 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1433 != SY1432 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2403,plain,
! [SV125: $i,SV659: $i] :
( ( ( in @ SV659 @ SV125 )
= $false )
| ( ( ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SV125 )
| ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1435: $i] :
( ~ ( ~ $false
| ( SY1435 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1435 != SY1434 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2404,plain,
! [SV791: $o,SV126: $i,SV433: $i] :
( ( ( ~ ! [SY1606: $i] :
( ~ ( in @ SV433 @ SY1606 )
| ~ ( in @ SY1606 @ SV126 )
| SV791 )
| SV791 )
= $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2109]) ).
thf(2405,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $true )
| $true )
= $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2109]) ).
thf(2406,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $false )
| $false )
= $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2109]) ).
thf(2407,plain,
! [SV434: $i,SV127: $i,SV660: $i] :
( ( ( in @ SV660 @ ( cartprod @ SV127 @ SV434 ) )
= $false )
| ( ( in @ ( ksnd @ SV660 ) @ SV434 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2408,plain,
! [SV435: $i,SV792: $i,SV128: $i] :
( ( ( ~ ( breln1 @ SV128 @ SV792 )
| ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SV792 ) ) )
= $true )
| ( ( breln1 @ SV128 @ SV435 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2409,plain,
! [SV436: $i,SV661: $i,SV129: $i] :
( ( ( subset @ SV129 @ SV661 )
= $false )
| ( ( subset @ SV129 @ ( setadjoin @ SV436 @ SV661 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2112]) ).
thf(2410,plain,
! [SV438: $i,SV131: $i,SV662: $i] :
( ( ( in @ SV662 @ SV131 )
= $false )
| ( ( ~ ~ ( in @ SV662 @ SV438 )
| ~ ( subset @ SV131 @ SV438 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2411,plain,
! [SV751: $i,SV663: $i,SV439: $i,SV132: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SV751 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV663 != SV751 )
| ( SV439 = SV751 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2114]) ).
thf(2412,plain,
! [SV440: $i,SV133: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( powerset @ SV133 ) )
| ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV133 )
| ~ ( in @ SY1607 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SY1607 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) ) )
= $true )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2413,plain,
! [SV441: $i,SV134: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( powerset @ SV134 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ ( powerset @ SV134 ) )
| ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1608 )
| ~ ( subset @ SV794 @ SY1609 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SY1608 @ SY1609 ) ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2414,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ~ ( ~ ( SV136 @ SV795 )
| ~ ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2415,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ~ ( ~ ( SV138 @ SV796 )
| ~ ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2416,plain,
! [SV664: $i,SV444: $i,SV139: $i] :
( ( ( func @ SV139 @ SV444 @ SV664 )
= $false )
| ( ( ! [SY1437: $i] :
( ~ ( func @ SV139 @ SV444 @ SY1437 )
| ~ ! [SY1438: $i] :
( ~ ( in @ SY1438 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1438 )
= ( ap @ SV139 @ SV444 @ SY1437 @ SY1438 ) ) )
| ( SV664 = SY1437 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2417,plain,
! [SV140: $i,SV445: $i > $i] :
( ( ~ ( ~ ! [SY1557: $i] :
~ ( ~ ( ~ ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) )
| ~ ! [SY1560: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1560 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1560 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SY1560 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2121]) ).
thf(2418,plain,
! [SV665: $i > $i > $o,SV446: $i,SV141: $i,SV797: $i,SV752: $i] :
( ( ~ ( in @ ( kpair @ SV752 @ SV797 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SY1441: $i,SY1442: $i] : ( SV665 @ SY1441 @ SY1442 ) ) )
| ( in @ SV752 @ SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2419,plain,
! [SV447: $i,SV142: $i,SV753: $i,SV666: $i] :
( ( ( ~ ( in @ ( kpair @ SV666 @ SV753 ) @ ( cartprod @ SV142 @ SV447 ) ) )
= $true )
| ( ( in @ SV666 @ SV142 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2123]) ).
thf(2420,plain,
! [SV448: $i,SV143: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ ( powerset @ SV143 ) )
| ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( powerset @ SV143 ) )
| ~ ( subset @ SV798 @ SY1614 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SY1614 ) ) )
= $true )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2421,plain,
! [SV449: $i > $o,SV144: $i] :
( ( ( ! [SY1085: $i] :
~ ~ ( ~ ( in @ SY1085 @ SV144 )
| ~ ( SV449 @ SY1085 ) ) )
= $false )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2422,plain,
! [SV145: $i,SV450: $i] :
( ( ( ~ ( in @ ( sK17_SY1086 @ SV450 @ SV145 ) @ SV145 )
| ( in @ ( sK17_SY1086 @ SV450 @ SV145 ) @ SV450 ) )
= $false )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2126]) ).
thf(2423,plain,
! [SV799: $i > $o,SV451: $i,SV146: $i] :
( ( ( ~ ! [SY1615: $i] :
( ~ ( in @ SY1615 @ SV146 )
| ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV146 )
| ~ ( in @ ( kpair @ SY1615 @ SY1616 ) @ SV451 )
| ( SV799 @ ( kpair @ SY1615 @ SY1616 ) ) ) )
| ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2424,plain,
! [SV453: $i > $i,SV148: $i,SV667: $i] :
( ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false )
| ( ( ~ ! [SY1445: $i] :
~ ~ ( ~ ( in @ SY1445 @ SV148 )
| ( SV667
!= ( SV453 @ SY1445 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2425,plain,
! [SV454: $i,SV149: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ ( powerset @ SV149 ) )
| ~ ! [SY1618: $i] :
( ~ ( in @ SY1618 @ SV149 )
| ~ ( in @ SY1618 @ SV454 )
| ( in @ SY1618 @ SV800 ) )
| ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2426,plain,
! [SV455: $i,SV150: $i,SV668: $i] :
( ( ( in @ SV668 @ ( injFuncSet @ SV150 @ SV455 ) )
= $false )
| ( ( injective @ SV150 @ SV455 @ SV668 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2131]) ).
thf(2427,plain,
! [SV458: $i > $o,SV153: $i] :
( ( ( ! [SY1099: $i] :
~ ~ ( ~ ( in @ SY1099 @ SV153 )
| ~ ( SV458 @ SY1099 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2133]) ).
thf(2428,plain,
! [SV459: $i,SV801: $i,SV154: $i] :
( ( ( ~ ( breln1 @ SV154 @ SV801 )
| ! [SY1620: $i] :
( ~ ( breln1 @ SV154 @ SY1620 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SY1620 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2429,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ~ ( ~ ( SV155 @ SV802 )
| ~ ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2430,plain,
! [SV803: $i > $o,SV460: $i,SV156: $i] :
( ( ( ~ ! [SY1622: $i] :
( ~ ( in @ SY1622 @ SV156 )
| ! [SY1623: $i] :
( ~ ( in @ SY1623 @ SV156 )
| ~ ( in @ ( kpair @ SY1622 @ SY1623 ) @ SV460 )
| ( SV803 @ ( kpair @ SY1622 @ SY1623 ) ) ) )
| ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2431,plain,
! [SV461: $i,SV157: $i,SV669: $i] :
( ( ( in @ SV669 @ SV157 )
= $false )
| ( ( ! [SY1446: $i] :
( ~ ( in @ SY1446 @ SV461 )
| ( in @ ( kpair @ SV669 @ SY1446 ) @ ( cartprod @ SV157 @ SV461 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2137]) ).
thf(2432,plain,
! [SV462: $o,SV158: $i,SV670: $i] :
( ( ( in @ SV670 @ SV158 )
= $false )
| ( ( ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SV158 )
| ~ ~ SV462
| ( in @ SY1447
@ ( dsetconstr @ SV158
@ ^ [SY1448: $i] :
( ~ ( ~ SV462
| ( SY1448 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1448 != SY1447 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2138]) ).
thf(2433,plain,
! [SV158: $i,SV671: $i] :
( ( ( in @ SV671 @ SV158 )
= $false )
| ( ( ! [SY1449: $i] :
( ~ ( in @ SY1449 @ SV158 )
| ~ ~ $true
| ( in @ SY1449
@ ( dsetconstr @ SV158
@ ^ [SY1450: $i] :
( ~ ( ~ $true
| ( SY1450 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1450 != SY1449 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2139]) ).
thf(2434,plain,
! [SV158: $i,SV672: $i] :
( ( ( in @ SV672 @ SV158 )
= $false )
| ( ( ! [SY1451: $i] :
( ~ ( in @ SY1451 @ SV158 )
| ~ ~ $false
| ( in @ SY1451
@ ( dsetconstr @ SV158
@ ^ [SY1452: $i] :
( ~ ( ~ $false
| ( SY1452 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1452 != SY1451 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2140]) ).
thf(2435,plain,
! [SV673: $i,SV159: $i,SV463: $i] :
( ( ( in @ SV463 @ ( powerset @ SV159 ) )
= $false )
| ( ( ~ ( in @ SV673 @ SV463 )
| ( in @ SV673 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2141]) ).
thf(2436,plain,
! [SV464: $i,SV160: $i,SV674: $i] :
( ( ( in @ SV674 @ SV160 )
= $false )
| ( ( ~ ~ ( in @ SV674 @ SV464 )
| ( SV160 != SV464 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2142]) ).
thf(2437,plain,
! [SV675: $i,SV465: $i,SV161: $i] :
( ( ( subset @ SV161 @ SV465 )
= $false )
| ( ( ~ ( subset @ SV465 @ SV675 )
| ( subset @ SV161 @ SV675 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2143]) ).
thf(2438,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV163 )
| ~ ~ ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SV804 @ SV467 ) )
= $true )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2439,plain,
! [SV468: $i,SV164: $i,SV676: $i] :
( ( ( in @ SV676 @ SV164 )
= $false )
| ( ( ~ ~ ( in @ SV676 @ SV468 )
| ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2146]) ).
thf(2440,plain,
! [SV469: $i > $o,SV165: $i,SV677: $i] :
( ( ( in @ SV677 @ SV165 )
= $false )
| ( ( ~ ( SV469 @ SV677 )
| ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2147]) ).
thf(2441,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV805 ) )
= $true )
| ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2442,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ~ ( ~ ( SV167 @ SV806 )
| ~ ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2443,plain,
! [SV678: $i,SV470: $i,SV168: $i] :
( ( ( breln @ SV168 @ SV470 @ SV678 )
= $false )
| ( ( ! [SY1454: $i] :
( ~ ( breln @ SV168 @ SV470 @ SY1454 )
| ~ ! [SY1455: $i] :
( ~ ( in @ SY1455 @ SV168 )
| ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV470 )
| ~ ( in @ ( kpair @ SY1455 @ SY1456 ) @ SV678 )
| ( in @ ( kpair @ SY1455 @ SY1456 ) @ SY1454 ) ) )
| ~ ! [SY1457: $i] :
( ~ ( in @ SY1457 @ SV168 )
| ! [SY1458: $i] :
( ~ ( in @ SY1458 @ SV470 )
| ~ ( in @ ( kpair @ SY1457 @ SY1458 ) @ SY1454 )
| ( in @ ( kpair @ SY1457 @ SY1458 ) @ SV678 ) ) )
| ( SV678 = SY1454 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2444,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ~ ( ~ ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
| ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2445,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ~ ( ~ ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) )
| ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2151]) ).
thf(2446,plain,
! [SV473: $i,SV171: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ ( powerset @ SV171 ) )
| ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV171 )
| ~ ~ ( in @ SY1626 @ SV807 )
| ~ ( in @ SY1626 @ ( binintersect @ SV473 @ SV807 ) ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2447,plain,
! [SV474: $i,SV680: $i > $i,SV172: $i] :
( ( ( ! [SY1463: $i] :
( ~ ( in @ SY1463 @ SV172 )
| ( in @ ( SV680 @ SY1463 ) @ SV474 ) ) )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2153]) ).
thf(2448,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ! [SY1627: $i] :
~ ( ~ ( ~ ( SV174 @ SY1627 )
| ( SY1627 = SV808 ) )
| ~ ( ( SY1627 != SV808 )
| ( SV174 @ SY1627 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2449,plain,
! [SV475: $i,SV175: $i,SV809: $i] :
( ( ( ! [SY1628: $i] :
( ( SV809 != SY1628 )
| ( ( setadjoin @ SV175 @ SV809 )
= ( setadjoin @ SV475 @ SY1628 ) ) ) )
= $true )
| ( ( SV175 = SV475 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2450,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( in @ SV681 @ SV176 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) )
| ~ ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2451,plain,
! [SV477: $i,SV177: $i,SV682: $i] :
( ( ( in @ SV682 @ SV177 )
= $false )
| ( ( in @ SV682 @ ( binunion @ SV177 @ SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2157]) ).
thf(2452,plain,
! [SV478: $i,SV178: $i] :
( ( ( ! [SY1142: $i] :
~ ~ ( ~ ( in @ SY1142 @ SV178 )
| ~ ( in @ SV478 @ SY1142 ) ) )
= $false )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2453,plain,
! [SV479: $i,SV179: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ ( powerset @ SV179 ) )
| ! [SY1629: $i] :
( ~ ( in @ SY1629 @ ( powerset @ SV179 ) )
| ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV179 )
| ~ ( in @ SY1630 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1630 @ ( binunion @ SV810 @ SY1629 ) ) ) ) )
= $true )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2454,plain,
! [SV480: $o,SV181: $i,SV683: $i] :
( ( ( in @ SV683 @ SV181 )
= $false )
| ( ( ! [SY1468: $i] :
( ~ ( in @ SY1468 @ SV181 )
| ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SY1468 )
= SV683 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2455,plain,
! [SV181: $i,SV684: $i] :
( ( ( in @ SV684 @ SV181 )
= $false )
| ( ( ! [SY1469: $i] :
( ~ ( in @ SY1469 @ SV181 )
| ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SY1469 )
= SV684 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2161]) ).
thf(2456,plain,
! [SV181: $i,SV685: $i] :
( ( ( in @ SV685 @ SV181 )
= $false )
| ( ( ! [SY1470: $i] :
( ~ ( in @ SY1470 @ SV181 )
| ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SY1470 )
= SV685 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2457,plain,
! [SV481: $i,SV182: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV182 ) )
= $false )
| ( ( ~ ( in @ SV686 @ SV481 )
| ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2458,plain,
! [SV687: $i,SV482: $i,SV183: $i] :
( ( ( breln @ SV183 @ SV482 @ SV687 )
= $false )
| ( ( ! [SY1471: $i > $o] :
( ~ ! [SY1472: $i] :
( ~ ( in @ SY1472 @ SV183 )
| ! [SY1473: $i] :
( ~ ( in @ SY1473 @ SV482 )
| ~ ( in @ ( kpair @ SY1472 @ SY1473 ) @ SV687 )
| ( SY1471 @ ( kpair @ SY1472 @ SY1473 ) ) ) )
| ! [SY1474: $i] :
( ~ ( in @ SY1474 @ SV687 )
| ( SY1471 @ SY1474 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2164]) ).
thf(2459,plain,
! [SV688: $i,SV483: $i,SV184: $i] :
( ( ( subset @ SV184 @ SV483 )
= $false )
| ( ( ~ ~ ( in @ SV688 @ SV483 )
| ~ ( in @ SV688 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2460,plain,
! [SV185: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ SV185 ) )
= $true )
| ( ( SV185 = SV484 )
= $true )
| ( ( subset @ SV185 @ SV484 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2461,plain,
! [SV485: $i,SV186: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ ( powerset @ SV186 ) )
| ( in @ ( binunion @ SV485 @ SV811 ) @ ( powerset @ SV186 ) ) )
= $true )
| ( ( in @ SV485 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2462,plain,
! [SV486: $i,SV188: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( powerset @ SV188 ) )
| ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV188 )
| ~ ( in @ SY1631 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SY1631 @ ( setminus @ SV188 @ SV486 ) ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2463,plain,
! [SV487: $i > $o,SV189: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV189 )
| ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV189 )
| ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SY1632 )
| ( SV813 = SY1632 ) ) )
= $true )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2464,plain,
! [SV488: $o,SV190: $i,SV689: $i] :
( ( ( in @ SV689 @ SV190 )
= $false )
| ( ( ! [SY1475: $i] :
( ~ ( in @ SY1475 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1476: $i] :
( ~ ( ~ SV488
| ( SY1476 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1476 != SY1475 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2465,plain,
! [SV190: $i,SV690: $i] :
( ( ( in @ SV690 @ SV190 )
= $false )
| ( ( ! [SY1477: $i] :
( ~ ( in @ SY1477 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1478: $i] :
( ~ ( ~ $true
| ( SY1478 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1478 != SY1477 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2171]) ).
thf(2466,plain,
! [SV190: $i,SV691: $i] :
( ( ( in @ SV691 @ SV190 )
= $false )
| ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1480: $i] :
( ~ ( ~ $false
| ( SY1480 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1480 != SY1479 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2467,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
| ~ ! [SY1633: $i] :
~ ~ ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1633 )
| ~ ! [SY1634: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1634 )
| ( SY1633 = SY1634 ) ) ) )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2173]) ).
thf(2468,plain,
! [SV490: $i,SV192: $i] :
( ( ( subset @ SV192 @ SV490 )
= $true )
| ( ( SV192 != SV490 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2174]) ).
thf(2469,plain,
! [SV492: $i,SV194: $i,SV692: $i] :
( ( ( in @ SV692 @ ( surjFuncSet @ SV194 @ SV492 ) )
= $false )
| ( ( surjective @ SV194 @ SV492 @ SV692 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2176]) ).
thf(2470,plain,
! [SV494: $i,SV196: $i,SV693: $i] :
( ( ( in @ SV693 @ SV196 )
= $false )
| ( ( in @ ( setadjoin @ SV693 @ emptyset ) @ ( powerset @ ( binunion @ SV196 @ SV494 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2471,plain,
! [SV496: $i,SV198: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ ( powerset @ SV198 ) )
| ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV198 )
| ~ ( in @ SY1635 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SY1635 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) ) )
= $true )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2472,plain,
! [SV497: $i,SV199: $i,SV694: $i] :
( ( ( in @ SV694 @ ( funcSet @ SV199 @ SV497 ) )
= $false )
| ( ( ~ ( injective @ SV199 @ SV497 @ SV694 )
| ( in @ SV694 @ ( injFuncSet @ SV199 @ SV497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2473,plain,
! [SV200: $i] :
( ( ( ~ ( in @ ( sK9_SY527 @ SV200 ) @ SV200 ) )
= $false )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2474,plain,
! [SV200: $i] :
( ( ( subset @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $false )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2181]) ).
thf(2475,plain,
! [SV499: $i,SV695: $i > $i,SV202: $i] :
( ( ( ! [SY1481: $i] :
( ~ ( in @ SY1481 @ SV202 )
| ( in @ ( SV695 @ SY1481 ) @ SV499 ) ) )
= $false )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2182]) ).
thf(2476,plain,
! [SV204: $i,SV754: $i] :
( ( ( ~ ( in @ SV754 @ SV204 ) )
= $true )
| ( ( ( setunion @ SV204 )
= SV754 )
= $true )
| ( ( singleton @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2183]) ).
thf(2477,plain,
! [SV500: $i,SV205: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV205 )
| ~ ( in @ SV815 @ SV500 )
| ( in @ SV815 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2478,plain,
! [SV502: $i > $o,SV207: $i,SV696: $i] :
( ( ( in @ SV696 @ SV207 )
= $false )
| ( ( ~ ( SV502 @ SV696 )
| ( in @ SV696
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2185]) ).
thf(2479,plain,
! [SV697: $i > $i > $o,SV503: $i,SV208: $i,SV816: $i,SV755: $i] :
( ( ~ ( in @ ( kpair @ SV755 @ SV816 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SY1487: $i,SY1488: $i] : ( SV697 @ SY1487 @ SY1488 ) ) )
| ( in @ SV816 @ SV503 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2480,plain,
! [SV504: $i,SV817: $i,SV209: $i] :
( ( ( ~ ( breln1 @ SV209 @ SV817 )
| ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV209 )
| ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV209 )
| ~ ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV504 )
| ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV817 ) ) )
| ( subset @ SV504 @ SV817 ) )
= $true )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2481,plain,
! [SV506: $i,SV211: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ ( powerset @ SV211 ) )
| ! [SY1640: $i] :
( ~ ( in @ SY1640 @ ( powerset @ SV211 ) )
| ! [SY1641: $i] :
( ~ ( in @ SY1641 @ SV211 )
| ~ ( in @ SY1641 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1641 @ ( binunion @ SV506 @ SY1640 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2482,plain,
! [SV212: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
| ~ ! [SY1498: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY1498 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1498 ) )
| ~ ! [SY1501: $i] :
~ ~ ! [SY1502: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1501 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1502 @ SY1498 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1501 )
| ~ ( in @ SX5 @ SY1498 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1501 ) )
| ( in @ SY1502 @ SY1504 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2483,plain,
! [SV507: $i,SV213: $i,SV698: $i] :
( ( ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) )
= $false )
| ( ( ! [SY1506: $i] :
( ~ ( in @ SY1506 @ SV213 )
| ( ( ap @ SV213 @ SV507 @ SV698 @ SY1506 )
= ( ap @ SV213 @ SV507 @ SV698 @ SY1506 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2191]) ).
thf(2484,plain,
! [SV508: $o,SV214: $i,SV699: $i] :
( ( ( in @ SV699 @ SV214 )
= $false )
| ( ( ! [SY1507: $i] :
( ~ ( in @ SY1507 @ SV214 )
| ( in @ ( if @ SV214 @ SV508 @ SV699 @ SY1507 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SY1507 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2485,plain,
! [SV214: $i,SV700: $i] :
( ( ( in @ SV700 @ SV214 )
= $false )
| ( ( ! [SY1508: $i] :
( ~ ( in @ SY1508 @ SV214 )
| ( in @ ( if @ SV214 @ $true @ SV700 @ SY1508 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SY1508 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2486,plain,
! [SV214: $i,SV701: $i] :
( ( ( in @ SV701 @ SV214 )
= $false )
| ( ( ! [SY1509: $i] :
( ~ ( in @ SY1509 @ SV214 )
| ( in @ ( if @ SV214 @ $false @ SV701 @ SY1509 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SY1509 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2487,plain,
! [SV702: $i > $i > $o,SV509: $i,SV215: $i] :
( ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV215 )
| ~ ! [SY1511: $i] :
~ ~ ( ~ ( in @ SY1511 @ SV509 )
| ~ ( SV702 @ SY1510 @ SY1511 ) ) ) )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2195]) ).
thf(2488,plain,
! [SV512: $i,SV220: $i,SV703: $i] :
( ( ( in @ SV703 @ ( cartprod @ SV220 @ SV512 ) )
= $false )
| ( ( in @ ( kfst @ SV703 ) @ SV220 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2198]) ).
thf(2489,plain,
! [SV704: $i,SV514: $i,SV222: $i] :
( ( ( ( setadjoin @ SV222 @ ( setadjoin @ SV514 @ emptyset ) )
= ( setadjoin @ SV704 @ emptyset ) )
= $false )
| ( ( SV222 = SV514 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2200]) ).
thf(2490,plain,
! [SV705: $i,SV516: $i,SV225: $i] :
( ( ( func @ SV225 @ SV516 @ SV705 )
= $false )
| ( ( ! [SY1516: $i] :
( ~ ( in @ SY1516 @ SV225 )
| ! [SY1517: $i] :
( ~ ( in @ SY1517 @ SV516 )
| ~ ( in @ ( kpair @ SY1516 @ SY1517 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SY1516 )
= SY1517 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2201]) ).
thf(2491,plain,
! [SV226: $i] :
( ( ( ~ ( in @ emptyset @ SV226 ) )
= $true )
| ( ( ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) )
= $true )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2492,plain,
! [SV517: $i,SV227: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ ( powerset @ SV227 ) )
| ~ ( subset @ SV517 @ ( setminus @ SV227 @ SV819 ) )
| ( subset @ SV819 @ ( setminus @ SV227 @ SV517 ) ) )
= $true )
| ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2203]) ).
thf(2493,plain,
! [SV228: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV228 ) )
= $true )
| ( ( SV228 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2494,plain,
! [SV518: $i,SV229: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ ( powerset @ SV229 ) )
| ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SV821 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) ) )
= $true )
| ( ( in @ SV518 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2495,plain,
! [SV230: $i,SV519: $i] :
( ( ( ~ ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
| ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 ) )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2206]) ).
thf(2496,plain,
! [SV521: $i > $o,SV232: $i] :
( ( ( ! [SY1214: $i] :
( ~ ( in @ SY1214 @ SV232 )
| ( SV521 @ SY1214 ) ) )
= $true )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2208]) ).
thf(2497,plain,
! [SV522: $i,SV233: $i,SV706: $i] :
( ( ( in @ SV706 @ ( funcSet @ SV233 @ SV522 ) )
= $false )
| ( ( func @ SV233 @ SV522 @ SV706 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2498,plain,
! [SV523: $i,SV822: $i,SV234: $i] :
( ( ( ~ ( breln1 @ SV234 @ SV822 )
| ! [SY1642: $i] :
( ~ ( in @ SY1642 @ SV234 )
| ! [SY1643: $i] :
( ~ ( in @ SY1643 @ SV234 )
| ! [SY1644: $i] :
( ~ ( in @ SY1644 @ SV234 )
| ~ ( in @ ( kpair @ SY1642 @ SY1644 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1644 @ SY1643 ) @ SV822 )
| ( in @ ( kpair @ SY1642 @ SY1643 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2499,plain,
! [SV524: $i,SV235: $i] :
( ( ( ~ ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV235 )
| ~ ( in @ SY1221 @ SV524 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2211]) ).
thf(2500,plain,
! [SV525: $i,SV236: $i,SV707: $i] :
( ( ( in @ SV707 @ SV236 )
= $false )
| ( ( ~ ( in @ SV707 @ SV525 )
| ( in @ SV707 @ ( binintersect @ SV236 @ SV525 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2212]) ).
thf(2501,plain,
! [SV756: $i,SV708: $i,SV526: $i,SV237: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SV526 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV708 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV708 @ ( setadjoin @ SV756 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV237 = SV708 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2502,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i,SV757: $i] :
( ( ( ~ ( in @ SV757 @ SV238 ) )
= $true )
| ( ( ! [SY1570: $i] :
( ~ ( in @ SY1570 @ SV527 )
| ~ ( in @ ( kpair @ SV757 @ SY1570 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SY1570 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2214]) ).
thf(2503,plain,
! [SV528: $i,SV239: $i,SV710: $i] :
( ( ( in @ SV710 @ SV239 )
= $false )
| ( ( ! [SY1523: $i] :
( ~ ( in @ SY1523 @ SV528 )
| ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SY1523 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2504,plain,
! [SV529: $i,SV240: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( powerset @ SV240 ) )
| ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SV823 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2505,plain,
! [SV530: $o,SV241: $i,SV711: $i] :
( ( ( in @ SV711 @ SV241 )
= $false )
| ( ( ! [SY1524: $i] :
( ~ ( in @ SY1524 @ SV241 )
| ( in @ ( if @ SV241 @ SV530 @ SV711 @ SY1524 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2217]) ).
thf(2506,plain,
! [SV241: $i,SV712: $i] :
( ( ( in @ SV712 @ SV241 )
= $false )
| ( ( ! [SY1525: $i] :
( ~ ( in @ SY1525 @ SV241 )
| ( in @ ( if @ SV241 @ $true @ SV712 @ SY1525 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2218]) ).
thf(2507,plain,
! [SV241: $i,SV713: $i] :
( ( ( in @ SV713 @ SV241 )
= $false )
| ( ( ! [SY1526: $i] :
( ~ ( in @ SY1526 @ SV241 )
| ( in @ ( if @ SV241 @ $false @ SV713 @ SY1526 ) @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2219]) ).
thf(2508,plain,
! [SV714: $i,SV532: $i,SV243: $i] :
( ( ( func @ SV243 @ SV532 @ SV714 )
= $false )
| ( ( ( lam @ SV243 @ SV532
@ ^ [SY1527: $i] : ( ap @ SV243 @ SV532 @ SV714 @ SY1527 ) )
= SV714 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2220]) ).
thf(2509,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
| ! [SY1645: $i] :
( ~ ( in @ SY1645 @ SV245 )
| ~ ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
| ~ ( SV534 @ SY1645 )
| ( ( sK20_SY1240 @ SV534 @ SV245 )
= SY1645 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2221]) ).
thf(2510,plain,
! [SV758: $i,SV715: $i,SV535: $i,SV246: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SV535 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV715 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV715 @ ( setadjoin @ SV758 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV535 = SV758 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2222]) ).
thf(2511,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ( in @ SV537 @ ( powerset @ SV248 ) )
| ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2224]) ).
thf(2512,plain,
! [SV248: $i,SV537: $i] :
( ( ~ ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) )
| ( in @ SV537 @ ( powerset @ SV248 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2513,plain,
! [SV538: $i,SV250: $i,SV716: $i] :
( ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false )
| ( ( ! [SY1529: $i] :
( ~ ( in @ SY1529 @ SV250 )
| ! [SY1530: $i] :
( ~ ( in @ SY1530 @ SV538 )
| ~ ( in @ ( kpair @ SY1529 @ SY1530 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SY1529 )
= SY1530 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2514,plain,
! [SV539: $i,SV251: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ SV251 )
| ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV251 )
| ~ ( in @ ( kpair @ SV824 @ SY1646 ) @ SV539 )
| ( in @ ( kpair @ SY1646 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) )
= $true )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2515,plain,
! [SV540: $i,SV252: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV252 )
| ! [SY1647: $i] :
( ~ ( in @ SY1647 @ SV252 )
| ~ ( in @ ( kpair @ SY1647 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SY1647 ) @ SV540 ) ) )
= $true )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2516,plain,
! [SV544: $i,SV254: $i,SV717: $i] :
( ( ( in @ SV717 @ ( binintersect @ SV254 @ SV544 ) )
= $false )
| ( ( in @ SV717 @ SV254 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2232]) ).
thf(2517,plain,
! [SV545: $i,SV826: $i,SV255: $i] :
( ( ( ~ ( breln1 @ SV255 @ SV826 )
| ! [SY1648: $i] :
( ~ ( in @ SY1648 @ SV255 )
| ! [SY1649: $i] :
( ~ ( in @ SY1649 @ SV255 )
| ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1650: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV545 )
| SY1650 )
| ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV826 )
| SY1650 )
| SY1650 ) ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2233]) ).
thf(2518,plain,
! [SV256: $i,SV546: $i,SV718: $i] :
( ( ( in @ SV718 @ SV546 )
= $false )
| ( ( in @ SV718 @ ( setadjoin @ SV256 @ SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2519,plain,
! [SV547: $i,SV257: $i,SV719: $i] :
( ( ( in @ SV719 @ SV257 )
= $false )
| ( ( ! [SY1531: $i] :
( ~ ( in @ SY1531 @ SV547 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SY1531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2520,plain,
! [SV548: $i,SV258: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ ( powerset @ SV258 ) )
| ! [SY1651: $i] :
( ~ ( in @ SY1651 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1651 ) @ ( binunion @ SV827 @ SY1651 ) ) ) ) ) )
= $true )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2521,plain,
! [SV549: $i,SV259: $i,SV720: $i] :
( ( ( in @ SV720 @ ( surjFuncSet @ SV259 @ SV549 ) )
= $false )
| ( ( in @ SV720 @ ( funcSet @ SV259 @ SV549 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2522,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1652: $i] :
( ( ( sK21_SY1266 @ SV550 @ SV260 )
!= SY1652 )
| ~ ( ~ ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ SY1652 ) )
| ~ ( ~ ( SV550 @ SY1652 )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2238]) ).
thf(2523,plain,
! [SV551: $i,SV261: $i] :
( ( ( surjective @ SV261 @ ( powerset @ SV261 ) @ SV551 )
= $false )
| ( ( in @ SV551 @ ( funcSet @ SV261 @ ( powerset @ SV261 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2524,plain,
! [SV552: $i,SV263: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ ( powerset @ SV263 ) )
| ! [SY1653: $i] :
( ~ ( in @ SY1653 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1653 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SY1653 ) ) )
= $true )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2241]) ).
thf(2525,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV829 )
| ~ ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV264 )
| ! [SY1655: $i] :
( ~ ( in @ SY1655 @ SV264 )
| ~ ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV553 )
| ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV829 ) ) )
| ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2526,plain,
! [SV554: $i,SV265: $i,SV721: $i] :
( ( ( in @ SV721 @ SV265 )
= $false )
| ( ( ~ ( in @ SV721 @ SV554 )
| ~ ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2527,plain,
! [SV555: $i,SV266: $i,SV722: $i] :
( ( ( in @ SV722 @ ( cartprod @ SV266 @ SV555 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV722 ) @ ( ksnd @ SV722 ) )
= SV722 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2528,plain,
! [SV557: $i,SV268: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ SV268 )
| ~ ( in @ SV830 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SV830 @ SV557 ) )
= $true )
| ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2529,plain,
! [SV558: $i > $o,SV269: $i] :
( ( ( ! [SY1284: $i] :
~ ~ ( ~ ( in @ SY1284 @ SV269 )
| ~ ~ ( SV558 @ SY1284 ) ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2246]) ).
thf(2530,plain,
! [SV559: $i,SV270: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV723 @ SV559 )
| ~ ( in @ SV723 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2531,plain,
! [SV560: $i,SV271: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( powerset @ SV271 ) )
| ! [SY1658: $i] :
( ~ ( in @ SY1658 @ SV271 )
| ~ ( in @ SY1658 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SY1658 @ ( setminus @ SV271 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2248]) ).
thf(2532,plain,
! [SV272: $i] :
( ( ( in @ ( sK10_SY725 @ SV272 ) @ SV272 )
= $true )
| ( ( SV272 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2249]) ).
thf(2533,plain,
! [SV562: $i,SV832: $i,SV274: $i] :
( ( ( ~ ( breln1 @ SV274 @ SV832 )
| ! [SY1659: $i] :
( ~ ( in @ SY1659 @ SV274 )
| ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV274 )
| ~ ( in @ ( kpair @ SY1659 @ SY1660 ) @ SV562 )
| ( in @ ( kpair @ SY1659 @ SY1660 ) @ ( binunion @ SV562 @ SV832 ) ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2534,plain,
! [SV563: $i,SV275: $i,SV724: $i] :
( ( ( in @ SV724 @ ( binintersect @ SV275 @ SV563 ) )
= $false )
| ( ( in @ SV724 @ SV563 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2535,plain,
! [SV564: $i,SV276: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV276 ) )
= $false )
| ( ( ~ ~ ( in @ SV725 @ SV564 )
| ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2253]) ).
thf(2536,plain,
! [SV566: $i,SV278: $i,SV726: $i] :
( ( ( in @ SV726 @ SV278 )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( in @ SY1532 @ SV566 )
| ( ( kfst @ ( kpair @ SV726 @ SY1532 ) )
= SV726 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2254]) ).
thf(2537,plain,
! [SV280: $i,SV568: $i,SV727: $i] :
( ( ( in @ SV727 @ SV568 )
= $false )
| ( ( in @ SV727 @ ( binunion @ SV280 @ SV568 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2256]) ).
thf(2538,plain,
! [SV281: $i] :
( ( ( ! [SY742: $i] :
~ ~ ( ~ ( in @ SY742 @ SV281 )
| ~ $true ) )
= $false )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2539,plain,
! [SV833: $i > $o,SV569: $i,SV283: $i] :
( ( ( ! [SY1661: $i > $o] :
( ~ ! [SY1662: $i] :
( ~ ( in @ SY1662 @ SV283 )
| ! [SY1663: $i] :
( ~ ( in @ SY1663 @ SV569 )
| ( SY1662 != SY1663 )
| ~ ( ~ ( ~ ( SV833 @ SY1662 )
| ( SY1661 @ SY1663 ) )
| ~ ( ~ ( SY1661 @ SY1663 )
| ( SV833 @ SY1662 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SX4: $i] : ( SY1661 @ SX4 ) ) ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2258]) ).
thf(2540,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ~ ( ~ ( SV284 @ SV834 )
| ~ ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2259]) ).
thf(2541,plain,
! [SV570: $i,SV285: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( powerset @ SV285 ) )
| ! [SY1667: $i] :
( ~ ( in @ SY1667 @ SV285 )
| ~ ( in @ SY1667 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1667 @ ( binintersect @ SV570 @ SV835 ) ) ) )
= $true )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2542,plain,
! [SV571: $i > $o,SV286: $i,SV728: $i] :
( ( ( in @ SV728
@ ( dsetconstr @ SV286
@ ^ [SY1306: $i] : ( SV571 @ SY1306 ) ) )
= $false )
| ( ( SV571 @ SV728 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2543,plain,
! [SV759: $o,SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| SV759 )
| ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2544,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $true )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2545,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $false )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2546,plain,
! [SV573: $i,SV836: $i,SV288: $i] :
( ( ( ~ ( breln1 @ SV288 @ SV836 )
| ! [SY1668: $i] :
( ~ ( in @ SY1668 @ SV288 )
| ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV288 )
| ~ ( in @ ( kpair @ SY1668 @ SY1669 ) @ SV836 )
| ( in @ ( kpair @ SY1668 @ SY1669 ) @ ( binunion @ SV573 @ SV836 ) ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2547,plain,
! [SV576: $o,SV291: $i,SV731: $i] :
( ( ( in @ SV731 @ SV291 )
= $false )
| ( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV291 )
| ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SY1537 )
= SY1537 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2267]) ).
thf(2548,plain,
! [SV291: $i,SV732: $i] :
( ( ( in @ SV732 @ SV291 )
= $false )
| ( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV291 )
| ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SY1538 )
= SY1538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2268]) ).
thf(2549,plain,
! [SV291: $i,SV733: $i] :
( ( ( in @ SV733 @ SV291 )
= $false )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV291 )
| ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SY1539 )
= SY1539 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2550,plain,
! [SV578: $i,SV837: $i,SV294: $i] :
( ( ( ~ ( breln1 @ SV294 @ SV837 )
| ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SV837 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SV837 ) @ ( breln1invset @ SV294 @ SV578 ) ) ) )
= $true )
| ( ( breln1 @ SV294 @ SV578 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2551,plain,
! [SV580: $i,SV296: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( powerset @ SV296 ) )
| ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV296 )
| ~ ( in @ SY1670 @ SV580 )
| ( in @ SY1670 @ SV838 ) )
| ( in @ SV580 @ ( powerset @ SV838 ) ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2552,plain,
! [SV581: $i,SV839: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV839 )
| ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV297 )
| ! [SY1672: $i] :
( ~ ( in @ SY1672 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV581 )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV839 ) )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ ( binunion @ SV581 @ SV839 ) ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2553,plain,
! [SV734: $i,SV582: $i,SV298: $i] :
( ( ( breln @ SV298 @ SV582 @ SV734 )
= $false )
| ( ( ! [SY1540: $i] :
( ~ ( breln @ SV298 @ SV582 @ SY1540 )
| ~ ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV298 )
| ! [SY1542: $i] :
( ~ ( in @ SY1542 @ SV582 )
| ~ ( in @ ( kpair @ SY1541 @ SY1542 ) @ SV734 )
| ( in @ ( kpair @ SY1541 @ SY1542 ) @ SY1540 ) ) )
| ( subset @ SV734 @ SY1540 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2554,plain,
! [SV583: $i,SV299: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( powerset @ SV299 ) )
| ! [SY1673: $i] :
( ~ ( in @ SY1673 @ SV299 )
| ~ ( in @ SY1673 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SY1673 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) ) )
= $true )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2555,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ~ ( ~ ( SV300 @ SV841 )
| ~ ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2556,plain,
! [SV584: $i,SV301: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ ( powerset @ SV301 ) )
| ! [SY1675: $i] :
( ~ ( in @ SY1675 @ SV301 )
| ~ ( in @ SY1675 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1675 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2557,plain,
! [SV585: $i,SV302: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ ( powerset @ SV302 ) )
| ! [SY1676: $i] :
( ~ ( in @ SY1676 @ SV302 )
| ~ ( in @ SY1676 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SY1676 @ ( setminus @ SV302 @ SV585 ) ) ) )
= $true )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2277]) ).
thf(2558,plain,
! [SV304: $i] :
( ( ( ! [SY804: $i] :
~ ( in @ SY804 @ SV304 ) )
= $false )
| ( ( SV304 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2559,plain,
! [SV587: $i,SV305: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ ( powerset @ SV305 ) )
| ! [SY1677: $i] :
( ~ ( in @ SY1677 @ ( binintersect @ SV587 @ SV844 ) )
| ( in @ SY1677 @ SV305 ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2560,plain,
! [SV306: $i,SV735: $i,SV588: $i] :
( ( ( in @ SV588 @ SV735 )
= $false )
| ( ( ~ ( in @ SV735 @ SV306 )
| ( in @ SV588 @ ( setunion @ SV306 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2561,plain,
! [SV589: $i,SV307: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ SV307 )
| ~ ( in @ SV845 @ SV589 )
| ~ ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2562,plain,
! [SV590: $i,SV308: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ ( powerset @ SV308 ) )
| ( ( setminus @ SV308 @ ( binunion @ SV590 @ SV846 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SV846 ) ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2563,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false )
| ( ( ! [SY1543: $o] :
( ~ ( ( SV736 != SV309 )
| SY1543 )
| ~ ( ~ ( in @ SV736 @ SV591 )
| SY1543 )
| SY1543 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2284]) ).
thf(2564,plain,
! [SV592: $i,SV310: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( powerset @ SV310 ) )
| ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV310 )
| ~ ( in @ SY1678 @ SV592 )
| ( in @ SY1678 @ SV847 ) )
| ( subset @ SV592 @ SV847 ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2565,plain,
! [SV594: $i,SV312: $i,SV737: $i] :
( ( ( in @ SV737 @ ( binunion @ SV312 @ SV594 ) )
= $false )
| ( ( ( in @ SV737 @ SV312 )
| ( in @ SV737 @ SV594 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2287]) ).
thf(2566,plain,
! [SV595: $i,SV313: $i,SV738: $i] :
( ( ( in @ SV738 @ SV313 )
= $false )
| ( ( ! [SY1544: $i] :
( ~ ( in @ SY1544 @ SV595 )
| ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SY1544 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2288]) ).
thf(2567,plain,
! [SV739: $i > $i > $o,SV596: $i,SV314: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ SV314 ) )
= $true )
| ( ( ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV596 )
| ~ ( SV739 @ SV760 @ SY1573 )
| ( in @ ( kpair @ SV760 @ SY1573 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2568,plain,
! [SV597: $i,SV315: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ ( powerset @ SV315 ) )
| ! [SY1679: $o,SY1680: $i] :
( ~ ( in @ SY1680 @ SV315 )
| ~ ( in @ SY1680 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SY1680 @ SV597 )
| SY1679 )
| ~ ( ~ ( in @ SY1680 @ SV848 )
| SY1679 )
| SY1679 ) )
= $true )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2290]) ).
thf(2569,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ ( powerset @ SV317 ) )
| ! [SY1681: $i] :
( ~ ( in @ SY1681 @ ( powerset @ SV317 ) )
| ! [SY1682: $i] :
( ~ ( in @ SY1682 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SY1681 @ SY1682 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1681 ) @ ( setminus @ SV317 @ SY1682 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2570,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ ( powerset @ SV318 ) )
| ! [SY1683: $i] :
( ~ ( in @ SY1683 @ SV318 )
| ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SY1683 @ SV850 )
| ~ ( in @ SY1683 @ SV600 ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2571,plain,
! [SV740: $i,SV601: $i,SV319: $i] :
( ( ( func @ SV319 @ SV601 @ SV740 )
= $false )
| ( ( ! [SY1549: $i] :
( ~ ( in @ SY1549 @ SV319 )
| ( in @ ( kpair @ SY1549 @ ( ap @ SV319 @ SV601 @ SV740 @ SY1549 ) ) @ SV740 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2294]) ).
thf(2572,plain,
! [SV741: $i,SV602: $i,SV320: $i] :
( ( ( subset @ SV320 @ SV602 )
= $false )
| ( ( ~ ( in @ SV741 @ SV320 )
| ( in @ SV741 @ SV602 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2295]) ).
thf(2573,plain,
! [SV603: $i,SV321: $i,SV742: $i] :
( ( ( subset @ SV742 @ SV321 )
= $false )
| ( ( ~ ( subset @ SV742 @ SV603 )
| ( subset @ SV742 @ ( binintersect @ SV321 @ SV603 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2296]) ).
thf(2574,plain,
! [SV604: $i,SV322: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ ( powerset @ SV322 ) )
| ( in @ ( binintersect @ SV604 @ SV851 ) @ ( powerset @ SV322 ) ) )
= $true )
| ( ( in @ SV604 @ ( powerset @ SV322 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2297]) ).
thf(2575,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ~ ( ~ ( SV323 @ SV852 )
| ~ ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2576,plain,
! [SV605: $i,SV324: $i,SV743: $i] :
( ( ( in @ SV743 @ SV324 )
= $false )
| ( ( ! [SY1550: $i] :
( ~ ( in @ SY1550 @ SV605 )
| ( ( kpair @ SV743 @ SY1550 )
= ( kpair @ SV743 @ SY1550 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2577,plain,
! [SV607: $i,SV326: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( powerset @ SV326 ) )
| ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SV853 ) ) ) ) )
= $true )
| ( ( in @ SV607 @ ( powerset @ SV326 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2578,plain,
! [SV2: $i,SV328: $i] :
( ( ( in @ SV328 @ ( setadjoin @ SV2 @ emptyset ) )
= $false )
| ( ( SV2 = SV328 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2579,plain,
! [SV3: $i] :
( ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true )
| ( ( ! [SY6: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SY6 )
| ( subset @ SX2 @ SY6 ) )
| ! [SY8: $i] :
( ~ ( in @ SY8 @ ( binintersect @ SV3 @ SY6 ) )
| ( subset @ SY8 @ ( binintersect @ SV3 @ SY6 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2303]) ).
thf(2580,plain,
! [SV3: $i,SV854: $i] :
( ( ( ~ ! [SY1685: $i] :
( ~ ( in @ SY1685 @ SV854 )
| ( subset @ SY1685 @ SV854 ) )
| ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2304]) ).
thf(2581,plain,
! [SV4: $i,SV608: $i > $i,SV329: $i] :
( ( ( ~ ( in @ ( sK22_SY1366 @ SV329 @ SV608 @ SV4 ) @ SV4 )
| ( in @ ( SV608 @ ( sK22_SY1366 @ SV329 @ SV608 @ SV4 ) ) @ SV329 ) )
= $false )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2305]) ).
thf(2582,plain,
! [SV6: $i,SV609: $i,SV330: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV330 )
| ( ( ksnd @ ( kpair @ SV609 @ SV855 ) )
= SV855 ) )
= $true )
| ( ( in @ SV609 @ SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2583,plain,
! [SV8: $i,SV611: $i,SV332: $i > $o] :
( ( ( ~ ( SV332 @ SV611 ) )
= $true )
| ( ( ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) )
= $true )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2584,plain,
! [SV612: $i,SV333: $i,SV9: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV9 )
| ( ( ap @ SV9 @ SV333 @ SV612 @ SV856 )
= ( ap @ SV9 @ SV333 @ SV612 @ SV856 ) ) )
= $true )
| ( ( func @ SV9 @ SV333 @ SV612 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2585,plain,
! [SV10: $i,SV613: $i,SV334: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ SV334 )
| ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SV857 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) ) )
= $true )
| ( ( in @ SV613 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2586,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i] :
( ( ( ~ ( func @ SV11 @ SV335 @ SV858 )
| ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1687 )
= ( ap @ SV11 @ SV335 @ SV858 @ SY1687 ) ) )
| ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2312]) ).
thf(2587,plain,
! [SV14: $i,SV615: $i > $i,SV337: $i] :
( ( ( ~ ( in @ ( sK23_SY1378 @ SV337 @ SV615 @ SV14 ) @ SV14 )
| ( in @ ( SV615 @ ( sK23_SY1378 @ SV337 @ SV615 @ SV14 ) ) @ SV337 ) )
= $false )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2313]) ).
thf(2588,plain,
! [SV340: $i,SV17: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY1576 ) @ ( binunion @ SV761 @ SY1576 ) ) ) ) ) )
= $true )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2589,plain,
! [SV859: $i > $o,SV618: $i,SV342: $i,SV19: $i] :
( ( ( ~ ! [SY1690: $i] :
( ~ ( in @ SY1690 @ SV19 )
| ! [SY1691: $i] :
( ~ ( in @ SY1691 @ SV342 )
| ~ ( in @ ( kpair @ SY1690 @ SY1691 ) @ SV618 )
| ( SV859 @ ( kpair @ SY1690 @ SY1691 ) ) ) )
| ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2316]) ).
thf(2590,plain,
! [SV343: $i,SV20: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV20 ) ) )
= $true )
| ( ( ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV20 )
| ~ ~ ( in @ SY1577 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SY1577 @ SV762 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2317]) ).
thf(2591,plain,
! [SV344: $i,SV21: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV21 ) ) )
= $true )
| ( ( ~ ( subset @ SV344 @ ( setminus @ SV21 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV21 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2592,plain,
! [SV346: $i,SV24: $i,SV860: $i,SV764: $i] :
( ( ( ( SV764 != SV860 )
| ~ ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) )
| ~ ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2319]) ).
thf(2593,plain,
! [SV347: $i > $o,SV26: $i] :
( ( ( ! [SY899: $i] :
~ ~ ( ~ ( in @ SY899 @ SV26 )
| ~ ( SV347 @ SY899 ) ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2594,plain,
! [SV27: $i,SV348: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 ) )
= $false )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2595,plain,
! [SV27: $i,SV348: $i > $o] :
( ( ( ~ ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) ) )
= $false )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2596,plain,
! [SV619: $i,SV349: $i,SV28: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV28 )
| ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SV861 ) @ SV349 ) )
= $true )
| ( ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2597,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
| ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2598,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ~ ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
| ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2325]) ).
thf(2599,plain,
! [SV353: $i,SV34: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ ( powerset @ SV34 ) ) )
= $true )
| ( ( ! [SY1579: $i] :
( ~ ( in @ SY1579 @ SV34 )
| ~ ~ ( in @ SY1579 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SY1579 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2600,plain,
! [SV354: $i,SV35: $i,SV766: $i] :
( ( ( ~ ( in @ SV766 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SV766 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SV766 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2601,plain,
! [SV355: $i,SV37: $i,SV622: $i] :
( ( ( SV622 = SV37 )
= $true )
| ( ( SV622 = SV355 )
= $true )
| ( ( in @ SV622 @ ( setadjoin @ SV37 @ ( setadjoin @ SV355 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2602,plain,
! [SV356: $i,SV38: $i,SV767: $i] :
( ( ( ~ ( in @ SV767 @ ( powerset @ SV38 ) ) )
= $true )
| ( ( in @ ( setminus @ SV356 @ SV767 ) @ ( powerset @ SV38 ) )
= $true )
| ( ( in @ SV356 @ ( powerset @ SV38 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2603,plain,
! [SV357: $i,SV768: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV768 ) )
= $true )
| ( ( ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SV40 )
| ! [SY1581: $i] :
( ~ ( in @ SY1581 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1581 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1582: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1582 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1582 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1582 @ SY1581 ) @ SV768 ) ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2604,plain,
! [SV358: $i,SV769: $i,SV41: $i] :
( ( ( ~ ( breln1 @ SV41 @ SV769 ) )
= $true )
| ( ( ! [SY1583: $i] :
( ~ ( breln1 @ SV41 @ SY1583 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SY1583 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY1583 ) @ ( breln1compset @ SV41 @ SV769 @ SY1583 ) ) ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2605,plain,
! [SV359: $i,SV42: $i,SV770: $i] :
( ( ( ~ ( in @ SV770 @ ( powerset @ SV42 ) ) )
= $true )
| ( ( ! [SY1584: $i] :
( ~ ( in @ SY1584 @ SV42 )
| ~ ( in @ SY1584 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SY1584 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) ) )
= $true )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2606,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i] :
( ( ( ! [SY1387: $i] :
~ ~ ( ~ ( in @ SY1387 @ SV43 )
| ( SV623
!= ( SV360 @ SY1387 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2607,plain,
! [SV362: $i,SV771: $i,SV45: $i] :
( ( ( ~ ( breln1 @ SV45 @ SV771 ) )
= $true )
| ( ( breln1 @ SV45 @ ( binunion @ SV362 @ SV771 ) )
= $true )
| ( ( breln1 @ SV45 @ SV362 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2335]) ).
thf(2608,plain,
! [SV745: $i,SV625: $i,SV363: $i,SV46: $i] :
( ( ( ( kpair @ SV46 @ SV363 )
= ( kpair @ SV625 @ SV745 ) )
= $false )
| ( ( SV46 = SV625 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2609,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ ( setunion @ SV47 ) ) )
= $true )
| ( ( ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2337]) ).
thf(2610,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2338]) ).
thf(2611,plain,
! [SV365: $i,SV48: $i,SV626: $i] :
( ( ( SV626 = SV48 )
= $true )
| ( ( in @ SV626 @ SV365 )
= $true )
| ( ( in @ SV626 @ ( setadjoin @ SV48 @ SV365 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2612,plain,
! [SV366: $i,SV772: $i,SV49: $i] :
( ( ( ~ ( breln1 @ SV49 @ SV772 ) )
= $true )
| ( ( ( binunion @ SV366 @ SV772 )
= ( binunion @ SV772 @ SV366 ) )
= $true )
| ( ( breln1 @ SV49 @ SV366 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2340]) ).
thf(2613,plain,
! [SV51: $i,SV746: $i] :
( ( ( in @ SV746 @ omega )
= $false )
| ( ( ( ( omegaS @ SV51 )
!= ( omegaS @ SV746 ) )
| ( SV51 = SV746 ) )
= $true )
| ( ( in @ SV51 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2614,plain,
! [SV367: $i,SV52: $i,SV773: $i] :
( ( ( ~ ( in @ SV773 @ ( powerset @ SV52 ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( in @ SY1585 @ SV52 )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SY1585 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) ) )
= $true )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2615,plain,
! [SV368: $i,SV53: $i,SV774: $i] :
( ( ( ~ ( in @ SV774 @ ( powerset @ SV53 ) ) )
= $true )
| ( ( ~ ( subset @ SV368 @ SV774 )
| ( subset @ ( setminus @ SV53 @ SV774 ) @ ( setminus @ SV53 @ SV368 ) ) )
= $true )
| ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2616,plain,
! [SV369: $i,SV54: $i,SV775: $i] :
( ( ( ~ ( in @ SV775 @ ( powerset @ SV54 ) ) )
= $true )
| ( ( ~ ( subset @ ( setminus @ SV54 @ SV775 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SV775 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2617,plain,
! [SV370: $i,SV55: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV55 ) ) )
= $true )
| ( ( ~ ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
| ! [SY1586: $i] :
( ~ ( in @ SY1586 @ SV55 )
| ~ ( in @ SY1586 @ SV776 )
| ( in @ SY1586 @ ( setminus @ SV55 @ SV370 ) ) ) )
= $true )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2618,plain,
! [SV372: $i,SV57: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( in @ SY1587 @ SV57 )
| ~ ( in @ SY1587 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SY1587 @ SV372 ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2346]) ).
thf(2619,plain,
! [SV373: $i > $o,SV58: $i] :
( ( ( ! [SY940: $i] :
~ ~ ( ~ ( in @ SY940 @ SV58 )
| ~ ( SV373 @ SY940 ) ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2620,plain,
! [SV59: $i,SV374: $i,SV627: $i] :
( ( ( in @ SV627 @ SV374 )
= $false )
| ( ( in @ SV627 @ ( setminus @ SV59 @ SV374 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2621,plain,
! [SV375: $i,SV60: $i,SV628: $i] :
( ( ( SV628 = SV60 )
= $true )
| ( ( SV628 = SV375 )
= $true )
| ( ( in @ SV628 @ ( setadjoin @ SV60 @ ( setadjoin @ SV375 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2349]) ).
thf(2622,plain,
! [SV376: $i > $o,SV61: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV61 )
| ( SV376 @ SV862 ) )
= $true )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2623,plain,
! [SV62: $i,SV629: $i > $i,SV377: $i] :
( ( ( ~ ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 )
| ( in @ ( SV629 @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) ) @ SV377 ) )
= $false )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2351]) ).
thf(2624,plain,
! [SV378: $i,SV63: $i,SV630: $i] :
( ( ( in @ SV630 @ SV63 )
= $true )
| ( ( ~ ( in @ SV630 @ ( setminus @ SV63 @ SV378 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2352]) ).
thf(2625,plain,
! [SV380: $i,SV66: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ! [SY1588: $i] :
( ~ ( in @ SY1588 @ SV66 )
| ~ ~ ( in @ SY1588 @ SV380 )
| ~ ~ ( in @ SY1588 @ SV778 )
| ~ ( in @ SY1588 @ ( binunion @ SV380 @ SV778 ) ) ) )
= $true )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2626,plain,
! [SV381: $i,SV67: $i,SV863: $i,SV779: $i] :
( ( ( ( SV779 != SV863 )
| ~ ( in @ SV779 @ SV67 )
| ( in @ SV863 @ SV381 ) )
= $true )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2354]) ).
thf(2627,plain,
! [SV382: $i,SV69: $i,SV631: $i] :
( ( ( in @ SV631 @ ( setminus @ SV69 @ SV382 ) )
= $false )
| ( ( in @ SV631 @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2628,plain,
! [SV632: $i,SV383: $o,SV70: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV70 )
| ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) ) )
= $true )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2356]) ).
thf(2629,plain,
! [SV633: $i,SV70: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ SV70 )
| ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) ) )
= $true )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2630,plain,
! [SV634: $i,SV70: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV70 )
| ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) ) )
= $true )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2358]) ).
thf(2631,plain,
! [SV73: $i,SV780: $i] :
( ( ( in @ SV780 @ SV73 )
= $false )
| ( ( ~ ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2632,plain,
! [SV635: $i,SV385: $i,SV75: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV75 )
| ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SV867 ) @ SV385 ) )
= $true )
| ( ( func @ SV75 @ SV385 @ SV635 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2633,plain,
! [SV386: $i,SV76: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ ( powerset @ SV76 ) ) )
= $true )
| ( ( ! [SY1590: $i] :
( ~ ( in @ SY1590 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SY1590 @ SV386 )
| ( in @ SY1590 @ SV781 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2634,plain,
! [SV387: $i,SV77: $i,SV782: $i] :
( ( ( ~ ( in @ SV782 @ ( powerset @ SV77 ) ) )
= $true )
| ( ( ! [SY1591: $i] :
( ~ ( in @ SY1591 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SY1591 @ SV782 )
| ~ ( in @ SY1591 @ SV387 ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2635,plain,
! [SV388: $i,SV78: $i,SV747: $i,SV636: $i] :
( ( ( in @ ( kpair @ SV636 @ SV747 ) @ ( cartprod @ SV78 @ SV388 ) )
= $false )
| ( ( in @ SV747 @ SV388 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2636,plain,
! [SV79: $i,SV637: $i,SV389: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV389 )
| ( in @ ( kpair @ SV637 @ SV868 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) ) )
= $true )
| ( ( in @ SV637 @ SV79 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2637,plain,
! [SV390: $i,SV80: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ ( powerset @ SV80 ) ) )
= $true )
| ( ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SV783 ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2638,plain,
! [SV392: $i,SV82: $i,SV784: $i] :
( ( ( ~ ( in @ SV784 @ ( powerset @ SV82 ) ) )
= $true )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV82 )
| ~ ~ ( in @ SY1592 @ SV392 )
| ~ ( in @ SY1592 @ ( binintersect @ SV392 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2639,plain,
! [SV638: $i > $i > $o,SV393: $i,SV83: $i,SV785: $i,SV748: $i] :
( ( ( ~ ( in @ ( kpair @ SV748 @ SV785 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SY1404: $i,SY1405: $i] : ( SV638 @ SY1404 @ SY1405 ) ) ) )
= $true )
| ( ( SV638 @ SV748 @ SV785 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2640,plain,
! [SV639: $i,SV394: $i,SV84: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ SV84 )
| ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1696: $i] : ( in @ ( kpair @ SV869 @ SY1696 ) @ SV639 ) ) ) )
= $true )
| ( ( func @ SV84 @ SV394 @ SV639 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2368]) ).
thf(2641,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) )
= $true )
| ( ( ~ ( in @ SV640 @ SV85 )
| ( in @ SV640 @ SV395 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2642,plain,
! [SV87: $i,SV397: $i,SV641: $i] :
( ( ( ~ ~ ( in @ SV641 @ SV397 ) )
= $true )
| ( ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) )
= $true )
| ( ( in @ SV641 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2643,plain,
! [SV89: $i,SV642: $i > $i,SV399: $i] :
( ( ( ~ ( in @ ( sK25_SY1408 @ SV399 @ SV642 @ SV89 ) @ SV89 )
| ( in @ ( SV642 @ ( sK25_SY1408 @ SV399 @ SV642 @ SV89 ) ) @ SV399 ) )
= $false )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2371]) ).
thf(2644,plain,
! [SV643: $i,SV401: $i,SV91: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ SV91 )
| ( in @ ( kpair @ SV870 @ ( ap @ SV91 @ SV401 @ SV643 @ SV870 ) ) @ SV643 ) )
= $true )
| ( ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2645,plain,
! [SV402: $i,SV786: $i,SV93: $i] :
( ( ( ~ ( breln1 @ SV93 @ SV786 ) )
= $true )
| ( ( ! [SY1595: $i] :
( ~ ( in @ SY1595 @ SV93 )
| ! [SY1596: $i] :
( ~ ( in @ SY1596 @ SV93 )
| ~ ( in @ ( kpair @ SY1595 @ SY1596 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV402 )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV786 ) ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2373]) ).
thf(2646,plain,
! [SV644: $i,SV403: $o,SV94: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV94 )
| ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1697: $i] :
( ~ ( ~ SV403
| ( SY1697 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1697 != SV871 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2374]) ).
thf(2647,plain,
! [SV645: $i,SV94: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ SV94 )
| ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1698: $i] :
( ~ ( ~ $true
| ( SY1698 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1698 != SV872 ) ) ) ) ) )
= $true )
| ( ( in @ SV645 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2375]) ).
thf(2648,plain,
! [SV646: $i,SV94: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ SV94 )
| ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1699: $i] :
( ~ ( ~ $false
| ( SY1699 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1699 != SV873 ) ) ) ) ) )
= $true )
| ( ( in @ SV646 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2376]) ).
thf(2649,plain,
! [SV404: $i,SV95: $i] :
( ( ( ~ ( in @ ( sK12_SY994 @ SV95 @ SV404 ) @ SV404 ) )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2650,plain,
! [SV404: $i,SV95: $i] :
( ( ( in @ ( sK12_SY994 @ SV95 @ SV404 ) @ SV95 )
= $false )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2651,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SV874 )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2378]) ).
thf(2652,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $true )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2378]) ).
thf(2653,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $false )
| ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2378]) ).
thf(2654,plain,
! [SV408: $i,SV787: $i,SV99: $i] :
( ( ( ~ ( breln1 @ SV99 @ SV787 ) )
= $true )
| ( ( ! [SY1597: $i] :
( ~ ( in @ SY1597 @ SV99 )
| ! [SY1598: $i] :
( ~ ( in @ SY1598 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1598 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1599: $o] :
( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1600 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1600 @ SY1598 ) @ SV787 )
| SY1599 )
| SY1599 ) ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2655,plain,
! [SV749: $i,SV649: $i,SV410: $i,SV102: $i] :
( ( ( ( kpair @ SV102 @ SV410 )
= ( kpair @ SV649 @ SV749 ) )
= $false )
| ( ( SV410 = SV749 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2656,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ( ( sK13_SY1008 @ SV415 @ SV107 )
!= ( sK26_SY1601 @ SV107 @ SV415 ) )
| ~ ( ~ ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
| ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2383]) ).
thf(2657,plain,
! [SV416: $i,SV108: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( ! [SY1602: $i] :
( ~ ( in @ SY1602 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SY1602 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SY1602 ) ) ) )
= $true )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2658,plain,
! [SV651: $i,SV417: $i,SV109: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
| ~ ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1700 )
= ( ap @ SV109 @ SV417 @ SV875 @ SY1700 ) ) )
| ( SV651 = SV875 ) )
= $true )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2385]) ).
thf(2659,plain,
! [SV653: $i,SV419: $i,SV111: $i] :
( ( ( ! [SY1424: $i] :
~ ~ ( ~ ( in @ SY1424 @ SV111 )
| ~ ~ ! [SY1425: $i] :
~ ~ ( ~ ( in @ SY1425 @ SV419 )
| ( SV653
!= ( kpair @ SY1424 @ SY1425 ) ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2660,plain,
! [SV113: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY275 @ SV113 ) @ SV113 )
| ( ( binintersect @ ( sK27_SY275 @ SV113 ) @ SV113 )
!= emptyset ) ) )
= $false )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2388]) ).
thf(2661,plain,
! [SV423: $i,SV116: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ ( powerset @ SV116 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SV789 ) ) )
= $true )
| ( ( in @ SV423 @ ( powerset @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2390]) ).
thf(2662,plain,
! [SV424: $i,SV117: $i,SV790: $i] :
( ( ( ~ ( in @ SV790 @ ( powerset @ SV117 ) ) )
= $true )
| ( ( ! [SY1603: $i] :
( ~ ( in @ SY1603 @ ( powerset @ SV117 ) )
| ! [SY1604: $i] :
( ~ ( in @ SY1604 @ SV117 )
| ~ ( in @ SY1604 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1604 @ ( binintersect @ ( binunion @ SV424 @ SY1603 ) @ ( binunion @ SV790 @ SY1603 ) ) ) ) ) )
= $true )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2391]) ).
thf(2663,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2664,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1605: $i] :
( ~ ( in @ SY1605 @ SV118 )
| ~ ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
| ~ ( SV425 @ SY1605 )
| ( ( sK14_SY1032 @ SV425 @ SV118 )
= SY1605 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2392]) ).
thf(2665,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ~ ( ~ ( ~ ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
| ~ ( ~ ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) )
| ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2666,plain,
! [SV655: $i,SV427: $i,SV120: $i,SV877: $i] :
( ( ( ~ ( in @ SV877 @ SV120 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1703: $i] : ( in @ ( kpair @ SV877 @ SY1703 ) @ SV655 ) ) )
@ SV427 ) )
= $true )
| ( ( func @ SV120 @ SV427 @ SV655 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2394]) ).
thf(2667,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) )
| ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2395]) ).
thf(2668,plain,
! [SV122: $i,SV429: $i] :
( ( ( ~ ( in @ ( sK16_SY1044 @ SV429 @ SV122 ) @ SV122 ) )
= $false )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2396]) ).
thf(2669,plain,
! [SV122: $i,SV429: $i] :
( ( ( in @ ( sK16_SY1044 @ SV429 @ SV122 ) @ SV429 )
= $false )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2396]) ).
thf(2670,plain,
! [SV750: $i] :
( ( ( in @ SV750 @ sK1_X )
= $false )
| ( ( subset @ SV750 @ sK1_X )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2397]) ).
thf(2671,plain,
( ( in @ sK2_SY0 @ sK1_X )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2398]) ).
thf(2672,plain,
( ( ~ ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2673,plain,
! [SV124: $i,SV656: $i > $i,SV431: $i] :
( ( ( ~ ( in @ ( sK28_SY1428 @ SV431 @ SV656 @ SV124 ) @ SV124 )
| ( in @ ( SV656 @ ( sK28_SY1428 @ SV431 @ SV656 @ SV124 ) ) @ SV431 ) )
= $false )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2400]) ).
thf(2674,plain,
! [SV657: $i,SV432: $o,SV125: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV125 )
| ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1704: $i] :
( ~ ( ~ SV432
| ( SY1704 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1704 != SV878 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2401]) ).
thf(2675,plain,
! [SV658: $i,SV125: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV125 )
| ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1705: $i] :
( ~ ( ~ $true
| ( SY1705 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1705 != SV879 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2402]) ).
thf(2676,plain,
! [SV659: $i,SV125: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV125 )
| ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1706: $i] :
( ~ ( ~ $false
| ( SY1706 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1706 != SV880 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2403]) ).
thf(2677,plain,
! [SV791: $o,SV126: $i,SV433: $i] :
( ( ( ~ ! [SY1606: $i] :
( ~ ( in @ SV433 @ SY1606 )
| ~ ( in @ SY1606 @ SV126 )
| SV791 ) )
= $true )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2678,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2405]) ).
thf(2679,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2406]) ).
thf(2680,plain,
! [SV435: $i,SV792: $i,SV128: $i] :
( ( ( ~ ( breln1 @ SV128 @ SV792 ) )
= $true )
| ( ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SV792 ) )
= $true )
| ( ( breln1 @ SV128 @ SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2408]) ).
thf(2681,plain,
! [SV131: $i,SV438: $i,SV662: $i] :
( ( ( ~ ~ ( in @ SV662 @ SV438 ) )
= $true )
| ( ( ~ ( subset @ SV131 @ SV438 ) )
= $true )
| ( ( in @ SV662 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2410]) ).
thf(2682,plain,
! [SV751: $i,SV663: $i,SV439: $i,SV132: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SV751 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV663 != SV751 )
| ( SV439 = SV751 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2683,plain,
! [SV440: $i,SV133: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ ( powerset @ SV133 ) ) )
= $true )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV133 )
| ~ ( in @ SY1607 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SY1607 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) ) )
= $true )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2684,plain,
! [SV441: $i,SV134: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ ( powerset @ SV134 ) )
| ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1608 )
| ~ ( subset @ SV794 @ SY1609 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SY1608 @ SY1609 ) ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2685,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ( ~ ( SV136 @ SV795 )
| ~ ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) ) )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2686,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ( ~ ( SV138 @ SV796 )
| ~ ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) ) )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2687,plain,
! [SV664: $i,SV881: $i,SV444: $i,SV139: $i] :
( ( ( ~ ( func @ SV139 @ SV444 @ SV881 )
| ~ ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1707 )
= ( ap @ SV139 @ SV444 @ SV881 @ SY1707 ) ) )
| ( SV664 = SV881 ) )
= $true )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2416]) ).
thf(2688,plain,
! [SV140: $i,SV445: $i > $i] :
( ( ~ ! [SY1557: $i] :
~ ( ~ ( ~ ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) )
| ~ ! [SY1560: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1560 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1560 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SY1560 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2689,plain,
! [SV665: $i > $i > $o,SV446: $i,SV141: $i,SV797: $i,SV752: $i] :
( ( ( ~ ( in @ ( kpair @ SV752 @ SV797 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SY1441: $i,SY1442: $i] : ( SV665 @ SY1441 @ SY1442 ) ) ) )
= $true )
| ( ( in @ SV752 @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2690,plain,
! [SV447: $i,SV142: $i,SV753: $i,SV666: $i] :
( ( ( in @ ( kpair @ SV666 @ SV753 ) @ ( cartprod @ SV142 @ SV447 ) )
= $false )
| ( ( in @ SV666 @ SV142 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2691,plain,
! [SV448: $i,SV143: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( powerset @ SV143 ) )
| ~ ( subset @ SV798 @ SY1614 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SY1614 ) ) )
= $true )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2692,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY1085 @ SV449 @ SV144 ) @ SV144 )
| ~ ( SV449 @ ( sK29_SY1085 @ SV449 @ SV144 ) ) ) )
= $false )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2421]) ).
thf(2693,plain,
! [SV145: $i,SV450: $i] :
( ( ( ~ ( in @ ( sK17_SY1086 @ SV450 @ SV145 ) @ SV145 ) )
= $false )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2694,plain,
! [SV145: $i,SV450: $i] :
( ( ( in @ ( sK17_SY1086 @ SV450 @ SV145 ) @ SV450 )
= $false )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2422]) ).
thf(2695,plain,
! [SV799: $i > $o,SV451: $i,SV146: $i] :
( ( ( ~ ! [SY1615: $i] :
( ~ ( in @ SY1615 @ SV146 )
| ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV146 )
| ~ ( in @ ( kpair @ SY1615 @ SY1616 ) @ SV451 )
| ( SV799 @ ( kpair @ SY1615 @ SY1616 ) ) ) ) )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2423]) ).
thf(2696,plain,
! [SV453: $i > $i,SV667: $i,SV148: $i] :
( ( ( ! [SY1445: $i] :
~ ~ ( ~ ( in @ SY1445 @ SV148 )
| ( SV667
!= ( SV453 @ SY1445 ) ) ) )
= $false )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2697,plain,
! [SV454: $i,SV149: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ ( powerset @ SV149 ) ) )
= $true )
| ( ( ~ ! [SY1618: $i] :
( ~ ( in @ SY1618 @ SV149 )
| ~ ( in @ SY1618 @ SV454 )
| ( in @ SY1618 @ SV800 ) )
| ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2425]) ).
thf(2698,plain,
! [SV458: $i > $o,SV153: $i,SV882: $i] :
( ( ( ~ ~ ( ~ ( in @ SV882 @ SV153 )
| ~ ( SV458 @ SV882 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2699,plain,
! [SV459: $i,SV801: $i,SV154: $i] :
( ( ( ~ ( breln1 @ SV154 @ SV801 ) )
= $true )
| ( ( ! [SY1620: $i] :
( ~ ( breln1 @ SV154 @ SY1620 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SY1620 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2428]) ).
thf(2700,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( ~ ( SV155 @ SV802 )
| ~ ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) ) )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2701,plain,
! [SV803: $i > $o,SV460: $i,SV156: $i] :
( ( ( ~ ! [SY1622: $i] :
( ~ ( in @ SY1622 @ SV156 )
| ! [SY1623: $i] :
( ~ ( in @ SY1623 @ SV156 )
| ~ ( in @ ( kpair @ SY1622 @ SY1623 ) @ SV460 )
| ( SV803 @ ( kpair @ SY1622 @ SY1623 ) ) ) ) )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2702,plain,
! [SV157: $i,SV669: $i,SV461: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV461 )
| ( in @ ( kpair @ SV669 @ SV883 ) @ ( cartprod @ SV157 @ SV461 ) ) )
= $true )
| ( ( in @ SV669 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2431]) ).
thf(2703,plain,
! [SV670: $i,SV462: $o,SV158: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV158 )
| ~ ~ SV462
| ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) ) )
= $true )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2432]) ).
thf(2704,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ SV158 )
| ~ ~ $true
| ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) ) )
= $true )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2705,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV158 )
| ~ ~ $false
| ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) ) )
= $true )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2434]) ).
thf(2706,plain,
! [SV159: $i,SV463: $i,SV673: $i] :
( ( ( ~ ( in @ SV673 @ SV463 ) )
= $true )
| ( ( in @ SV673 @ SV159 )
= $true )
| ( ( in @ SV463 @ ( powerset @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2707,plain,
! [SV160: $i,SV464: $i,SV674: $i] :
( ( ( ~ ~ ( in @ SV674 @ SV464 ) )
= $true )
| ( ( SV160 != SV464 )
= $true )
| ( ( in @ SV674 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2708,plain,
! [SV161: $i,SV675: $i,SV465: $i] :
( ( ( ~ ( subset @ SV465 @ SV675 ) )
= $true )
| ( ( subset @ SV161 @ SV675 )
= $true )
| ( ( subset @ SV161 @ SV465 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2437]) ).
thf(2709,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV163 ) )
= $true )
| ( ( ~ ~ ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SV804 @ SV467 ) )
= $true )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2438]) ).
thf(2710,plain,
! [SV164: $i,SV468: $i,SV676: $i] :
( ( ( ~ ~ ( in @ SV676 @ SV468 ) )
= $true )
| ( ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) )
= $true )
| ( ( in @ SV676 @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2711,plain,
! [SV165: $i,SV677: $i,SV469: $i > $o] :
( ( ( ~ ( SV469 @ SV677 ) )
= $true )
| ( ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset )
= $true )
| ( ( in @ SV677 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2712,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ SV805 )
= $false )
| ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) )
| ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2441]) ).
thf(2713,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV806 )
| ~ ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) ) )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2442]) ).
thf(2714,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV470 @ SV887 )
| ~ ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV168 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SV470 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV678 )
| ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV887 ) ) )
| ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2443]) ).
thf(2715,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ~ ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
| ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2716,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ~ ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) )
| ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2445]) ).
thf(2717,plain,
! [SV473: $i,SV171: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ ( powerset @ SV171 ) ) )
= $true )
| ( ( ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV171 )
| ~ ~ ( in @ SY1626 @ SV807 )
| ~ ( in @ SY1626 @ ( binintersect @ SV473 @ SV807 ) ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2718,plain,
! [SV172: $i,SV680: $i > $i,SV474: $i] :
( ( ( ~ ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 )
| ( in @ ( SV680 @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) ) @ SV474 ) )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2447]) ).
thf(2719,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY1627: $i] :
~ ( ~ ( ~ ( SV174 @ SY1627 )
| ( SY1627 = SV808 ) )
| ~ ( ( SY1627 != SV808 )
| ( SV174 @ SY1627 ) ) ) )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2720,plain,
! [SV475: $i,SV175: $i,SV888: $i,SV809: $i] :
( ( ( ( SV809 != SV888 )
| ( ( setadjoin @ SV175 @ SV809 )
= ( setadjoin @ SV475 @ SV888 ) ) )
= $true )
| ( ( SV175 = SV475 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2449]) ).
thf(2721,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( ~ ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) )
| ~ ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) )
= $false )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2722,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_SY1142 @ SV478 @ SV178 ) @ SV178 )
| ~ ( in @ SV478 @ ( sK31_SY1142 @ SV478 @ SV178 ) ) ) )
= $false )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2452]) ).
thf(2723,plain,
! [SV479: $i,SV179: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ! [SY1629: $i] :
( ~ ( in @ SY1629 @ ( powerset @ SV179 ) )
| ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV179 )
| ~ ( in @ SY1630 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1630 @ ( binunion @ SV810 @ SY1629 ) ) ) ) )
= $true )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2453]) ).
thf(2724,plain,
! [SV683: $i,SV480: $o,SV181: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ SV181 )
| ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SV889 )
= SV683 ) )
= $true )
| ( ( in @ SV683 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2454]) ).
thf(2725,plain,
! [SV684: $i,SV181: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV181 )
| ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SV890 )
= SV684 ) )
= $true )
| ( ( in @ SV684 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2726,plain,
! [SV685: $i,SV181: $i,SV891: $i] :
( ( ( ~ ( in @ SV891 @ SV181 )
| ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SV891 )
= SV685 ) )
= $true )
| ( ( in @ SV685 @ SV181 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2456]) ).
thf(2727,plain,
! [SV481: $i,SV182: $i,SV686: $i] :
( ( ( in @ SV686 @ SV182 )
= $true )
| ( ( ~ ( in @ SV686 @ SV481 )
| ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2728,plain,
! [SV892: $i > $o,SV687: $i,SV482: $i,SV183: $i] :
( ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV183 )
| ! [SY1716: $i] :
( ~ ( in @ SY1716 @ SV482 )
| ~ ( in @ ( kpair @ SY1715 @ SY1716 ) @ SV687 )
| ( SV892 @ ( kpair @ SY1715 @ SY1716 ) ) ) )
| ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2458]) ).
thf(2729,plain,
! [SV184: $i,SV483: $i,SV688: $i] :
( ( ( ~ ~ ( in @ SV688 @ SV483 ) )
= $true )
| ( ( ~ ( in @ SV688 @ SV184 ) )
= $true )
| ( ( subset @ SV184 @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2459]) ).
thf(2730,plain,
! [SV185: $i,SV484: $i] :
( ( ( subset @ SV484 @ SV185 )
= $false )
| ( ( SV185 = SV484 )
= $true )
| ( ( subset @ SV185 @ SV484 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2731,plain,
! [SV485: $i,SV186: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ ( powerset @ SV186 ) ) )
= $true )
| ( ( in @ ( binunion @ SV485 @ SV811 ) @ ( powerset @ SV186 ) )
= $true )
| ( ( in @ SV485 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2732,plain,
! [SV486: $i,SV188: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ ( powerset @ SV188 ) ) )
= $true )
| ( ( ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV188 )
| ~ ( in @ SY1631 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SY1631 @ ( setminus @ SV188 @ SV486 ) ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2462]) ).
thf(2733,plain,
! [SV487: $i > $o,SV189: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV189 ) )
= $true )
| ( ( ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV189 )
| ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SY1632 )
| ( SV813 = SY1632 ) ) )
= $true )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2463]) ).
thf(2734,plain,
! [SV689: $i,SV488: $o,SV190: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1718: $i] :
( ~ ( ~ SV488
| ( SY1718 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1718 != SV893 ) ) ) ) ) )
= $true )
| ( ( in @ SV689 @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2464]) ).
thf(2735,plain,
! [SV690: $i,SV190: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1719: $i] :
( ~ ( ~ $true
| ( SY1719 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1719 != SV894 ) ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2465]) ).
thf(2736,plain,
! [SV691: $i,SV190: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV190 )
| ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1720: $i] :
( ~ ( ~ $false
| ( SY1720 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1720 != SV895 ) ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2466]) ).
thf(2737,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 ) )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2738,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ! [SY1633: $i] :
~ ~ ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1633 )
| ~ ! [SY1634: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1634 )
| ( SY1633 = SY1634 ) ) ) )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2467]) ).
thf(2739,plain,
! [SV490: $i,SV192: $i] :
( ( ( SV192 = SV490 )
= $false )
| ( ( subset @ SV192 @ SV490 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2740,plain,
! [SV496: $i,SV198: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ ( powerset @ SV198 ) ) )
= $true )
| ( ( ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV198 )
| ~ ( in @ SY1635 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SY1635 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) ) )
= $true )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2741,plain,
! [SV694: $i,SV497: $i,SV199: $i] :
( ( ( ~ ( injective @ SV199 @ SV497 @ SV694 ) )
= $true )
| ( ( in @ SV694 @ ( injFuncSet @ SV199 @ SV497 ) )
= $true )
| ( ( in @ SV694 @ ( funcSet @ SV199 @ SV497 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2742,plain,
! [SV200: $i] :
( ( ( in @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $true )
| ( ( ! [SY528: $i] :
( ~ ( in @ SY528 @ SV200 )
| ( subset @ SY528 @ SV200 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2473]) ).
thf(2743,plain,
! [SV200: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV200 )
| ( subset @ SV896 @ SV200 ) )
= $true )
| ( ( subset @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2744,plain,
! [SV202: $i,SV695: $i > $i,SV499: $i] :
( ( ( ~ ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
| ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 ) )
= $false )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2475]) ).
thf(2745,plain,
! [SV204: $i,SV754: $i] :
( ( ( in @ SV754 @ SV204 )
= $false )
| ( ( ( setunion @ SV204 )
= SV754 )
= $true )
| ( ( singleton @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2746,plain,
! [SV500: $i,SV205: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV205 ) )
= $true )
| ( ( ~ ( in @ SV815 @ SV500 )
| ( in @ SV815 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2747,plain,
! [SV207: $i,SV696: $i,SV502: $i > $o] :
( ( ( ~ ( SV502 @ SV696 ) )
= $true )
| ( ( in @ SV696
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) )
= $true )
| ( ( in @ SV696 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2748,plain,
! [SV697: $i > $i > $o,SV503: $i,SV208: $i,SV816: $i,SV755: $i] :
( ( ( ~ ( in @ ( kpair @ SV755 @ SV816 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SY1487: $i,SY1488: $i] : ( SV697 @ SY1487 @ SY1488 ) ) ) )
= $true )
| ( ( in @ SV816 @ SV503 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2749,plain,
! [SV504: $i,SV817: $i,SV209: $i] :
( ( ( ~ ( breln1 @ SV209 @ SV817 ) )
= $true )
| ( ( ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV209 )
| ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV209 )
| ~ ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV504 )
| ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV817 ) ) )
| ( subset @ SV504 @ SV817 ) )
= $true )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2480]) ).
thf(2750,plain,
! [SV506: $i,SV211: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ ( powerset @ SV211 ) ) )
= $true )
| ( ( ! [SY1640: $i] :
( ~ ( in @ SY1640 @ ( powerset @ SV211 ) )
| ! [SY1641: $i] :
( ~ ( in @ SY1641 @ SV211 )
| ~ ( in @ SY1641 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1641 @ ( binunion @ SV506 @ SY1640 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2481]) ).
thf(2751,plain,
! [SV212: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2752,plain,
! [SV212: $i] :
( ( ~ ! [SY1498: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY1498 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1498 ) )
| ~ ! [SY1501: $i] :
~ ~ ! [SY1502: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1501 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1502 @ SY1498 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1501 )
| ~ ( in @ SX5 @ SY1498 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1501 ) )
| ( in @ SY1502 @ SY1504 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2482]) ).
thf(2753,plain,
! [SV698: $i,SV507: $i,SV213: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV213 )
| ( ( ap @ SV213 @ SV507 @ SV698 @ SV897 )
= ( ap @ SV213 @ SV507 @ SV698 @ SV897 ) ) )
= $true )
| ( ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2483]) ).
thf(2754,plain,
! [SV699: $i,SV508: $o,SV214: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV214 )
| ( in @ ( if @ SV214 @ SV508 @ SV699 @ SV898 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SV898 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV699 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2484]) ).
thf(2755,plain,
! [SV700: $i,SV214: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV214 )
| ( in @ ( if @ SV214 @ $true @ SV700 @ SV899 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SV899 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV700 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2485]) ).
thf(2756,plain,
! [SV701: $i,SV214: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV214 )
| ( in @ ( if @ SV214 @ $false @ SV701 @ SV900 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SV900 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV701 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2486]) ).
thf(2757,plain,
! [SV215: $i,SV509: $i,SV702: $i > $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
| ~ ! [SY1721: $i] :
~ ~ ( ~ ( in @ SY1721 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SY1721 ) ) )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2487]) ).
thf(2758,plain,
! [SV705: $i,SV516: $i,SV225: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ SV225 )
| ! [SY1722: $i] :
( ~ ( in @ SY1722 @ SV516 )
| ~ ( in @ ( kpair @ SV901 @ SY1722 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SY1722 ) ) )
= $true )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2490]) ).
thf(2759,plain,
! [SV226: $i] :
( ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ~ ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) )
= $true )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2760,plain,
! [SV517: $i,SV227: $i,SV819: $i] :
( ( ( ~ ( in @ SV819 @ ( powerset @ SV227 ) ) )
= $true )
| ( ( ~ ( subset @ SV517 @ ( setminus @ SV227 @ SV819 ) )
| ( subset @ SV819 @ ( setminus @ SV227 @ SV517 ) ) )
= $true )
| ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2761,plain,
! [SV228: $i,SV820: $i] :
( ( ( in @ SV820 @ SV228 )
= $false )
| ( ( SV228 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2762,plain,
! [SV518: $i,SV229: $i,SV821: $i] :
( ( ( ~ ( in @ SV821 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SV821 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) )
= $true )
| ( ( in @ SV518 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2763,plain,
! [SV230: $i,SV519: $i] :
( ( ( ~ ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 ) )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2764,plain,
! [SV230: $i,SV519: $i] :
( ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2495]) ).
thf(2765,plain,
! [SV521: $i > $o,SV232: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV232 )
| ( SV521 @ SV902 ) )
= $true )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2766,plain,
! [SV523: $i,SV822: $i,SV234: $i] :
( ( ( ~ ( breln1 @ SV234 @ SV822 ) )
= $true )
| ( ( ! [SY1642: $i] :
( ~ ( in @ SY1642 @ SV234 )
| ! [SY1643: $i] :
( ~ ( in @ SY1643 @ SV234 )
| ! [SY1644: $i] :
( ~ ( in @ SY1644 @ SV234 )
| ~ ( in @ ( kpair @ SY1642 @ SY1644 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1644 @ SY1643 ) @ SV822 )
| ( in @ ( kpair @ SY1642 @ SY1643 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2767,plain,
! [SV524: $i,SV235: $i] :
( ( ( ! [SY1221: $i] :
~ ~ ( ~ ( in @ SY1221 @ SV235 )
| ~ ( in @ SY1221 @ SV524 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2768,plain,
! [SV236: $i,SV525: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ SV525 ) )
= $true )
| ( ( in @ SV707 @ ( binintersect @ SV236 @ SV525 ) )
= $true )
| ( ( in @ SV707 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2769,plain,
! [SV756: $i,SV708: $i,SV526: $i,SV237: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV237 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV237 @ ( setadjoin @ SV526 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV708 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV708 @ ( setadjoin @ SV756 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV237 = SV708 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2770,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i,SV757: $i] :
( ( ( in @ SV757 @ SV238 )
= $false )
| ( ( ! [SY1570: $i] :
( ~ ( in @ SY1570 @ SV527 )
| ~ ( in @ ( kpair @ SV757 @ SY1570 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SY1570 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2771,plain,
! [SV239: $i,SV710: $i,SV528: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV528 )
| ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SV903 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) ) )
= $true )
| ( ( in @ SV710 @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2503]) ).
thf(2772,plain,
! [SV529: $i,SV240: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ ( powerset @ SV240 ) ) )
= $true )
| ( ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SV823 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2504]) ).
thf(2773,plain,
! [SV711: $i,SV530: $o,SV241: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV241 )
| ( in @ ( if @ SV241 @ SV530 @ SV711 @ SV904 ) @ SV241 ) )
= $true )
| ( ( in @ SV711 @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2505]) ).
thf(2774,plain,
! [SV712: $i,SV241: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ SV241 )
| ( in @ ( if @ SV241 @ $true @ SV712 @ SV905 ) @ SV241 ) )
= $true )
| ( ( in @ SV712 @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2775,plain,
! [SV713: $i,SV241: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ SV241 )
| ( in @ ( if @ SV241 @ $false @ SV713 @ SV906 ) @ SV241 ) )
= $true )
| ( ( in @ SV713 @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2507]) ).
thf(2776,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2777,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1645: $i] :
( ~ ( in @ SY1645 @ SV245 )
| ~ ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
| ~ ( SV534 @ SY1645 )
| ( ( sK20_SY1240 @ SV534 @ SV245 )
= SY1645 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2509]) ).
thf(2778,plain,
! [SV758: $i,SV715: $i,SV535: $i,SV246: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV246 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV246 @ ( setadjoin @ SV535 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV715 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV715 @ ( setadjoin @ SV758 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV535 = SV758 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2779,plain,
! [SV248: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ ( powerset @ SV248 ) ) )
= $true )
| ( ( ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2780,plain,
! [SV248: $i,SV537: $i] :
( ( ( ~ ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) ) )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2781,plain,
! [SV716: $i,SV538: $i,SV250: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV250 )
| ! [SY1723: $i] :
( ~ ( in @ SY1723 @ SV538 )
| ~ ( in @ ( kpair @ SV907 @ SY1723 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SY1723 ) ) )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2513]) ).
thf(2782,plain,
! [SV539: $i,SV251: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ SV251 ) )
= $true )
| ( ( ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV251 )
| ~ ( in @ ( kpair @ SV824 @ SY1646 ) @ SV539 )
| ( in @ ( kpair @ SY1646 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) )
= $true )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2783,plain,
! [SV540: $i,SV252: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV252 ) )
= $true )
| ( ( ! [SY1647: $i] :
( ~ ( in @ SY1647 @ SV252 )
| ~ ( in @ ( kpair @ SY1647 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SY1647 ) @ SV540 ) ) )
= $true )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2515]) ).
thf(2784,plain,
! [SV545: $i,SV826: $i,SV255: $i] :
( ( ( ~ ( breln1 @ SV255 @ SV826 ) )
= $true )
| ( ( ! [SY1648: $i] :
( ~ ( in @ SY1648 @ SV255 )
| ! [SY1649: $i] :
( ~ ( in @ SY1649 @ SV255 )
| ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1650: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV545 )
| SY1650 )
| ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV826 )
| SY1650 )
| SY1650 ) ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2785,plain,
! [SV257: $i,SV719: $i,SV547: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV547 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SV908 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) ) )
= $true )
| ( ( in @ SV719 @ SV257 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2519]) ).
thf(2786,plain,
! [SV548: $i,SV258: $i,SV827: $i] :
( ( ( ~ ( in @ SV827 @ ( powerset @ SV258 ) ) )
= $true )
| ( ( ! [SY1651: $i] :
( ~ ( in @ SY1651 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1651 ) @ ( binunion @ SV827 @ SY1651 ) ) ) ) ) )
= $true )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2787,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ( ( sK21_SY1266 @ SV550 @ SV260 )
!= ( sK34_SY1652 @ SV260 @ SV550 ) )
| ~ ( ~ ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
| ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2522]) ).
thf(2788,plain,
! [SV552: $i,SV263: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ ( powerset @ SV263 ) ) )
= $true )
| ( ( ! [SY1653: $i] :
( ~ ( in @ SY1653 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1653 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SY1653 ) ) )
= $true )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2524]) ).
thf(2789,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ( breln1 @ SV264 @ SV829 ) )
= $true )
| ( ( ~ ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV264 )
| ! [SY1655: $i] :
( ~ ( in @ SY1655 @ SV264 )
| ~ ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV553 )
| ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV829 ) ) )
| ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2790,plain,
! [SV265: $i,SV554: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ SV554 ) )
= $true )
| ( ( ~ ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) ) )
= $true )
| ( ( in @ SV721 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2791,plain,
! [SV557: $i,SV268: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ SV268 ) )
= $true )
| ( ( ~ ( in @ SV830 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SV830 @ SV557 ) )
= $true )
| ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2528]) ).
thf(2792,plain,
! [SV558: $i > $o,SV269: $i,SV909: $i] :
( ( ( ~ ~ ( ~ ( in @ SV909 @ SV269 )
| ~ ~ ( SV558 @ SV909 ) ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2529]) ).
thf(2793,plain,
! [SV559: $i,SV270: $i,SV723: $i] :
( ( ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
= $true )
| ( ( ~ ~ ( in @ SV723 @ SV559 )
| ~ ( in @ SV723 @ SV270 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2530]) ).
thf(2794,plain,
! [SV560: $i,SV271: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ ( powerset @ SV271 ) ) )
= $true )
| ( ( ! [SY1658: $i] :
( ~ ( in @ SY1658 @ SV271 )
| ~ ( in @ SY1658 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SY1658 @ ( setminus @ SV271 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2795,plain,
! [SV562: $i,SV832: $i,SV274: $i] :
( ( ( ~ ( breln1 @ SV274 @ SV832 ) )
= $true )
| ( ( ! [SY1659: $i] :
( ~ ( in @ SY1659 @ SV274 )
| ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV274 )
| ~ ( in @ ( kpair @ SY1659 @ SY1660 ) @ SV562 )
| ( in @ ( kpair @ SY1659 @ SY1660 ) @ ( binunion @ SV562 @ SV832 ) ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2796,plain,
! [SV564: $i,SV276: $i,SV725: $i] :
( ( ( in @ SV725 @ SV276 )
= $true )
| ( ( ~ ~ ( in @ SV725 @ SV564 )
| ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2797,plain,
! [SV278: $i,SV726: $i,SV566: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV566 )
| ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 ) )
= $true )
| ( ( in @ SV726 @ SV278 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2536]) ).
thf(2798,plain,
! [SV281: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY742 @ SV281 ) @ SV281 )
| ~ $true ) )
= $false )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2538]) ).
thf(2799,plain,
! [SV911: $i > $o,SV833: $i > $o,SV569: $i,SV283: $i] :
( ( ( ~ ! [SY1724: $i] :
( ~ ( in @ SY1724 @ SV283 )
| ! [SY1725: $i] :
( ~ ( in @ SY1725 @ SV569 )
| ( SY1724 != SY1725 )
| ~ ( ~ ( ~ ( SV833 @ SY1724 )
| ( SV911 @ SY1725 ) )
| ~ ( ~ ( SV911 @ SY1725 )
| ( SV833 @ SY1724 ) ) ) ) )
| ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2800,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( ~ ( SV284 @ SV834 )
| ~ ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) ) )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2540]) ).
thf(2801,plain,
! [SV570: $i,SV285: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ ( powerset @ SV285 ) ) )
= $true )
| ( ( ! [SY1667: $i] :
( ~ ( in @ SY1667 @ SV285 )
| ~ ( in @ SY1667 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1667 @ ( binintersect @ SV570 @ SV835 ) ) ) )
= $true )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2802,plain,
! [SV759: $o,SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| SV759 )
| ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2543]) ).
thf(2803,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $true )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2804,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $false )
| ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2805,plain,
! [SV573: $i,SV836: $i,SV288: $i] :
( ( ( ~ ( breln1 @ SV288 @ SV836 ) )
= $true )
| ( ( ! [SY1668: $i] :
( ~ ( in @ SY1668 @ SV288 )
| ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV288 )
| ~ ( in @ ( kpair @ SY1668 @ SY1669 ) @ SV836 )
| ( in @ ( kpair @ SY1668 @ SY1669 ) @ ( binunion @ SV573 @ SV836 ) ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2546]) ).
thf(2806,plain,
! [SV731: $i,SV576: $o,SV291: $i,SV912: $i] :
( ( ( ~ ( in @ SV912 @ SV291 )
| ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 ) )
= $true )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2547]) ).
thf(2807,plain,
! [SV732: $i,SV291: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV291 )
| ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 ) )
= $true )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2548]) ).
thf(2808,plain,
! [SV733: $i,SV291: $i,SV914: $i] :
( ( ( ~ ( in @ SV914 @ SV291 )
| ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 ) )
= $true )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2809,plain,
! [SV578: $i,SV837: $i,SV294: $i] :
( ( ( ~ ( breln1 @ SV294 @ SV837 ) )
= $true )
| ( ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SV837 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SV837 ) @ ( breln1invset @ SV294 @ SV578 ) ) )
= $true )
| ( ( breln1 @ SV294 @ SV578 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2810,plain,
! [SV580: $i,SV296: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ ( powerset @ SV296 ) ) )
= $true )
| ( ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV296 )
| ~ ( in @ SY1670 @ SV580 )
| ( in @ SY1670 @ SV838 ) )
| ( in @ SV580 @ ( powerset @ SV838 ) ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2551]) ).
thf(2811,plain,
! [SV581: $i,SV839: $i,SV297: $i] :
( ( ( ~ ( breln1 @ SV297 @ SV839 ) )
= $true )
| ( ( ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV297 )
| ! [SY1672: $i] :
( ~ ( in @ SY1672 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV581 )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV839 ) )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ ( binunion @ SV581 @ SV839 ) ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2552]) ).
thf(2812,plain,
! [SV734: $i,SV915: $i,SV582: $i,SV298: $i] :
( ( ( ~ ( breln @ SV298 @ SV582 @ SV915 )
| ~ ! [SY1728: $i] :
( ~ ( in @ SY1728 @ SV298 )
| ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV582 )
| ~ ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV734 )
| ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV915 ) ) )
| ( subset @ SV734 @ SV915 ) )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2553]) ).
thf(2813,plain,
! [SV583: $i,SV299: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ ( powerset @ SV299 ) ) )
= $true )
| ( ( ! [SY1673: $i] :
( ~ ( in @ SY1673 @ SV299 )
| ~ ( in @ SY1673 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SY1673 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) ) )
= $true )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2814,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( ~ ( SV300 @ SV841 )
| ~ ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) ) )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2815,plain,
! [SV584: $i,SV301: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ ( powerset @ SV301 ) ) )
= $true )
| ( ( ! [SY1675: $i] :
( ~ ( in @ SY1675 @ SV301 )
| ~ ( in @ SY1675 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1675 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2816,plain,
! [SV585: $i,SV302: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ ( powerset @ SV302 ) ) )
= $true )
| ( ( ! [SY1676: $i] :
( ~ ( in @ SY1676 @ SV302 )
| ~ ( in @ SY1676 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SY1676 @ ( setminus @ SV302 @ SV585 ) ) ) )
= $true )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2817,plain,
! [SV304: $i] :
( ( ( ~ ( in @ ( sK36_SY804 @ SV304 ) @ SV304 ) )
= $false )
| ( ( SV304 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2558]) ).
thf(2818,plain,
! [SV587: $i,SV305: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ ( powerset @ SV305 ) ) )
= $true )
| ( ( ! [SY1677: $i] :
( ~ ( in @ SY1677 @ ( binintersect @ SV587 @ SV844 ) )
| ( in @ SY1677 @ SV305 ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2559]) ).
thf(2819,plain,
! [SV588: $i,SV306: $i,SV735: $i] :
( ( ( ~ ( in @ SV735 @ SV306 ) )
= $true )
| ( ( in @ SV588 @ ( setunion @ SV306 ) )
= $true )
| ( ( in @ SV588 @ SV735 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2560]) ).
thf(2820,plain,
! [SV589: $i,SV307: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ SV307 ) )
= $true )
| ( ( ~ ( in @ SV845 @ SV589 )
| ~ ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2561]) ).
thf(2821,plain,
! [SV590: $i,SV308: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ ( powerset @ SV308 ) ) )
= $true )
| ( ( ( setminus @ SV308 @ ( binunion @ SV590 @ SV846 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SV846 ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2822,plain,
! [SV591: $i,SV916: $o,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| SV916 )
| ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2563]) ).
thf(2823,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| $true )
| ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2563]) ).
thf(2824,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| $false )
| ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2563]) ).
thf(2825,plain,
! [SV592: $i,SV310: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ ( powerset @ SV310 ) ) )
= $true )
| ( ( ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV310 )
| ~ ( in @ SY1678 @ SV592 )
| ( in @ SY1678 @ SV847 ) )
| ( subset @ SV592 @ SV847 ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2826,plain,
! [SV594: $i,SV312: $i,SV737: $i] :
( ( ( in @ SV737 @ SV312 )
= $true )
| ( ( in @ SV737 @ SV594 )
= $true )
| ( ( in @ SV737 @ ( binunion @ SV312 @ SV594 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2565]) ).
thf(2827,plain,
! [SV313: $i,SV738: $i,SV595: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV595 )
| ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SV917 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) ) )
= $true )
| ( ( in @ SV738 @ SV313 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2828,plain,
! [SV739: $i > $i > $o,SV596: $i,SV314: $i,SV760: $i] :
( ( ( in @ SV760 @ SV314 )
= $false )
| ( ( ! [SY1573: $i] :
( ~ ( in @ SY1573 @ SV596 )
| ~ ( SV739 @ SV760 @ SY1573 )
| ( in @ ( kpair @ SV760 @ SY1573 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2567]) ).
thf(2829,plain,
! [SV597: $i,SV315: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ ( powerset @ SV315 ) ) )
= $true )
| ( ( ! [SY1679: $o,SY1680: $i] :
( ~ ( in @ SY1680 @ SV315 )
| ~ ( in @ SY1680 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SY1680 @ SV597 )
| SY1679 )
| ~ ( ~ ( in @ SY1680 @ SV848 )
| SY1679 )
| SY1679 ) )
= $true )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2830,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( ~ ( in @ SV849 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY1681: $i] :
( ~ ( in @ SY1681 @ ( powerset @ SV317 ) )
| ! [SY1682: $i] :
( ~ ( in @ SY1682 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SY1681 @ SY1682 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1681 ) @ ( setminus @ SV317 @ SY1682 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2831,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ ( powerset @ SV318 ) ) )
= $true )
| ( ( ! [SY1683: $i] :
( ~ ( in @ SY1683 @ SV318 )
| ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SY1683 @ SV850 )
| ~ ( in @ SY1683 @ SV600 ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2570]) ).
thf(2832,plain,
! [SV740: $i,SV601: $i,SV319: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV319 )
| ( in @ ( kpair @ SV918 @ ( ap @ SV319 @ SV601 @ SV740 @ SV918 ) ) @ SV740 ) )
= $true )
| ( ( func @ SV319 @ SV601 @ SV740 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2833,plain,
! [SV602: $i,SV320: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ SV320 ) )
= $true )
| ( ( in @ SV741 @ SV602 )
= $true )
| ( ( subset @ SV320 @ SV602 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2834,plain,
! [SV321: $i,SV603: $i,SV742: $i] :
( ( ( ~ ( subset @ SV742 @ SV603 ) )
= $true )
| ( ( subset @ SV742 @ ( binintersect @ SV321 @ SV603 ) )
= $true )
| ( ( subset @ SV742 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2573]) ).
thf(2835,plain,
! [SV604: $i,SV322: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ ( powerset @ SV322 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV604 @ SV851 ) @ ( powerset @ SV322 ) )
= $true )
| ( ( in @ SV604 @ ( powerset @ SV322 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2836,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ( ~ ( SV323 @ SV852 )
| ~ ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) ) )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2837,plain,
! [SV324: $i,SV743: $i,SV605: $i,SV919: $i] :
( ( ( ~ ( in @ SV919 @ SV605 )
| ( ( kpair @ SV743 @ SV919 )
= ( kpair @ SV743 @ SV919 ) ) )
= $true )
| ( ( in @ SV743 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2576]) ).
thf(2838,plain,
! [SV607: $i,SV326: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( powerset @ SV326 ) ) )
= $true )
| ( ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SV853 ) ) ) )
= $true )
| ( ( in @ SV607 @ ( powerset @ SV326 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2839,plain,
! [SV3: $i,SV920: $i] :
( ( ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ SV920 )
| ( subset @ SY1730 @ SV920 ) )
| ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2579]) ).
thf(2840,plain,
! [SV3: $i,SV854: $i] :
( ( ( ~ ! [SY1685: $i] :
( ~ ( in @ SY1685 @ SV854 )
| ( subset @ SY1685 @ SV854 ) ) )
= $true )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2841,plain,
! [SV4: $i,SV608: $i > $i,SV329: $i] :
( ( ( ~ ( in @ ( sK22_SY1366 @ SV329 @ SV608 @ SV4 ) @ SV4 ) )
= $false )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2842,plain,
! [SV4: $i,SV329: $i,SV608: $i > $i] :
( ( ( in @ ( SV608 @ ( sK22_SY1366 @ SV329 @ SV608 @ SV4 ) ) @ SV329 )
= $false )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2581]) ).
thf(2843,plain,
! [SV6: $i,SV609: $i,SV330: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV330 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV609 @ SV855 ) )
= SV855 )
= $true )
| ( ( in @ SV609 @ SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2844,plain,
! [SV8: $i,SV611: $i,SV332: $i > $o] :
( ( ( SV332 @ SV611 )
= $false )
| ( ( ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) )
| ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) ) )
= $true )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2845,plain,
! [SV612: $i,SV333: $i,SV9: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV9 ) )
= $true )
| ( ( ( ap @ SV9 @ SV333 @ SV612 @ SV856 )
= ( ap @ SV9 @ SV333 @ SV612 @ SV856 ) )
= $true )
| ( ( func @ SV9 @ SV333 @ SV612 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2584]) ).
thf(2846,plain,
! [SV10: $i,SV613: $i,SV334: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ SV334 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SV857 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) )
= $true )
| ( ( in @ SV613 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2585]) ).
thf(2847,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i] :
( ( ( ~ ( func @ SV11 @ SV335 @ SV858 ) )
= $true )
| ( ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1687 )
= ( ap @ SV11 @ SV335 @ SV858 @ SY1687 ) ) )
| ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2586]) ).
thf(2848,plain,
! [SV14: $i,SV615: $i > $i,SV337: $i] :
( ( ( ~ ( in @ ( sK23_SY1378 @ SV337 @ SV615 @ SV14 ) @ SV14 ) )
= $false )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2587]) ).
thf(2849,plain,
! [SV14: $i,SV337: $i,SV615: $i > $i] :
( ( ( in @ ( SV615 @ ( sK23_SY1378 @ SV337 @ SV615 @ SV14 ) ) @ SV337 )
= $false )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2587]) ).
thf(2850,plain,
! [SV340: $i,SV17: $i,SV761: $i] :
( ( ( in @ SV761 @ ( powerset @ SV17 ) )
= $false )
| ( ( ! [SY1576: $i] :
( ~ ( in @ SY1576 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SY1576 ) @ ( binunion @ SV761 @ SY1576 ) ) ) ) ) )
= $true )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2851,plain,
! [SV859: $i > $o,SV618: $i,SV342: $i,SV19: $i] :
( ( ( ~ ! [SY1690: $i] :
( ~ ( in @ SY1690 @ SV19 )
| ! [SY1691: $i] :
( ~ ( in @ SY1691 @ SV342 )
| ~ ( in @ ( kpair @ SY1690 @ SY1691 ) @ SV618 )
| ( SV859 @ ( kpair @ SY1690 @ SY1691 ) ) ) ) )
= $true )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2589]) ).
thf(2852,plain,
! [SV343: $i,SV20: $i,SV762: $i] :
( ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( ! [SY1577: $i] :
( ~ ( in @ SY1577 @ SV20 )
| ~ ~ ( in @ SY1577 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SY1577 @ SV762 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2853,plain,
! [SV344: $i,SV21: $i,SV763: $i] :
( ( ( in @ SV763 @ ( powerset @ SV21 ) )
= $false )
| ( ( ~ ( subset @ SV344 @ ( setminus @ SV21 @ SV763 ) )
| ( subset @ SV763 @ ( setminus @ SV21 @ SV344 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2854,plain,
! [SV346: $i,SV24: $i,SV860: $i,SV764: $i] :
( ( ( SV764 != SV860 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) )
| ~ ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2592]) ).
thf(2855,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
| ~ ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) ) ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2593]) ).
thf(2856,plain,
! [SV27: $i,SV348: $i > $o] :
( ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2594]) ).
thf(2857,plain,
! [SV27: $i,SV348: $i > $o] :
( ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true )
| ( ( ~ ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2858,plain,
! [SV619: $i,SV349: $i,SV28: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV28 ) )
= $true )
| ( ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SV861 ) @ SV349 )
= $true )
| ( ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2596]) ).
thf(2859,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( ~ ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) ) )
= $true )
| ( ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2597]) ).
thf(2860,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( ~ ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) ) )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2861,plain,
! [SV353: $i,SV34: $i,SV765: $i] :
( ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( ! [SY1579: $i] :
( ~ ( in @ SY1579 @ SV34 )
| ~ ~ ( in @ SY1579 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SY1579 @ SV353 ) ) )
= $true )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2862,plain,
! [SV354: $i,SV35: $i,SV766: $i] :
( ( ( in @ SV766 @ ( powerset @ SV35 ) )
= $false )
| ( ( ( setminus @ SV35 @ ( binintersect @ SV354 @ SV766 ) )
= ( binunion @ ( setminus @ SV35 @ SV354 ) @ ( setminus @ SV35 @ SV766 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2863,plain,
! [SV356: $i,SV38: $i,SV767: $i] :
( ( ( in @ SV767 @ ( powerset @ SV38 ) )
= $false )
| ( ( in @ ( setminus @ SV356 @ SV767 ) @ ( powerset @ SV38 ) )
= $true )
| ( ( in @ SV356 @ ( powerset @ SV38 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2864,plain,
! [SV357: $i,SV768: $i,SV40: $i] :
( ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SV40 )
| ! [SY1581: $i] :
( ~ ( in @ SY1581 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1581 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1582: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1582 @ SV40 )
| ~ ( in @ ( kpair @ SY1580 @ SY1582 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1582 @ SY1581 ) @ SV768 ) ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2603]) ).
thf(2865,plain,
! [SV358: $i,SV769: $i,SV41: $i] :
( ( ( breln1 @ SV41 @ SV769 )
= $false )
| ( ( ! [SY1583: $i] :
( ~ ( breln1 @ SV41 @ SY1583 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SY1583 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SY1583 ) @ ( breln1compset @ SV41 @ SV769 @ SY1583 ) ) ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2866,plain,
! [SV359: $i,SV42: $i,SV770: $i] :
( ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( ! [SY1584: $i] :
( ~ ( in @ SY1584 @ SV42 )
| ~ ( in @ SY1584 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SY1584 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) ) )
= $true )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2867,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i,SV921: $i] :
( ( ( ~ ~ ( ~ ( in @ SV921 @ SV43 )
| ( SV623
!= ( SV360 @ SV921 ) ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2606]) ).
thf(2868,plain,
! [SV362: $i,SV771: $i,SV45: $i] :
( ( ( breln1 @ SV45 @ SV771 )
= $false )
| ( ( breln1 @ SV45 @ ( binunion @ SV362 @ SV771 ) )
= $true )
| ( ( breln1 @ SV45 @ SV362 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2607]) ).
thf(2869,plain,
! [SV47: $i,SV364: $i] :
( ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false )
| ( ( ~ ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2870,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2871,plain,
! [SV366: $i,SV772: $i,SV49: $i] :
( ( ( breln1 @ SV49 @ SV772 )
= $false )
| ( ( ( binunion @ SV366 @ SV772 )
= ( binunion @ SV772 @ SV366 ) )
= $true )
| ( ( breln1 @ SV49 @ SV366 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2872,plain,
! [SV746: $i,SV51: $i] :
( ( ( ( omegaS @ SV51 )
!= ( omegaS @ SV746 ) )
= $true )
| ( ( SV51 = SV746 )
= $true )
| ( ( in @ SV746 @ omega )
= $false )
| ( ( in @ SV51 @ omega )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2873,plain,
! [SV367: $i,SV52: $i,SV773: $i] :
( ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( in @ SY1585 @ SV52 )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SY1585 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SY1585 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) ) )
= $true )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2874,plain,
! [SV368: $i,SV53: $i,SV774: $i] :
( ( ( in @ SV774 @ ( powerset @ SV53 ) )
= $false )
| ( ( ~ ( subset @ SV368 @ SV774 )
| ( subset @ ( setminus @ SV53 @ SV774 ) @ ( setminus @ SV53 @ SV368 ) ) )
= $true )
| ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2875,plain,
! [SV369: $i,SV54: $i,SV775: $i] :
( ( ( in @ SV775 @ ( powerset @ SV54 ) )
= $false )
| ( ( ~ ( subset @ ( setminus @ SV54 @ SV775 ) @ ( setminus @ SV54 @ SV369 ) )
| ( subset @ SV369 @ SV775 ) )
= $true )
| ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2616]) ).
thf(2876,plain,
! [SV370: $i,SV55: $i,SV776: $i] :
( ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( ~ ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
| ! [SY1586: $i] :
( ~ ( in @ SY1586 @ SV55 )
| ~ ( in @ SY1586 @ SV776 )
| ( in @ SY1586 @ ( setminus @ SV55 @ SV370 ) ) ) )
= $true )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2617]) ).
thf(2877,plain,
! [SV372: $i,SV57: $i,SV777: $i] :
( ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( in @ SY1587 @ SV57 )
| ~ ( in @ SY1587 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SY1587 @ SV372 ) ) )
= $true )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2878,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
| ~ ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) ) ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2619]) ).
thf(2879,plain,
! [SV376: $i > $o,SV61: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV61 ) )
= $true )
| ( ( SV376 @ SV862 )
= $true )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2622]) ).
thf(2880,plain,
! [SV62: $i,SV629: $i > $i,SV377: $i] :
( ( ( ~ ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 ) )
= $false )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2881,plain,
! [SV62: $i,SV377: $i,SV629: $i > $i] :
( ( ( in @ ( SV629 @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) ) @ SV377 )
= $false )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2623]) ).
thf(2882,plain,
! [SV378: $i,SV63: $i,SV630: $i] :
( ( ( in @ SV630 @ ( setminus @ SV63 @ SV378 ) )
= $false )
| ( ( in @ SV630 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2883,plain,
! [SV380: $i,SV66: $i,SV778: $i] :
( ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( ! [SY1588: $i] :
( ~ ( in @ SY1588 @ SV66 )
| ~ ~ ( in @ SY1588 @ SV380 )
| ~ ~ ( in @ SY1588 @ SV778 )
| ~ ( in @ SY1588 @ ( binunion @ SV380 @ SV778 ) ) ) )
= $true )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2884,plain,
! [SV381: $i,SV67: $i,SV863: $i,SV779: $i] :
( ( ( SV779 != SV863 )
= $true )
| ( ( ~ ( in @ SV779 @ SV67 )
| ( in @ SV863 @ SV381 ) )
= $true )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2626]) ).
thf(2885,plain,
! [SV632: $i,SV383: $o,SV70: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV70 ) )
= $true )
| ( ( ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) ) )
= $true )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2628]) ).
thf(2886,plain,
! [SV633: $i,SV70: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ SV70 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) ) )
= $true )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2629]) ).
thf(2887,plain,
! [SV634: $i,SV70: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV70 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) ) )
= $true )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2630]) ).
thf(2888,plain,
! [SV780: $i,SV73: $i] :
( ( ( ! [SY168: $i] :
~ ~ ( ~ ( in @ SY168 @ SV73 )
| ~ ~ ~ ! [SY169: $i] :
~ ~ ( ~ ( in @ SY169 @ SY168 )
| ~ ( in @ SY169 @ SV73 ) ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2889,plain,
! [SV635: $i,SV385: $i,SV75: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV75 ) )
= $true )
| ( ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SV867 ) @ SV385 )
= $true )
| ( ( func @ SV75 @ SV385 @ SV635 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2890,plain,
! [SV386: $i,SV76: $i,SV781: $i] :
( ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( ! [SY1590: $i] :
( ~ ( in @ SY1590 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SY1590 @ SV386 )
| ( in @ SY1590 @ SV781 ) ) )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2633]) ).
thf(2891,plain,
! [SV387: $i,SV77: $i,SV782: $i] :
( ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( ! [SY1591: $i] :
( ~ ( in @ SY1591 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SY1591 @ SV782 )
| ~ ( in @ SY1591 @ SV387 ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2892,plain,
! [SV79: $i,SV637: $i,SV389: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ SV389 ) )
= $true )
| ( ( in @ ( kpair @ SV637 @ SV868 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) )
= $true )
| ( ( in @ SV637 @ SV79 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2893,plain,
! [SV390: $i,SV80: $i,SV783: $i] :
( ( ( in @ SV783 @ ( powerset @ SV80 ) )
= $false )
| ( ( in @ ( setminus @ SV80 @ SV390 ) @ ( powerset @ ( setminus @ SV80 @ ( binintersect @ SV390 @ SV783 ) ) ) )
= $true )
| ( ( in @ SV390 @ ( powerset @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2894,plain,
! [SV392: $i,SV82: $i,SV784: $i] :
( ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( ! [SY1592: $i] :
( ~ ( in @ SY1592 @ SV82 )
| ~ ~ ( in @ SY1592 @ SV392 )
| ~ ( in @ SY1592 @ ( binintersect @ SV392 @ SV784 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2895,plain,
! [SV638: $i > $i > $o,SV393: $i,SV83: $i,SV785: $i,SV748: $i] :
( ( ( in @ ( kpair @ SV748 @ SV785 )
@ ( dpsetconstr @ SV83 @ SV393
@ ^ [SY1404: $i,SY1405: $i] : ( SV638 @ SY1404 @ SY1405 ) ) )
= $false )
| ( ( SV638 @ SV748 @ SV785 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2896,plain,
! [SV639: $i,SV394: $i,SV84: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ SV84 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1696: $i] : ( in @ ( kpair @ SV869 @ SY1696 ) @ SV639 ) ) )
= $true )
| ( ( func @ SV84 @ SV394 @ SV639 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2640]) ).
thf(2897,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ( ~ ( in @ SV640 @ SV85 ) )
= $true )
| ( ( in @ SV640 @ SV395 )
= $true )
| ( ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2641]) ).
thf(2898,plain,
! [SV87: $i,SV397: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV397 ) )
= $false )
| ( ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) )
= $true )
| ( ( in @ SV641 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2642]) ).
thf(2899,plain,
! [SV89: $i,SV642: $i > $i,SV399: $i] :
( ( ( ~ ( in @ ( sK25_SY1408 @ SV399 @ SV642 @ SV89 ) @ SV89 ) )
= $false )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2643]) ).
thf(2900,plain,
! [SV89: $i,SV399: $i,SV642: $i > $i] :
( ( ( in @ ( SV642 @ ( sK25_SY1408 @ SV399 @ SV642 @ SV89 ) ) @ SV399 )
= $false )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2643]) ).
thf(2901,plain,
! [SV643: $i,SV401: $i,SV91: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ SV91 ) )
= $true )
| ( ( in @ ( kpair @ SV870 @ ( ap @ SV91 @ SV401 @ SV643 @ SV870 ) ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2902,plain,
! [SV402: $i,SV786: $i,SV93: $i] :
( ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( ! [SY1595: $i] :
( ~ ( in @ SY1595 @ SV93 )
| ! [SY1596: $i] :
( ~ ( in @ SY1596 @ SV93 )
| ~ ( in @ ( kpair @ SY1595 @ SY1596 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV402 )
| ( in @ ( kpair @ SY1595 @ SY1596 ) @ SV786 ) ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2903,plain,
! [SV644: $i,SV403: $o,SV94: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV94 ) )
= $true )
| ( ( ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1697: $i] :
( ~ ( ~ SV403
| ( SY1697 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1697 != SV871 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2904,plain,
! [SV645: $i,SV94: $i,SV872: $i] :
( ( ( ~ ( in @ SV872 @ SV94 ) )
= $true )
| ( ( ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1698: $i] :
( ~ ( ~ $true
| ( SY1698 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1698 != SV872 ) ) ) ) ) )
= $true )
| ( ( in @ SV645 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2647]) ).
thf(2905,plain,
! [SV646: $i,SV94: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ SV94 ) )
= $true )
| ( ( ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1699: $i] :
( ~ ( ~ $false
| ( SY1699 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1699 != SV873 ) ) ) ) ) )
= $true )
| ( ( in @ SV646 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2648]) ).
thf(2906,plain,
! [SV404: $i,SV95: $i] :
( ( ( in @ ( sK12_SY994 @ SV95 @ SV404 ) @ SV404 )
= $true )
| ( ( in @ SV404 @ ( powerset @ SV95 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2649]) ).
thf(2907,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SV874 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2908,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2652]) ).
thf(2909,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2910,plain,
! [SV408: $i,SV787: $i,SV99: $i] :
( ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( ! [SY1597: $i] :
( ~ ( in @ SY1597 @ SV99 )
| ! [SY1598: $i] :
( ~ ( in @ SY1598 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1598 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1599: $o] :
( ~ ! [SY1600: $i] :
( ~ ( in @ SY1600 @ SV99 )
| ~ ( in @ ( kpair @ SY1597 @ SY1600 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1600 @ SY1598 ) @ SV787 )
| SY1599 )
| SY1599 ) ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2911,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ( sK13_SY1008 @ SV415 @ SV107 )
!= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2912,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
| ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2656]) ).
thf(2913,plain,
! [SV416: $i,SV108: $i,SV788: $i] :
( ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( ! [SY1602: $i] :
( ~ ( in @ SY1602 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SY1602 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SY1602 ) ) ) )
= $true )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2914,plain,
! [SV651: $i,SV417: $i,SV109: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) ) )
= $true )
| ( ( ~ ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1700 )
= ( ap @ SV109 @ SV417 @ SV875 @ SY1700 ) ) )
| ( SV651 = SV875 ) )
= $true )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2658]) ).
thf(2915,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SV111 )
| ~ ~ ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2659]) ).
thf(2916,plain,
! [SV113: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY275 @ SV113 ) @ SV113 )
| ( ( binintersect @ ( sK27_SY275 @ SV113 ) @ SV113 )
!= emptyset ) ) )
= $true )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2660]) ).
thf(2917,plain,
! [SV423: $i,SV116: $i,SV789: $i] :
( ( ( in @ SV789 @ ( powerset @ SV116 ) )
= $false )
| ( ( subset @ ( setminus @ SV116 @ SV423 ) @ ( setminus @ SV116 @ ( binintersect @ SV423 @ SV789 ) ) )
= $true )
| ( ( in @ SV423 @ ( powerset @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2918,plain,
! [SV424: $i,SV117: $i,SV790: $i] :
( ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( ! [SY1603: $i] :
( ~ ( in @ SY1603 @ ( powerset @ SV117 ) )
| ! [SY1604: $i] :
( ~ ( in @ SY1604 @ SV117 )
| ~ ( in @ SY1604 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1604 @ ( binintersect @ ( binunion @ SV424 @ SY1603 ) @ ( binunion @ SV790 @ SY1603 ) ) ) ) ) )
= $true )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2919,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2920,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
| ~ ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
| ~ ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
| ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2664]) ).
thf(2921,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ~ ( ~ ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
| ~ ( ~ ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) )
| ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2922,plain,
! [SV655: $i,SV427: $i,SV120: $i,SV877: $i] :
( ( ( ~ ( in @ SV877 @ SV120 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1703: $i] : ( in @ ( kpair @ SV877 @ SY1703 ) @ SV655 ) ) )
@ SV427 )
= $true )
| ( ( func @ SV120 @ SV427 @ SV655 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2666]) ).
thf(2923,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2924,plain,
! [SV122: $i,SV429: $i] :
( ( ( in @ ( sK16_SY1044 @ SV429 @ SV122 ) @ SV122 )
= $true )
| ( ( subset @ SV122 @ SV429 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2668]) ).
thf(2925,plain,
( ( ~ ( in @ sK3_SY2 @ sK2_SY0 )
| ~ ~ ( in @ sK3_SY2 @ sK1_X ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2926,plain,
! [SV124: $i,SV656: $i > $i,SV431: $i] :
( ( ( ~ ( in @ ( sK28_SY1428 @ SV431 @ SV656 @ SV124 ) @ SV124 ) )
= $false )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2927,plain,
! [SV124: $i,SV431: $i,SV656: $i > $i] :
( ( ( in @ ( SV656 @ ( sK28_SY1428 @ SV431 @ SV656 @ SV124 ) ) @ SV431 )
= $false )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2928,plain,
! [SV657: $i,SV432: $o,SV125: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ SV125 ) )
= $true )
| ( ( ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1704: $i] :
( ~ ( ~ SV432
| ( SY1704 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1704 != SV878 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2674]) ).
thf(2929,plain,
! [SV658: $i,SV125: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV125 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1705: $i] :
( ~ ( ~ $true
| ( SY1705 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1705 != SV879 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2930,plain,
! [SV659: $i,SV125: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV125 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1706: $i] :
( ~ ( ~ $false
| ( SY1706 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1706 != SV880 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2676]) ).
thf(2931,plain,
! [SV791: $o,SV126: $i,SV433: $i] :
( ( ( ! [SY1606: $i] :
( ~ ( in @ SV433 @ SY1606 )
| ~ ( in @ SY1606 @ SV126 )
| SV791 ) )
= $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2932,plain,
! [SV126: $i,SV433: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2933,plain,
! [SV126: $i,SV433: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV433 @ SX0 )
| ~ ( in @ SX0 @ SV126 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2679]) ).
thf(2934,plain,
! [SV435: $i,SV792: $i,SV128: $i] :
( ( ( breln1 @ SV128 @ SV792 )
= $false )
| ( ( breln1 @ SV128 @ ( breln1compset @ SV128 @ SV435 @ SV792 ) )
= $true )
| ( ( breln1 @ SV128 @ SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2680]) ).
thf(2935,plain,
! [SV131: $i,SV438: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV438 ) )
= $false )
| ( ( ~ ( subset @ SV131 @ SV438 ) )
= $true )
| ( ( in @ SV662 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2681]) ).
thf(2936,plain,
! [SV132: $i,SV439: $i,SV751: $i,SV663: $i] :
( ( ( SV663 != SV751 )
= $true )
| ( ( SV439 = SV751 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SV751 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2937,plain,
! [SV440: $i,SV133: $i,SV793: $i] :
( ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV133 )
| ~ ( in @ SY1607 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SY1607 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) ) )
= $true )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2683]) ).
thf(2938,plain,
! [SV441: $i,SV134: $i,SV794: $i] :
( ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ ( powerset @ SV134 ) )
| ! [SY1609: $i] :
( ~ ( in @ SY1609 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SY1608 )
| ~ ( subset @ SV794 @ SY1609 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SY1608 @ SY1609 ) ) ) ) )
= $true )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2684]) ).
thf(2939,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV795 )
| ~ ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2685]) ).
thf(2940,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV796 )
| ~ ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2686]) ).
thf(2941,plain,
! [SV664: $i,SV881: $i,SV444: $i,SV139: $i] :
( ( ( ~ ( func @ SV139 @ SV444 @ SV881 ) )
= $true )
| ( ( ~ ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1707 )
= ( ap @ SV139 @ SV444 @ SV881 @ SY1707 ) ) )
| ( SV664 = SV881 ) )
= $true )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2687]) ).
thf(2942,plain,
! [SV140: $i,SV445: $i > $i] :
( ( ~ ! [SY1557: $i] :
~ ( ~ ( ~ ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2688]) ).
thf(2943,plain,
! [SV445: $i > $i,SV140: $i] :
( ( ~ ! [SY1560: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1560 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1560 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SY1560 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2688]) ).
thf(2944,plain,
! [SV665: $i > $i > $o,SV446: $i,SV141: $i,SV797: $i,SV752: $i] :
( ( ( in @ ( kpair @ SV752 @ SV797 )
@ ( dpsetconstr @ SV141 @ SV446
@ ^ [SY1441: $i,SY1442: $i] : ( SV665 @ SY1441 @ SY1442 ) ) )
= $false )
| ( ( in @ SV752 @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2689]) ).
thf(2945,plain,
! [SV448: $i,SV143: $i,SV798: $i] :
( ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( ! [SY1614: $i] :
( ~ ( in @ SY1614 @ ( powerset @ SV143 ) )
| ~ ( subset @ SV798 @ SY1614 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SY1614 ) ) )
= $true )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2946,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK29_SY1085 @ SV449 @ SV144 ) @ SV144 )
| ~ ( SV449 @ ( sK29_SY1085 @ SV449 @ SV144 ) ) ) )
= $true )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2692]) ).
thf(2947,plain,
! [SV145: $i,SV450: $i] :
( ( ( in @ ( sK17_SY1086 @ SV450 @ SV145 ) @ SV145 )
= $true )
| ( ( subset @ SV145 @ SV450 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2948,plain,
! [SV799: $i > $o,SV451: $i,SV146: $i] :
( ( ( ! [SY1615: $i] :
( ~ ( in @ SY1615 @ SV146 )
| ! [SY1616: $i] :
( ~ ( in @ SY1616 @ SV146 )
| ~ ( in @ ( kpair @ SY1615 @ SY1616 ) @ SV451 )
| ( SV799 @ ( kpair @ SY1615 @ SY1616 ) ) ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2695]) ).
thf(2949,plain,
! [SV148: $i,SV667: $i,SV453: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) @ SV148 )
| ( SV667
!= ( SV453 @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) ) ) ) )
= $false )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2696]) ).
thf(2950,plain,
! [SV454: $i,SV149: $i,SV800: $i] :
( ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( ~ ! [SY1618: $i] :
( ~ ( in @ SY1618 @ SV149 )
| ~ ( in @ SY1618 @ SV454 )
| ( in @ SY1618 @ SV800 ) )
| ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2951,plain,
! [SV458: $i > $o,SV153: $i,SV882: $i] :
( ( ( ~ ( ~ ( in @ SV882 @ SV153 )
| ~ ( SV458 @ SV882 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2698]) ).
thf(2952,plain,
! [SV459: $i,SV801: $i,SV154: $i] :
( ( ( breln1 @ SV154 @ SV801 )
= $false )
| ( ( ! [SY1620: $i] :
( ~ ( breln1 @ SV154 @ SY1620 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SY1620 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SY1620 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2953,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV802 )
| ~ ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2700]) ).
thf(2954,plain,
! [SV803: $i > $o,SV460: $i,SV156: $i] :
( ( ( ! [SY1622: $i] :
( ~ ( in @ SY1622 @ SV156 )
| ! [SY1623: $i] :
( ~ ( in @ SY1623 @ SV156 )
| ~ ( in @ ( kpair @ SY1622 @ SY1623 ) @ SV460 )
| ( SV803 @ ( kpair @ SY1622 @ SY1623 ) ) ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2955,plain,
! [SV157: $i,SV669: $i,SV461: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV461 ) )
= $true )
| ( ( in @ ( kpair @ SV669 @ SV883 ) @ ( cartprod @ SV157 @ SV461 ) )
= $true )
| ( ( in @ SV669 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2702]) ).
thf(2956,plain,
! [SV670: $i,SV462: $o,SV158: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV158 ) )
= $true )
| ( ( ~ ~ SV462
| ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) ) )
= $true )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2703]) ).
thf(2957,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ SV158 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) ) )
= $true )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(2958,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV158 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) ) )
= $true )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2959,plain,
! [SV159: $i,SV463: $i,SV673: $i] :
( ( ( in @ SV673 @ SV463 )
= $false )
| ( ( in @ SV673 @ SV159 )
= $true )
| ( ( in @ SV463 @ ( powerset @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2960,plain,
! [SV160: $i,SV464: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV464 ) )
= $false )
| ( ( SV160 != SV464 )
= $true )
| ( ( in @ SV674 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2961,plain,
! [SV161: $i,SV675: $i,SV465: $i] :
( ( ( subset @ SV465 @ SV675 )
= $false )
| ( ( subset @ SV161 @ SV675 )
= $true )
| ( ( subset @ SV161 @ SV465 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2962,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( in @ SV804 @ SV163 )
= $false )
| ( ( ~ ~ ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) )
| ( in @ SV804 @ SV467 ) )
= $true )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2709]) ).
thf(2963,plain,
! [SV164: $i,SV468: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ SV468 ) )
= $false )
| ( ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) )
= $true )
| ( ( in @ SV676 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2964,plain,
! [SV165: $i,SV677: $i,SV469: $i > $o] :
( ( ( SV469 @ SV677 )
= $false )
| ( ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
!= emptyset )
= $true )
| ( ( in @ SV677 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2711]) ).
thf(2965,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) ) )
= $true )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2712]) ).
thf(2966,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV806 )
| ~ ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2713]) ).
thf(2967,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ( breln @ SV168 @ SV470 @ SV887 ) )
= $true )
| ( ( ~ ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV168 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SV470 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV678 )
| ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV887 ) ) )
| ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2714]) ).
thf(2968,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ( ~ ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) ) )
= $true )
| ( ( ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2969,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ( ~ ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2716]) ).
thf(2970,plain,
! [SV473: $i,SV171: $i,SV807: $i] :
( ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( ! [SY1626: $i] :
( ~ ( in @ SY1626 @ SV171 )
| ~ ~ ( in @ SY1626 @ SV807 )
| ~ ( in @ SY1626 @ ( binintersect @ SV473 @ SV807 ) ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2971,plain,
! [SV172: $i,SV680: $i > $i,SV474: $i] :
( ( ( ~ ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 ) )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2972,plain,
! [SV172: $i,SV474: $i,SV680: $i > $i] :
( ( ( in @ ( SV680 @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) ) @ SV474 )
= $false )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2973,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
| ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 ) )
| ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) ) )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2719]) ).
thf(2974,plain,
! [SV475: $i,SV175: $i,SV888: $i,SV809: $i] :
( ( ( SV809 != SV888 )
= $true )
| ( ( ( setadjoin @ SV175 @ SV809 )
= ( setadjoin @ SV475 @ SV888 ) )
= $true )
| ( ( SV175 = SV475 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2975,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( ~ ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) ) )
= $false )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2976,plain,
! [SV176: $i,SV681: $i,SV476: $i > $o] :
( ( ( ~ ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) ) )
= $false )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2721]) ).
thf(2977,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ( ~ ( in @ ( sK31_SY1142 @ SV478 @ SV178 ) @ SV178 )
| ~ ( in @ SV478 @ ( sK31_SY1142 @ SV478 @ SV178 ) ) ) )
= $true )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2722]) ).
thf(2978,plain,
! [SV479: $i,SV179: $i,SV810: $i] :
( ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( ! [SY1629: $i] :
( ~ ( in @ SY1629 @ ( powerset @ SV179 ) )
| ! [SY1630: $i] :
( ~ ( in @ SY1630 @ SV179 )
| ~ ( in @ SY1630 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1630 @ ( binunion @ SV810 @ SY1629 ) ) ) ) )
= $true )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2979,plain,
! [SV683: $i,SV480: $o,SV181: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ SV181 ) )
= $true )
| ( ( ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SV889 )
= SV683 ) )
= $true )
| ( ( in @ SV683 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2980,plain,
! [SV684: $i,SV181: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV181 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SV890 )
= SV684 ) )
= $true )
| ( ( in @ SV684 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2981,plain,
! [SV685: $i,SV181: $i,SV891: $i] :
( ( ( ~ ( in @ SV891 @ SV181 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SV891 )
= SV685 ) )
= $true )
| ( ( in @ SV685 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2982,plain,
! [SV182: $i,SV481: $i,SV686: $i] :
( ( ( ~ ( in @ SV686 @ SV481 ) )
= $true )
| ( ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) )
= $true )
| ( ( in @ SV686 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2727]) ).
thf(2983,plain,
! [SV892: $i > $o,SV687: $i,SV482: $i,SV183: $i] :
( ( ( ~ ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV183 )
| ! [SY1716: $i] :
( ~ ( in @ SY1716 @ SV482 )
| ~ ( in @ ( kpair @ SY1715 @ SY1716 ) @ SV687 )
| ( SV892 @ ( kpair @ SY1715 @ SY1716 ) ) ) ) )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2984,plain,
! [SV184: $i,SV483: $i,SV688: $i] :
( ( ( ~ ( in @ SV688 @ SV483 ) )
= $false )
| ( ( ~ ( in @ SV688 @ SV184 ) )
= $true )
| ( ( subset @ SV184 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2985,plain,
! [SV485: $i,SV186: $i,SV811: $i] :
( ( ( in @ SV811 @ ( powerset @ SV186 ) )
= $false )
| ( ( in @ ( binunion @ SV485 @ SV811 ) @ ( powerset @ SV186 ) )
= $true )
| ( ( in @ SV485 @ ( powerset @ SV186 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2731]) ).
thf(2986,plain,
! [SV486: $i,SV188: $i,SV812: $i] :
( ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( ! [SY1631: $i] :
( ~ ( in @ SY1631 @ SV188 )
| ~ ( in @ SY1631 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SY1631 @ ( setminus @ SV188 @ SV486 ) ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2987,plain,
! [SV487: $i > $o,SV189: $i,SV813: $i] :
( ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ! [SY1632: $i] :
( ~ ( in @ SY1632 @ SV189 )
| ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SY1632 )
| ( SV813 = SY1632 ) ) )
= $true )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2988,plain,
! [SV689: $i,SV488: $o,SV190: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ SV190 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1718: $i] :
( ~ ( ~ SV488
| ( SY1718 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1718 != SV893 ) ) ) ) )
= $true )
| ( ( in @ SV689 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2734]) ).
thf(2989,plain,
! [SV690: $i,SV190: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV190 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1719: $i] :
( ~ ( ~ $true
| ( SY1719 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1719 != SV894 ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2735]) ).
thf(2990,plain,
! [SV691: $i,SV190: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV190 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1720: $i] :
( ~ ( ~ $false
| ( SY1720 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1720 != SV895 ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2736]) ).
thf(2991,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2737]) ).
thf(2992,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ! [SY1633: $i] :
~ ~ ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1633 )
| ~ ! [SY1634: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1634 )
| ( SY1633 = SY1634 ) ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2738]) ).
thf(2993,plain,
! [SV496: $i,SV198: $i,SV814: $i] :
( ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( ! [SY1635: $i] :
( ~ ( in @ SY1635 @ SV198 )
| ~ ( in @ SY1635 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SY1635 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) ) )
= $true )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2994,plain,
! [SV694: $i,SV497: $i,SV199: $i] :
( ( ( injective @ SV199 @ SV497 @ SV694 )
= $false )
| ( ( in @ SV694 @ ( injFuncSet @ SV199 @ SV497 ) )
= $true )
| ( ( in @ SV694 @ ( funcSet @ SV199 @ SV497 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2995,plain,
! [SV200: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV200 )
| ( subset @ SV922 @ SV200 ) )
= $true )
| ( ( in @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2742]) ).
thf(2996,plain,
! [SV200: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV200 ) )
= $true )
| ( ( subset @ SV896 @ SV200 )
= $true )
| ( ( subset @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2997,plain,
! [SV202: $i,SV695: $i > $i,SV499: $i] :
( ( ( ~ ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 ) )
= $false )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2998,plain,
! [SV202: $i,SV499: $i,SV695: $i > $i] :
( ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2999,plain,
! [SV500: $i,SV205: $i,SV815: $i] :
( ( ( in @ SV815 @ SV205 )
= $false )
| ( ( ~ ( in @ SV815 @ SV500 )
| ( in @ SV815 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(3000,plain,
! [SV207: $i,SV696: $i,SV502: $i > $o] :
( ( ( SV502 @ SV696 )
= $false )
| ( ( in @ SV696
@ ( dsetconstr @ SV207
@ ^ [SY1182: $i] : ( SV502 @ SY1182 ) ) )
= $true )
| ( ( in @ SV696 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(3001,plain,
! [SV697: $i > $i > $o,SV503: $i,SV208: $i,SV816: $i,SV755: $i] :
( ( ( in @ ( kpair @ SV755 @ SV816 )
@ ( dpsetconstr @ SV208 @ SV503
@ ^ [SY1487: $i,SY1488: $i] : ( SV697 @ SY1487 @ SY1488 ) ) )
= $false )
| ( ( in @ SV816 @ SV503 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2748]) ).
thf(3002,plain,
! [SV504: $i,SV817: $i,SV209: $i] :
( ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV209 )
| ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV209 )
| ~ ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV504 )
| ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV817 ) ) )
| ( subset @ SV504 @ SV817 ) )
= $true )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(3003,plain,
! [SV506: $i,SV211: $i,SV818: $i] :
( ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( ! [SY1640: $i] :
( ~ ( in @ SY1640 @ ( powerset @ SV211 ) )
| ! [SY1641: $i] :
( ~ ( in @ SY1641 @ SV211 )
| ~ ( in @ SY1641 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1641 @ ( binunion @ SV506 @ SY1640 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(3004,plain,
! [SV212: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(3005,plain,
! [SV212: $i] :
( ( ! [SY1498: $i] :
( ~ ~ ( ~ ! [SY568: $i] :
( ~ ( in @ SY568 @ SY1498 )
| ( in @ SY568 @ SV212 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY1498 ) )
| ~ ! [SY1501: $i] :
~ ~ ! [SY1502: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1501 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1502 @ SY1498 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY1501 )
| ~ ( in @ SX5 @ SY1498 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1501 ) )
| ( in @ SY1502 @ SY1504 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2752]) ).
thf(3006,plain,
! [SV698: $i,SV507: $i,SV213: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV213 ) )
= $true )
| ( ( ( ap @ SV213 @ SV507 @ SV698 @ SV897 )
= ( ap @ SV213 @ SV507 @ SV698 @ SV897 ) )
= $true )
| ( ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2753]) ).
thf(3007,plain,
! [SV699: $i,SV508: $o,SV214: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV214 ) )
= $true )
| ( ( in @ ( if @ SV214 @ SV508 @ SV699 @ SV898 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SV898 @ emptyset ) ) )
= $true )
| ( ( in @ SV699 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2754]) ).
thf(3008,plain,
! [SV700: $i,SV214: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV214 ) )
= $true )
| ( ( in @ ( if @ SV214 @ $true @ SV700 @ SV899 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SV899 @ emptyset ) ) )
= $true )
| ( ( in @ SV700 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2755]) ).
thf(3009,plain,
! [SV701: $i,SV214: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV214 ) )
= $true )
| ( ( in @ ( if @ SV214 @ $false @ SV701 @ SV900 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SV900 @ emptyset ) ) )
= $true )
| ( ( in @ SV701 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2756]) ).
thf(3010,plain,
! [SV215: $i,SV509: $i,SV702: $i > $i > $o] :
( ( ( ~ ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 ) )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(3011,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i] :
( ( ( ~ ! [SY1721: $i] :
~ ~ ( ~ ( in @ SY1721 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SY1721 ) ) )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2757]) ).
thf(3012,plain,
! [SV705: $i,SV516: $i,SV225: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ SV225 ) )
= $true )
| ( ( ! [SY1722: $i] :
( ~ ( in @ SY1722 @ SV516 )
| ~ ( in @ ( kpair @ SV901 @ SY1722 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SY1722 ) ) )
= $true )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2758]) ).
thf(3013,plain,
! [SV226: $i] :
( ( ( ! [SY601: $i] :
( ~ ~ ( ~ ( in @ SY601 @ omega )
| ~ ( in @ SY601 @ SV226 ) )
| ( in @ ( setadjoin @ SY601 @ SY601 ) @ SV226 ) ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2759]) ).
thf(3014,plain,
! [SV517: $i,SV227: $i,SV819: $i] :
( ( ( in @ SV819 @ ( powerset @ SV227 ) )
= $false )
| ( ( ~ ( subset @ SV517 @ ( setminus @ SV227 @ SV819 ) )
| ( subset @ SV819 @ ( setminus @ SV227 @ SV517 ) ) )
= $true )
| ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(3015,plain,
! [SV820: $i,SV228: $i] :
( ( ( SV228 = emptyset )
= $false )
| ( ( in @ SV820 @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(3016,plain,
! [SV518: $i,SV229: $i,SV821: $i] :
( ( ( in @ SV821 @ ( powerset @ SV229 ) )
= $false )
| ( ( in @ ( setminus @ SV229 @ ( binunion @ SV518 @ SV821 ) ) @ ( powerset @ ( setminus @ SV229 @ SV518 ) ) )
= $true )
| ( ( in @ SV518 @ ( powerset @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(3017,plain,
! [SV230: $i,SV519: $i] :
( ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true )
| ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) )
| ( SV230 = SV519 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2763]) ).
thf(3018,plain,
! [SV230: $i,SV519: $i] :
( ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) ) )
= $true )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2764]) ).
thf(3019,plain,
! [SV521: $i > $o,SV232: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV232 ) )
= $true )
| ( ( SV521 @ SV902 )
= $true )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(3020,plain,
! [SV523: $i,SV822: $i,SV234: $i] :
( ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( ! [SY1642: $i] :
( ~ ( in @ SY1642 @ SV234 )
| ! [SY1643: $i] :
( ~ ( in @ SY1643 @ SV234 )
| ! [SY1644: $i] :
( ~ ( in @ SY1644 @ SV234 )
| ~ ( in @ ( kpair @ SY1642 @ SY1644 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1644 @ SY1643 ) @ SV822 )
| ( in @ ( kpair @ SY1642 @ SY1643 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(3021,plain,
! [SV235: $i,SV524: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV524 ) ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2767]) ).
thf(3022,plain,
! [SV236: $i,SV525: $i,SV707: $i] :
( ( ( in @ SV707 @ SV525 )
= $false )
| ( ( in @ SV707 @ ( binintersect @ SV236 @ SV525 ) )
= $true )
| ( ( in @ SV707 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(3023,plain,
! [SV709: $i > $i > $o,SV238: $i,SV757: $i,SV527: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ SV527 )
| ~ ( in @ ( kpair @ SV757 @ SV923 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SV923 ) )
= $true )
| ( ( in @ SV757 @ SV238 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2770]) ).
thf(3024,plain,
! [SV239: $i,SV710: $i,SV528: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV528 ) )
= $true )
| ( ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SV903 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) )
= $true )
| ( ( in @ SV710 @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(3025,plain,
! [SV529: $i,SV240: $i,SV823: $i] :
( ( ( in @ SV823 @ ( powerset @ SV240 ) )
= $false )
| ( ( in @ ( setminus @ SV240 @ ( binunion @ SV529 @ SV823 ) ) @ ( powerset @ ( setminus @ SV240 @ SV529 ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV240 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(3026,plain,
! [SV711: $i,SV530: $o,SV241: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV241 ) )
= $true )
| ( ( in @ ( if @ SV241 @ SV530 @ SV711 @ SV904 ) @ SV241 )
= $true )
| ( ( in @ SV711 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2773]) ).
thf(3027,plain,
! [SV712: $i,SV241: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ SV241 ) )
= $true )
| ( ( in @ ( if @ SV241 @ $true @ SV712 @ SV905 ) @ SV241 )
= $true )
| ( ( in @ SV712 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2774]) ).
thf(3028,plain,
! [SV713: $i,SV241: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ SV241 ) )
= $true )
| ( ( in @ ( if @ SV241 @ $false @ SV713 @ SV906 ) @ SV241 )
= $true )
| ( ( in @ SV713 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2775]) ).
thf(3029,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(3030,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
| ~ ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
| ~ ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
| ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2777]) ).
thf(3031,plain,
! [SV248: $i,SV537: $i] :
( ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $false )
| ( ( ! [SY1246: $i] :
( ~ ( in @ SY1246 @ SV537 )
| ( in @ SY1246 @ SV248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2779]) ).
thf(3032,plain,
! [SV248: $i,SV537: $i] :
( ( ( ! [SY1247: $i] :
( ~ ( in @ SY1247 @ SV537 )
| ( in @ SY1247 @ SV248 ) ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2780]) ).
thf(3033,plain,
! [SV716: $i,SV538: $i,SV250: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV250 ) )
= $true )
| ( ( ! [SY1723: $i] :
( ~ ( in @ SY1723 @ SV538 )
| ~ ( in @ ( kpair @ SV907 @ SY1723 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SY1723 ) ) )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2781]) ).
thf(3034,plain,
! [SV539: $i,SV251: $i,SV824: $i] :
( ( ( in @ SV824 @ SV251 )
= $false )
| ( ( ! [SY1646: $i] :
( ~ ( in @ SY1646 @ SV251 )
| ~ ( in @ ( kpair @ SV824 @ SY1646 ) @ SV539 )
| ( in @ ( kpair @ SY1646 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) ) )
= $true )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(3035,plain,
! [SV540: $i,SV252: $i,SV825: $i] :
( ( ( in @ SV825 @ SV252 )
= $false )
| ( ( ! [SY1647: $i] :
( ~ ( in @ SY1647 @ SV252 )
| ~ ( in @ ( kpair @ SY1647 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SY1647 ) @ SV540 ) ) )
= $true )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2783]) ).
thf(3036,plain,
! [SV545: $i,SV826: $i,SV255: $i] :
( ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( ! [SY1648: $i] :
( ~ ( in @ SY1648 @ SV255 )
| ! [SY1649: $i] :
( ~ ( in @ SY1649 @ SV255 )
| ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1650: $o] :
( ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV545 )
| SY1650 )
| ~ ( ~ ( in @ ( kpair @ SY1648 @ SY1649 ) @ SV826 )
| SY1650 )
| SY1650 ) ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(3037,plain,
! [SV257: $i,SV719: $i,SV547: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV547 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SV908 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) )
= $true )
| ( ( in @ SV719 @ SV257 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(3038,plain,
! [SV548: $i,SV258: $i,SV827: $i] :
( ( ( in @ SV827 @ ( powerset @ SV258 ) )
= $false )
| ( ( ! [SY1651: $i] :
( ~ ( in @ SY1651 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SY1651 ) @ ( binunion @ SV827 @ SY1651 ) ) ) ) ) )
= $true )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(3039,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ( sK21_SY1266 @ SV550 @ SV260 )
!= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2787]) ).
thf(3040,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
| ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2787]) ).
thf(3041,plain,
! [SV552: $i,SV263: $i,SV828: $i] :
( ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( ! [SY1653: $i] :
( ~ ( in @ SY1653 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SY1653 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SY1653 ) ) )
= $true )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(3042,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( ~ ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV264 )
| ! [SY1655: $i] :
( ~ ( in @ SY1655 @ SV264 )
| ~ ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV553 )
| ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV829 ) ) )
| ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(3043,plain,
! [SV265: $i,SV554: $i,SV721: $i] :
( ( ( in @ SV721 @ SV554 )
= $false )
| ( ( ~ ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) ) )
= $true )
| ( ( in @ SV721 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(3044,plain,
! [SV557: $i,SV268: $i,SV830: $i] :
( ( ( in @ SV830 @ SV268 )
= $false )
| ( ( ~ ( in @ SV830 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
| ( in @ SV830 @ SV557 ) )
= $true )
| ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(3045,plain,
! [SV558: $i > $o,SV269: $i,SV909: $i] :
( ( ( ~ ( ~ ( in @ SV909 @ SV269 )
| ~ ~ ( SV558 @ SV909 ) ) )
= $false )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(3046,plain,
! [SV270: $i,SV559: $i,SV723: $i] :
( ( ( ~ ~ ( in @ SV723 @ SV559 ) )
= $true )
| ( ( ~ ( in @ SV723 @ SV270 ) )
= $true )
| ( ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(3047,plain,
! [SV560: $i,SV271: $i,SV831: $i] :
( ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( ! [SY1658: $i] :
( ~ ( in @ SY1658 @ SV271 )
| ~ ( in @ SY1658 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SY1658 @ ( setminus @ SV271 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2794]) ).
thf(3048,plain,
! [SV562: $i,SV832: $i,SV274: $i] :
( ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( ! [SY1659: $i] :
( ~ ( in @ SY1659 @ SV274 )
| ! [SY1660: $i] :
( ~ ( in @ SY1660 @ SV274 )
| ~ ( in @ ( kpair @ SY1659 @ SY1660 ) @ SV562 )
| ( in @ ( kpair @ SY1659 @ SY1660 ) @ ( binunion @ SV562 @ SV832 ) ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(3049,plain,
! [SV276: $i,SV564: $i,SV725: $i] :
( ( ( ~ ~ ( in @ SV725 @ SV564 ) )
= $true )
| ( ( ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true )
| ( ( in @ SV725 @ SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(3050,plain,
! [SV278: $i,SV726: $i,SV566: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV566 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 )
= $true )
| ( ( in @ SV726 @ SV278 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(3051,plain,
! [SV281: $i] :
( ( ( ~ ( ~ ( in @ ( sK35_SY742 @ SV281 ) @ SV281 )
| ~ $true ) )
= $true )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(3052,plain,
! [SV911: $i > $o,SV833: $i > $o,SV569: $i,SV283: $i] :
( ( ( ~ ! [SY1724: $i] :
( ~ ( in @ SY1724 @ SV283 )
| ! [SY1725: $i] :
( ~ ( in @ SY1725 @ SV569 )
| ( SY1724 != SY1725 )
| ~ ( ~ ( ~ ( SV833 @ SY1724 )
| ( SV911 @ SY1725 ) )
| ~ ( ~ ( SV911 @ SY1725 )
| ( SV833 @ SY1724 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(3053,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV834 )
| ~ ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2800]) ).
thf(3054,plain,
! [SV570: $i,SV285: $i,SV835: $i] :
( ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( ! [SY1667: $i] :
( ~ ( in @ SY1667 @ SV285 )
| ~ ( in @ SY1667 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SY1667 @ ( binintersect @ SV570 @ SV835 ) ) ) )
= $true )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(3055,plain,
! [SV572: $i,SV759: $o,SV287: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| SV759 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(3056,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2803]) ).
thf(3057,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV287 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2804]) ).
thf(3058,plain,
! [SV573: $i,SV836: $i,SV288: $i] :
( ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( ! [SY1668: $i] :
( ~ ( in @ SY1668 @ SV288 )
| ! [SY1669: $i] :
( ~ ( in @ SY1669 @ SV288 )
| ~ ( in @ ( kpair @ SY1668 @ SY1669 ) @ SV836 )
| ( in @ ( kpair @ SY1668 @ SY1669 ) @ ( binunion @ SV573 @ SV836 ) ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(3059,plain,
! [SV731: $i,SV576: $o,SV291: $i,SV912: $i] :
( ( ( ~ ( in @ SV912 @ SV291 ) )
= $true )
| ( ( ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 ) )
= $true )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(3060,plain,
! [SV732: $i,SV291: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV291 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 ) )
= $true )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(3061,plain,
! [SV733: $i,SV291: $i,SV914: $i] :
( ( ( ~ ( in @ SV914 @ SV291 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 ) )
= $true )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(3062,plain,
! [SV578: $i,SV837: $i,SV294: $i] :
( ( ( breln1 @ SV294 @ SV837 )
= $false )
| ( ( ( breln1invset @ SV294 @ ( breln1compset @ SV294 @ SV578 @ SV837 ) )
= ( breln1compset @ SV294 @ ( breln1invset @ SV294 @ SV837 ) @ ( breln1invset @ SV294 @ SV578 ) ) )
= $true )
| ( ( breln1 @ SV294 @ SV578 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3063,plain,
! [SV580: $i,SV296: $i,SV838: $i] :
( ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV296 )
| ~ ( in @ SY1670 @ SV580 )
| ( in @ SY1670 @ SV838 ) )
| ( in @ SV580 @ ( powerset @ SV838 ) ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(3064,plain,
! [SV581: $i,SV839: $i,SV297: $i] :
( ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( ! [SY1671: $i] :
( ~ ( in @ SY1671 @ SV297 )
| ! [SY1672: $i] :
( ~ ( in @ SY1672 @ SV297 )
| ~ ( ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV581 )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ SV839 ) )
| ( in @ ( kpair @ SY1671 @ SY1672 ) @ ( binunion @ SV581 @ SV839 ) ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2811]) ).
thf(3065,plain,
! [SV734: $i,SV915: $i,SV582: $i,SV298: $i] :
( ( ( ~ ( breln @ SV298 @ SV582 @ SV915 ) )
= $true )
| ( ( ~ ! [SY1728: $i] :
( ~ ( in @ SY1728 @ SV298 )
| ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV582 )
| ~ ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV734 )
| ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV915 ) ) )
| ( subset @ SV734 @ SV915 ) )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(3066,plain,
! [SV583: $i,SV299: $i,SV840: $i] :
( ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( ! [SY1673: $i] :
( ~ ( in @ SY1673 @ SV299 )
| ~ ( in @ SY1673 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SY1673 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) ) )
= $true )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(3067,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ SV841 )
| ~ ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2814]) ).
thf(3068,plain,
! [SV584: $i,SV301: $i,SV842: $i] :
( ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( ! [SY1675: $i] :
( ~ ( in @ SY1675 @ SV301 )
| ~ ( in @ SY1675 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SY1675 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) ) )
= $true )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(3069,plain,
! [SV585: $i,SV302: $i,SV843: $i] :
( ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( ! [SY1676: $i] :
( ~ ( in @ SY1676 @ SV302 )
| ~ ( in @ SY1676 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SY1676 @ ( setminus @ SV302 @ SV585 ) ) ) )
= $true )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2816]) ).
thf(3070,plain,
! [SV304: $i] :
( ( ( in @ ( sK36_SY804 @ SV304 ) @ SV304 )
= $true )
| ( ( SV304 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(3071,plain,
! [SV587: $i,SV305: $i,SV844: $i] :
( ( ( in @ SV844 @ ( powerset @ SV305 ) )
= $false )
| ( ( ! [SY1677: $i] :
( ~ ( in @ SY1677 @ ( binintersect @ SV587 @ SV844 ) )
| ( in @ SY1677 @ SV305 ) ) )
= $true )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2818]) ).
thf(3072,plain,
! [SV588: $i,SV306: $i,SV735: $i] :
( ( ( in @ SV735 @ SV306 )
= $false )
| ( ( in @ SV588 @ ( setunion @ SV306 ) )
= $true )
| ( ( in @ SV588 @ SV735 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2819]) ).
thf(3073,plain,
! [SV589: $i,SV307: $i,SV845: $i] :
( ( ( in @ SV845 @ SV307 )
= $false )
| ( ( ~ ( in @ SV845 @ SV589 )
| ~ ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) ) )
= $true )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2820]) ).
thf(3074,plain,
! [SV590: $i,SV308: $i,SV846: $i] :
( ( ( in @ SV846 @ ( powerset @ SV308 ) )
= $false )
| ( ( ( setminus @ SV308 @ ( binunion @ SV590 @ SV846 ) )
= ( binintersect @ ( setminus @ SV308 @ SV590 ) @ ( setminus @ SV308 @ SV846 ) ) )
= $true )
| ( ( in @ SV590 @ ( powerset @ SV308 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2821]) ).
thf(3075,plain,
! [SV591: $i,SV916: $o,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| SV916 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2822]) ).
thf(3076,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2823]) ).
thf(3077,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ~ ( ( SV736 != SV309 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2824]) ).
thf(3078,plain,
! [SV592: $i,SV310: $i,SV847: $i] :
( ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV310 )
| ~ ( in @ SY1678 @ SV592 )
| ( in @ SY1678 @ SV847 ) )
| ( subset @ SV592 @ SV847 ) )
= $true )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(3079,plain,
! [SV313: $i,SV738: $i,SV595: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV595 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SV917 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) )
= $true )
| ( ( in @ SV738 @ SV313 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2827]) ).
thf(3080,plain,
! [SV314: $i,SV760: $i,SV739: $i > $i > $o,SV596: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ SV596 )
| ~ ( SV739 @ SV760 @ SV924 )
| ( in @ ( kpair @ SV760 @ SV924 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) )
= $true )
| ( ( in @ SV760 @ SV314 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2828]) ).
thf(3081,plain,
! [SV597: $i,SV315: $i,SV848: $i] :
( ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( ! [SY1679: $o,SY1680: $i] :
( ~ ( in @ SY1680 @ SV315 )
| ~ ( in @ SY1680 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SY1680 @ SV597 )
| SY1679 )
| ~ ( ~ ( in @ SY1680 @ SV848 )
| SY1679 )
| SY1679 ) )
= $true )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(3082,plain,
! [SV599: $i,SV317: $i,SV849: $i] :
( ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY1681: $i] :
( ~ ( in @ SY1681 @ ( powerset @ SV317 ) )
| ! [SY1682: $i] :
( ~ ( in @ SY1682 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SY1681 @ SY1682 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SY1681 ) @ ( setminus @ SV317 @ SY1682 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(3083,plain,
! [SV600: $i,SV318: $i,SV850: $i] :
( ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( ! [SY1683: $i] :
( ~ ( in @ SY1683 @ SV318 )
| ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SY1683 @ SV850 )
| ~ ( in @ SY1683 @ SV600 ) ) )
= $true )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3084,plain,
! [SV740: $i,SV601: $i,SV319: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV319 ) )
= $true )
| ( ( in @ ( kpair @ SV918 @ ( ap @ SV319 @ SV601 @ SV740 @ SV918 ) ) @ SV740 )
= $true )
| ( ( func @ SV319 @ SV601 @ SV740 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(3085,plain,
! [SV602: $i,SV320: $i,SV741: $i] :
( ( ( in @ SV741 @ SV320 )
= $false )
| ( ( in @ SV741 @ SV602 )
= $true )
| ( ( subset @ SV320 @ SV602 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3086,plain,
! [SV321: $i,SV603: $i,SV742: $i] :
( ( ( subset @ SV742 @ SV603 )
= $false )
| ( ( subset @ SV742 @ ( binintersect @ SV321 @ SV603 ) )
= $true )
| ( ( subset @ SV742 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3087,plain,
! [SV604: $i,SV322: $i,SV851: $i] :
( ( ( in @ SV851 @ ( powerset @ SV322 ) )
= $false )
| ( ( in @ ( binintersect @ SV604 @ SV851 ) @ ( powerset @ SV322 ) )
= $true )
| ( ( in @ SV604 @ ( powerset @ SV322 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(3088,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ( SV323 @ SV852 )
| ~ ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2836]) ).
thf(3089,plain,
! [SV324: $i,SV743: $i,SV605: $i,SV919: $i] :
( ( ( ~ ( in @ SV919 @ SV605 ) )
= $true )
| ( ( ( kpair @ SV743 @ SV919 )
= ( kpair @ SV743 @ SV919 ) )
= $true )
| ( ( in @ SV743 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2837]) ).
thf(3090,plain,
! [SV607: $i,SV326: $i,SV853: $i] :
( ( ( in @ SV853 @ ( powerset @ SV326 ) )
= $false )
| ( ( in @ ( setminus @ SV326 @ SV607 ) @ ( powerset @ ( setminus @ SV326 @ ( binintersect @ SV607 @ SV853 ) ) ) )
= $true )
| ( ( in @ SV607 @ ( powerset @ SV326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(3091,plain,
! [SV3: $i,SV920: $i] :
( ( ( ~ ! [SY1730: $i] :
( ~ ( in @ SY1730 @ SV920 )
| ( subset @ SY1730 @ SV920 ) ) )
= $true )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2839]) ).
thf(3092,plain,
! [SV3: $i,SV854: $i] :
( ( ( ! [SY1685: $i] :
( ~ ( in @ SY1685 @ SV854 )
| ( subset @ SY1685 @ SV854 ) ) )
= $false )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2840]) ).
thf(3093,plain,
! [SV4: $i,SV608: $i > $i,SV329: $i] :
( ( ( in @ ( sK22_SY1366 @ SV329 @ SV608 @ SV4 ) @ SV4 )
= $true )
| ( ( in
@ ( lam @ SV4 @ SV329
@ ^ [SY1367: $i] : ( SV608 @ SY1367 ) )
@ ( funcSet @ SV4 @ SV329 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(3094,plain,
! [SV6: $i,SV609: $i,SV330: $i,SV855: $i] :
( ( ( in @ SV855 @ SV330 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV609 @ SV855 ) )
= SV855 )
= $true )
| ( ( in @ SV609 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2843]) ).
thf(3095,plain,
! [SV611: $i,SV332: $i > $o,SV8: $i] :
( ( ( ~ ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) ) )
= $true )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3096,plain,
! [SV612: $i,SV333: $i,SV9: $i,SV856: $i] :
( ( ( in @ SV856 @ SV9 )
= $false )
| ( ( ( ap @ SV9 @ SV333 @ SV612 @ SV856 )
= ( ap @ SV9 @ SV333 @ SV612 @ SV856 ) )
= $true )
| ( ( func @ SV9 @ SV333 @ SV612 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2845]) ).
thf(3097,plain,
! [SV10: $i,SV613: $i,SV334: $i,SV857: $i] :
( ( ( in @ SV857 @ SV334 )
= $false )
| ( ( subset @ ( setadjoin @ SV613 @ ( setadjoin @ SV857 @ emptyset ) ) @ ( binunion @ SV10 @ SV334 ) )
= $true )
| ( ( in @ SV613 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(3098,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i] :
( ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1687 )
= ( ap @ SV11 @ SV335 @ SV858 @ SY1687 ) ) )
| ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(3099,plain,
! [SV14: $i,SV615: $i > $i,SV337: $i] :
( ( ( in @ ( sK23_SY1378 @ SV337 @ SV615 @ SV14 ) @ SV14 )
= $true )
| ( ( func @ SV14 @ SV337
@ ( dpsetconstr @ SV14 @ SV337
@ ^ [SY1379: $i,SY1380: $i] :
( ( SV615 @ SY1379 )
= SY1380 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2848]) ).
thf(3100,plain,
! [SV761: $i,SV340: $i,SV17: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ ( powerset @ SV17 ) )
| ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SV925 ) @ ( binunion @ SV761 @ SV925 ) ) ) ) )
= $true )
| ( ( in @ SV761 @ ( powerset @ SV17 ) )
= $false )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2850]) ).
thf(3101,plain,
! [SV859: $i > $o,SV618: $i,SV342: $i,SV19: $i] :
( ( ( ! [SY1690: $i] :
( ~ ( in @ SY1690 @ SV19 )
| ! [SY1691: $i] :
( ~ ( in @ SY1691 @ SV342 )
| ~ ( in @ ( kpair @ SY1690 @ SY1691 ) @ SV618 )
| ( SV859 @ ( kpair @ SY1690 @ SY1691 ) ) ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2851]) ).
thf(3102,plain,
! [SV762: $i,SV343: $i,SV20: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV20 )
| ~ ~ ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2852]) ).
thf(3103,plain,
! [SV763: $i,SV21: $i,SV344: $i] :
( ( ( ~ ( subset @ SV344 @ ( setminus @ SV21 @ SV763 ) ) )
= $true )
| ( ( subset @ SV763 @ ( setminus @ SV21 @ SV344 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2853]) ).
thf(3104,plain,
! [SV346: $i,SV24: $i,SV860: $i,SV764: $i] :
( ( ( SV764 = SV860 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) )
| ~ ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) ) ) )
= $true )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2854]) ).
thf(3105,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
| ~ ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) ) ) )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2855]) ).
thf(3106,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $false )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2856]) ).
thf(3107,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ~ ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $false )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2857]) ).
thf(3108,plain,
! [SV619: $i,SV349: $i,SV28: $i,SV861: $i] :
( ( ( in @ SV861 @ SV28 )
= $false )
| ( ( in @ ( ap @ SV28 @ SV349 @ SV619 @ SV861 ) @ SV349 )
= $true )
| ( ( in @ SV619 @ ( funcSet @ SV28 @ SV349 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2858]) ).
thf(3109,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $false )
| ( ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2859]) ).
thf(3110,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( ( SV621 = SV31 )
| ( in @ SV621 @ SV351 ) )
= $false )
| ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3111,plain,
! [SV765: $i,SV353: $i,SV34: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV34 )
| ~ ~ ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2861]) ).
thf(3112,plain,
! [SV768: $i,SV357: $i,SV40: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV40 )
| ! [SY1737: $i] :
( ~ ( in @ SY1737 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1737 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1738: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1738 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1738 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1738 @ SY1737 ) @ SV768 ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2864]) ).
thf(3113,plain,
! [SV769: $i,SV358: $i,SV929: $i,SV41: $i] :
( ( ( ~ ( breln1 @ SV41 @ SV929 )
| ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SV929 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SV929 ) @ ( breln1compset @ SV41 @ SV769 @ SV929 ) ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV769 )
= $false )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2865]) ).
thf(3114,plain,
! [SV770: $i,SV359: $i,SV42: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ SV42 )
| ~ ( in @ SV930 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SV930 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) )
= $true )
| ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2866]) ).
thf(3115,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i,SV921: $i] :
( ( ( ~ ( ~ ( in @ SV921 @ SV43 )
| ( SV623
!= ( SV360 @ SV921 ) ) ) )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(3116,plain,
! [SV47: $i,SV364: $i] :
( ( ( ! [SY928: $i] :
~ ~ ( ~ ( in @ SV364 @ SY928 )
| ~ ( in @ SY928 @ SV47 ) ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2869]) ).
thf(3117,plain,
! [SV47: $i,SV364: $i] :
( ( ( ! [SY929: $i] :
~ ~ ( ~ ( in @ SV364 @ SY929 )
| ~ ( in @ SY929 @ SV47 ) ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(3118,plain,
! [SV746: $i,SV51: $i] :
( ( ( ( omegaS @ SV51 )
= ( omegaS @ SV746 ) )
= $false )
| ( ( SV51 = SV746 )
= $true )
| ( ( in @ SV746 @ omega )
= $false )
| ( ( in @ SV51 @ omega )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3119,plain,
! [SV773: $i,SV367: $i,SV52: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ SV52 )
| ~ ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2873]) ).
thf(3120,plain,
! [SV53: $i,SV774: $i,SV368: $i] :
( ( ( ~ ( subset @ SV368 @ SV774 ) )
= $true )
| ( ( subset @ ( setminus @ SV53 @ SV774 ) @ ( setminus @ SV53 @ SV368 ) )
= $true )
| ( ( in @ SV774 @ ( powerset @ SV53 ) )
= $false )
| ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3121,plain,
! [SV369: $i,SV775: $i,SV54: $i] :
( ( ( ~ ( subset @ ( setminus @ SV54 @ SV775 ) @ ( setminus @ SV54 @ SV369 ) ) )
= $true )
| ( ( subset @ SV369 @ SV775 )
= $true )
| ( ( in @ SV775 @ ( powerset @ SV54 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3122,plain,
! [SV776: $i,SV55: $i,SV370: $i] :
( ( ( ~ ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) ) )
= $true )
| ( ( ! [SY1586: $i] :
( ~ ( in @ SY1586 @ SV55 )
| ~ ( in @ SY1586 @ SV776 )
| ( in @ SY1586 @ ( setminus @ SV55 @ SV370 ) ) ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3123,plain,
! [SV777: $i,SV372: $i,SV57: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV57 )
| ~ ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SV932 @ SV372 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(3124,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
| ~ ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) ) ) )
= $true )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(3125,plain,
! [SV376: $i > $o,SV61: $i,SV862: $i] :
( ( ( in @ SV862 @ SV61 )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( ~ ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(3126,plain,
! [SV62: $i,SV629: $i > $i,SV377: $i] :
( ( ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 )
= $true )
| ( ( ! [SY1391: $i] :
( ~ ( in @ SY1391 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SY1391 )
= ( SV629 @ SY1391 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2880]) ).
thf(3127,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV933 )
= ( SV629 @ SV933 ) ) )
= $true )
| ( ( in @ ( SV629 @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) ) @ SV377 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2881]) ).
thf(3128,plain,
! [SV778: $i,SV380: $i,SV66: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV66 )
| ~ ~ ( in @ SV934 @ SV380 )
| ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2883]) ).
thf(3129,plain,
! [SV381: $i,SV67: $i,SV863: $i,SV779: $i] :
( ( ( SV779 = SV863 )
= $false )
| ( ( ~ ( in @ SV779 @ SV67 )
| ( in @ SV863 @ SV381 ) )
= $true )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3130,plain,
! [SV632: $i,SV383: $o,SV70: $i,SV864: $i] :
( ( ( in @ SV864 @ SV70 )
= $false )
| ( ( ~ ~ SV383
| ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) ) )
= $true )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3131,plain,
! [SV633: $i,SV70: $i,SV865: $i] :
( ( ( in @ SV865 @ SV70 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) ) )
= $true )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2886]) ).
thf(3132,plain,
! [SV634: $i,SV70: $i,SV866: $i] :
( ( ( in @ SV866 @ SV70 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) ) )
= $true )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2887]) ).
thf(3133,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK45_SY168 @ SV780 @ SV73 ) @ SV73 )
| ~ ~ ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2888]) ).
thf(3134,plain,
! [SV635: $i,SV385: $i,SV75: $i,SV867: $i] :
( ( ( in @ SV867 @ SV75 )
= $false )
| ( ( in @ ( ap @ SV75 @ SV385 @ SV635 @ SV867 ) @ SV385 )
= $true )
| ( ( func @ SV75 @ SV385 @ SV635 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3135,plain,
! [SV781: $i,SV386: $i,SV76: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV76 )
| ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SV935 @ SV386 )
| ( in @ SV935 @ SV781 ) )
= $true )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2890]) ).
thf(3136,plain,
! [SV782: $i,SV387: $i,SV77: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV77 )
| ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SV936 @ SV782 )
| ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2891]) ).
thf(3137,plain,
! [SV79: $i,SV637: $i,SV389: $i,SV868: $i] :
( ( ( in @ SV868 @ SV389 )
= $false )
| ( ( in @ ( kpair @ SV637 @ SV868 ) @ ( powerset @ ( powerset @ ( binunion @ SV79 @ SV389 ) ) ) )
= $true )
| ( ( in @ SV637 @ SV79 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2892]) ).
thf(3138,plain,
! [SV784: $i,SV392: $i,SV82: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ SV82 )
| ~ ~ ( in @ SV937 @ SV392 )
| ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3139,plain,
! [SV639: $i,SV394: $i,SV84: $i,SV869: $i] :
( ( ( in @ SV869 @ SV84 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV394
@ ^ [SY1696: $i] : ( in @ ( kpair @ SV869 @ SY1696 ) @ SV639 ) ) )
= $true )
| ( ( func @ SV84 @ SV394 @ SV639 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2896]) ).
thf(3140,plain,
! [SV395: $i,SV85: $i,SV640: $i] :
( ( ( in @ SV640 @ SV85 )
= $false )
| ( ( in @ SV640 @ SV395 )
= $true )
| ( ( in @ SV640 @ ( setminus @ SV85 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2897]) ).
thf(3141,plain,
! [SV87: $i,SV397: $i,SV641: $i] :
( ( ( in @ SV641 @ SV397 )
= $true )
| ( ( in @ SV641 @ ( symdiff @ SV87 @ SV397 ) )
= $true )
| ( ( in @ SV641 @ SV87 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(3142,plain,
! [SV89: $i,SV642: $i > $i,SV399: $i] :
( ( ( in @ ( sK25_SY1408 @ SV399 @ SV642 @ SV89 ) @ SV89 )
= $true )
| ( ( ( lam @ SV89 @ SV399
@ ^ [SY1409: $i] : ( SV642 @ SY1409 ) )
= ( lam @ SV89 @ SV399
@ ^ [SY1410: $i] : ( SV642 @ SY1410 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2899]) ).
thf(3143,plain,
! [SV643: $i,SV401: $i,SV91: $i,SV870: $i] :
( ( ( in @ SV870 @ SV91 )
= $false )
| ( ( in @ ( kpair @ SV870 @ ( ap @ SV91 @ SV401 @ SV643 @ SV870 ) ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( funcSet @ SV91 @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3144,plain,
! [SV786: $i,SV402: $i,SV93: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV93 )
| ! [SY1741: $i] :
( ~ ( in @ SY1741 @ SV93 )
| ~ ( in @ ( kpair @ SV938 @ SY1741 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV786 ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2902]) ).
thf(3145,plain,
! [SV644: $i,SV403: $o,SV94: $i,SV871: $i] :
( ( ( in @ SV871 @ SV94 )
= $false )
| ( ( ~ SV403
| ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1697: $i] :
( ~ ( ~ SV403
| ( SY1697 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1697 != SV871 ) ) ) ) ) )
= $true )
| ( ( in @ SV644 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2903]) ).
thf(3146,plain,
! [SV645: $i,SV94: $i,SV872: $i] :
( ( ( in @ SV872 @ SV94 )
= $false )
| ( ( ~ $true
| ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1698: $i] :
( ~ ( ~ $true
| ( SY1698 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1698 != SV872 ) ) ) ) ) )
= $true )
| ( ( in @ SV645 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(3147,plain,
! [SV646: $i,SV94: $i,SV873: $i] :
( ( ( in @ SV873 @ SV94 )
= $false )
| ( ( ~ $false
| ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1699: $i] :
( ~ ( ~ $false
| ( SY1699 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1699 != SV873 ) ) ) ) ) )
= $true )
| ( ( in @ SV646 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(3148,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3149,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2908]) ).
thf(3150,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 )
| ~ ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2909]) ).
thf(3151,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ SV99 )
| ! [SY1742: $i] :
( ~ ( in @ SY1742 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1742 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1743: $o] :
( ~ ! [SY1744: $i] :
( ~ ( in @ SY1744 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1744 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1744 @ SY1742 ) @ SV787 )
| SY1743 )
| SY1743 ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2910]) ).
thf(3152,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2911]) ).
thf(3153,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
| ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2912]) ).
thf(3154,plain,
! [SV788: $i,SV416: $i,SV108: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ ( powerset @ SV108 ) )
| ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SV940 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) ) )
= $true )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2913]) ).
thf(3155,plain,
! [SV651: $i,SV417: $i,SV109: $i,SV875: $i] :
( ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( ~ ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1700 )
= ( ap @ SV109 @ SV417 @ SV875 @ SY1700 ) ) )
| ( SV651 = SV875 ) )
= $true )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(3156,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SV111 )
| ~ ~ ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) ) )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(3157,plain,
! [SV113: $i] :
( ( ( ~ ( in @ ( sK27_SY275 @ SV113 ) @ SV113 )
| ( ( binintersect @ ( sK27_SY275 @ SV113 ) @ SV113 )
!= emptyset ) )
= $false )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2916]) ).
thf(3158,plain,
! [SV790: $i,SV424: $i,SV117: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ ( powerset @ SV117 ) )
| ! [SY1745: $i] :
( ~ ( in @ SY1745 @ SV117 )
| ~ ( in @ SY1745 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1745 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) ) )
= $true )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2918]) ).
thf(3159,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2919]) ).
thf(3160,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(3161,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
| ~ ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
| ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2920]) ).
thf(3162,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ~ ( ~ ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3163,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ~ ( ~ ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) )
| ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2921]) ).
thf(3164,plain,
! [SV655: $i,SV427: $i,SV120: $i,SV877: $i] :
( ( ( in @ SV877 @ SV120 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV427
@ ^ [SY1703: $i] : ( in @ ( kpair @ SV877 @ SY1703 ) @ SV655 ) ) )
@ SV427 )
= $true )
| ( ( func @ SV120 @ SV427 @ SV655 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3165,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3166,plain,
( ( ~ ( in @ sK3_SY2 @ sK2_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3167,plain,
( ( ~ ~ ( in @ sK3_SY2 @ sK1_X ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2925]) ).
thf(3168,plain,
! [SV124: $i,SV656: $i > $i,SV431: $i] :
( ( ( in @ ( sK28_SY1428 @ SV431 @ SV656 @ SV124 ) @ SV124 )
= $true )
| ( ( func @ SV124 @ SV431
@ ( lam @ SV124 @ SV431
@ ^ [SY1429: $i] : ( SV656 @ SY1429 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2926]) ).
thf(3169,plain,
! [SV657: $i,SV432: $o,SV125: $i,SV878: $i] :
( ( ( in @ SV878 @ SV125 )
= $false )
| ( ( ~ SV432
| ( ( dsetconstr @ SV125
@ ^ [SY1704: $i] :
( ~ ( ~ SV432
| ( SY1704 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1704 != SV878 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) ) )
= $true )
| ( ( in @ SV657 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2928]) ).
thf(3170,plain,
! [SV658: $i,SV125: $i,SV879: $i] :
( ( ( in @ SV879 @ SV125 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV125
@ ^ [SY1705: $i] :
( ~ ( ~ $true
| ( SY1705 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1705 != SV879 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) ) )
= $true )
| ( ( in @ SV658 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3171,plain,
! [SV659: $i,SV125: $i,SV880: $i] :
( ( ( in @ SV880 @ SV125 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV125
@ ^ [SY1706: $i] :
( ~ ( ~ $false
| ( SY1706 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1706 != SV880 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) ) )
= $true )
| ( ( in @ SV659 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3172,plain,
! [SV126: $i,SV791: $o,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) )
| ~ ( in @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) @ SV126 )
| SV791 )
= $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2931]) ).
thf(3173,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK47_SX0 @ SV126 @ SV433 ) )
| ~ ( in @ ( sK47_SX0 @ SV126 @ SV433 ) @ SV126 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2932]) ).
thf(3174,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK48_SX0 @ SV126 @ SV433 ) )
| ~ ( in @ ( sK48_SX0 @ SV126 @ SV433 ) @ SV126 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2933]) ).
thf(3175,plain,
! [SV131: $i,SV438: $i,SV662: $i] :
( ( ( in @ SV662 @ SV438 )
= $true )
| ( ( ~ ( subset @ SV131 @ SV438 ) )
= $true )
| ( ( in @ SV662 @ SV131 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(3176,plain,
! [SV132: $i,SV439: $i,SV751: $i,SV663: $i] :
( ( ( SV663 = SV751 )
= $false )
| ( ( SV439 = SV751 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV132 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV132 @ ( setadjoin @ SV439 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV663 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV663 @ ( setadjoin @ SV751 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3177,plain,
! [SV793: $i,SV440: $i,SV133: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV133 )
| ~ ( in @ SV942 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SV942 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) )
= $true )
| ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2937]) ).
thf(3178,plain,
! [SV794: $i,SV441: $i,SV134: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ ( powerset @ SV134 ) )
| ! [SY1746: $i] :
( ~ ( in @ SY1746 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SY1746 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SY1746 ) ) ) )
= $true )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2938]) ).
thf(3179,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV795 ) )
= $true )
| ( ( ~ ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3180,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV796 ) )
= $true )
| ( ( ~ ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2940]) ).
thf(3181,plain,
! [SV664: $i,SV881: $i,SV444: $i,SV139: $i] :
( ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( ~ ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1707 )
= ( ap @ SV139 @ SV444 @ SV881 @ SY1707 ) ) )
| ( SV664 = SV881 ) )
= $true )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3182,plain,
! [SV140: $i,SV445: $i > $i] :
( ( ! [SY1557: $i] :
~ ( ~ ( ~ ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1069: $i] :
~ ~ ( ~ ( in @ SY1069 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1069 ) ) ) )
| ~ ( ~ ~ ! [SY1070: $i] :
~ ~ ( ~ ( in @ SY1070 @ SV140 )
| ( SY1557
!= ( SV445 @ SY1070 ) ) )
| ( in @ SY1557 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(3183,plain,
! [SV445: $i > $i,SV140: $i] :
( ( ! [SY1560: $i] :
( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ SY1560 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1072
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1072 @ SY1560 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SY1560 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(3184,plain,
! [SV448: $i,SV798: $i,SV143: $i,SV944: $i] :
( ( ( ~ ( in @ SV944 @ ( powerset @ SV143 ) )
| ~ ( subset @ SV798 @ SV944 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SV944 ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2945]) ).
thf(3185,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( ~ ( in @ ( sK29_SY1085 @ SV449 @ SV144 ) @ SV144 )
| ~ ( SV449 @ ( sK29_SY1085 @ SV449 @ SV144 ) ) )
= $false )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2946]) ).
thf(3186,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 )
| ! [SY1747: $i] :
( ~ ( in @ SY1747 @ SV146 )
| ~ ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SY1747 ) @ SV451 )
| ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SY1747 ) ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2948]) ).
thf(3187,plain,
! [SV148: $i,SV667: $i,SV453: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) @ SV148 )
| ( SV667
!= ( SV453 @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) ) ) ) )
= $true )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2949]) ).
thf(3188,plain,
! [SV800: $i,SV454: $i,SV149: $i] :
( ( ( ~ ! [SY1618: $i] :
( ~ ( in @ SY1618 @ SV149 )
| ~ ( in @ SY1618 @ SV454 )
| ( in @ SY1618 @ SV800 ) ) )
= $true )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3189,plain,
! [SV458: $i > $o,SV153: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV153 )
| ~ ( SV458 @ SV882 ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2951]) ).
thf(3190,plain,
! [SV801: $i,SV459: $i,SV945: $i,SV154: $i] :
( ( ( ~ ( breln1 @ SV154 @ SV945 )
| ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SV945 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV801 )
= $false )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2952]) ).
thf(3191,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV802 ) )
= $true )
| ( ( ~ ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2953]) ).
thf(3192,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 )
| ! [SY1748: $i] :
( ~ ( in @ SY1748 @ SV156 )
| ~ ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SY1748 ) @ SV460 )
| ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SY1748 ) ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2954]) ).
thf(3193,plain,
! [SV157: $i,SV669: $i,SV461: $i,SV883: $i] :
( ( ( in @ SV883 @ SV461 )
= $false )
| ( ( in @ ( kpair @ SV669 @ SV883 ) @ ( cartprod @ SV157 @ SV461 ) )
= $true )
| ( ( in @ SV669 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3194,plain,
! [SV670: $i,SV462: $o,SV158: $i,SV884: $i] :
( ( ( in @ SV884 @ SV158 )
= $false )
| ( ( ~ ~ SV462
| ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) ) )
= $true )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3195,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( ( in @ SV885 @ SV158 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) ) )
= $true )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3196,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( ( in @ SV886 @ SV158 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) ) )
= $true )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3197,plain,
! [SV160: $i,SV464: $i,SV674: $i] :
( ( ( in @ SV674 @ SV464 )
= $true )
| ( ( SV160 != SV464 )
= $true )
| ( ( in @ SV674 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3198,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( ~ ~ ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) ) )
= $true )
| ( ( in @ SV804 @ SV467 )
= $true )
| ( ( in @ SV804 @ SV163 )
= $false )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3199,plain,
! [SV164: $i,SV468: $i,SV676: $i] :
( ( ( in @ SV676 @ SV468 )
= $true )
| ( ( in @ SV676 @ ( setminus @ SV164 @ SV468 ) )
= $true )
| ( ( in @ SV676 @ SV164 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2963]) ).
thf(3200,plain,
! [SV677: $i,SV469: $i > $o,SV165: $i] :
( ( ( ( dsetconstr @ SV165
@ ^ [SY1118: $i] : ( SV469 @ SY1118 ) )
= emptyset )
= $false )
| ( ( SV469 @ SV677 )
= $false )
| ( ( in @ SV677 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3201,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY430: $i,SY431: $i] :
( ~ ( SV166 @ SY430 )
| ~ ( SV166 @ SY431 )
| ( SY430 = SY431 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2965]) ).
thf(3202,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV806 ) )
= $true )
| ( ( ~ ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2966]) ).
thf(3203,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( ~ ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV168 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SV470 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV678 )
| ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV887 ) ) )
| ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3204,plain,
! [SV472: $i > $i,SV170: $i,SV679: $i] :
( ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false )
| ( ( ~ ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3205,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ( ~ ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2969]) ).
thf(3206,plain,
! [SV473: $i,SV807: $i,SV171: $i,SV946: $i] :
( ( ( ~ ( in @ SV946 @ SV171 )
| ~ ~ ( in @ SV946 @ SV807 )
| ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2970]) ).
thf(3207,plain,
! [SV172: $i,SV680: $i > $i,SV474: $i] :
( ( ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 )
= $true )
| ( ( ! [SY1464: $i] :
( ~ ( in @ SY1464 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SY1464 )
= ( SV680 @ SY1464 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2971]) ).
thf(3208,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV947: $i] :
( ( ( ~ ( in @ SV947 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV947 )
= ( SV680 @ SV947 ) ) )
= $true )
| ( ( in @ ( SV680 @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) ) @ SV474 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2972]) ).
thf(3209,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
| ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 ) )
| ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2973]) ).
thf(3210,plain,
! [SV475: $i,SV175: $i,SV888: $i,SV809: $i] :
( ( ( SV809 = SV888 )
= $false )
| ( ( ( setadjoin @ SV175 @ SV809 )
= ( setadjoin @ SV475 @ SV888 ) )
= $true )
| ( ( SV175 = SV475 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3211,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
| ( SV476 @ SV681 ) )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2975]) ).
thf(3212,plain,
! [SV176: $i,SV681: $i,SV476: $i > $o] :
( ( ( ~ ( SV476 @ SV681 )
| ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) ) )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3213,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK31_SY1142 @ SV478 @ SV178 ) @ SV178 )
| ~ ( in @ SV478 @ ( sK31_SY1142 @ SV478 @ SV178 ) ) )
= $false )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3214,plain,
! [SV810: $i,SV479: $i,SV179: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ ( powerset @ SV179 ) )
| ! [SY1750: $i] :
( ~ ( in @ SY1750 @ SV179 )
| ~ ( in @ SY1750 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1750 @ ( binunion @ SV810 @ SV948 ) ) ) )
= $true )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2978]) ).
thf(3215,plain,
! [SV683: $i,SV480: $o,SV181: $i,SV889: $i] :
( ( ( in @ SV889 @ SV181 )
= $false )
| ( ( ~ SV480
| ( ( if @ SV181 @ SV480 @ SV683 @ SV889 )
= SV683 ) )
= $true )
| ( ( in @ SV683 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3216,plain,
! [SV684: $i,SV181: $i,SV890: $i] :
( ( ( in @ SV890 @ SV181 )
= $false )
| ( ( ~ $true
| ( ( if @ SV181 @ $true @ SV684 @ SV890 )
= SV684 ) )
= $true )
| ( ( in @ SV684 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3217,plain,
! [SV685: $i,SV181: $i,SV891: $i] :
( ( ( in @ SV891 @ SV181 )
= $false )
| ( ( ~ $false
| ( ( if @ SV181 @ $false @ SV685 @ SV891 )
= SV685 ) )
= $true )
| ( ( in @ SV685 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2981]) ).
thf(3218,plain,
! [SV182: $i,SV481: $i,SV686: $i] :
( ( ( in @ SV686 @ SV481 )
= $false )
| ( ( in @ SV686 @ ( symdiff @ SV182 @ SV481 ) )
= $true )
| ( ( in @ SV686 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3219,plain,
! [SV892: $i > $o,SV687: $i,SV482: $i,SV183: $i] :
( ( ( ! [SY1715: $i] :
( ~ ( in @ SY1715 @ SV183 )
| ! [SY1716: $i] :
( ~ ( in @ SY1716 @ SV482 )
| ~ ( in @ ( kpair @ SY1715 @ SY1716 ) @ SV687 )
| ( SV892 @ ( kpair @ SY1715 @ SY1716 ) ) ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3220,plain,
! [SV184: $i,SV483: $i,SV688: $i] :
( ( ( in @ SV688 @ SV483 )
= $true )
| ( ( ~ ( in @ SV688 @ SV184 ) )
= $true )
| ( ( subset @ SV184 @ SV483 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2984]) ).
thf(3221,plain,
! [SV812: $i,SV486: $i,SV188: $i,SV949: $i] :
( ( ( ~ ( in @ SV949 @ SV188 )
| ~ ( in @ SV949 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SV949 @ ( setminus @ SV188 @ SV486 ) ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2986]) ).
thf(3222,plain,
! [SV813: $i,SV487: $i > $o,SV189: $i,SV950: $i] :
( ( ( ~ ( in @ SV950 @ SV189 )
| ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SV950 )
| ( SV813 = SV950 ) )
= $true )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2987]) ).
thf(3223,plain,
! [SV689: $i,SV488: $o,SV190: $i,SV893: $i] :
( ( ( in @ SV893 @ SV190 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1718: $i] :
( ~ ( ~ SV488
| ( SY1718 != SV689 ) )
| ~ ( ~ ~ SV488
| ( SY1718 != SV893 ) ) ) ) )
= $true )
| ( ( in @ SV689 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3224,plain,
! [SV690: $i,SV190: $i,SV894: $i] :
( ( ( in @ SV894 @ SV190 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1719: $i] :
( ~ ( ~ $true
| ( SY1719 != SV690 ) )
| ~ ( ~ ~ $true
| ( SY1719 != SV894 ) ) ) ) )
= $true )
| ( ( in @ SV690 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3225,plain,
! [SV691: $i,SV190: $i,SV895: $i] :
( ( ( in @ SV895 @ SV190 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV190
@ ^ [SY1720: $i] :
( ~ ( ~ $false
| ( SY1720 != SV691 ) )
| ~ ( ~ ~ $false
| ( SY1720 != SV895 ) ) ) ) )
= $true )
| ( ( in @ SV691 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3226,plain,
! [SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3227,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
| ~ ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2992]) ).
thf(3228,plain,
! [SV814: $i,SV496: $i,SV198: $i,SV952: $i] :
( ( ( ~ ( in @ SV952 @ SV198 )
| ~ ( in @ SV952 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SV952 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) )
= $true )
| ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2993]) ).
thf(3229,plain,
! [SV200: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV200 ) )
= $true )
| ( ( subset @ SV922 @ SV200 )
= $true )
| ( ( in @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2995]) ).
thf(3230,plain,
! [SV200: $i,SV896: $i] :
( ( ( in @ SV896 @ SV200 )
= $false )
| ( ( subset @ SV896 @ SV200 )
= $true )
| ( ( subset @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3231,plain,
! [SV202: $i,SV695: $i > $i,SV499: $i] :
( ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true )
| ( ( ! [SY1482: $i] :
( ~ ( in @ SY1482 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1483: $i] :
( ~ ( in @ SY1483 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SY1482 @ ( SV695 @ SY1483 ) )
= SY1483 ) )
| ( surjective @ SV499 @ SV202 @ SY1482 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3232,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ SY1752 ) )
= SY1752 ) )
| ( surjective @ SV499 @ SV202 @ SV953 ) )
= $true )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2998]) ).
thf(3233,plain,
! [SV205: $i,SV500: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV500 ) )
= $true )
| ( ( in @ SV815 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) )
= $true )
| ( ( in @ SV815 @ SV205 )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2999]) ).
thf(3234,plain,
! [SV817: $i,SV504: $i,SV209: $i] :
( ( ( ~ ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV209 )
| ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV209 )
| ~ ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV504 )
| ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV817 ) ) ) )
= $true )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3235,plain,
! [SV818: $i,SV506: $i,SV211: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ ( powerset @ SV211 ) )
| ! [SY1753: $i] :
( ~ ( in @ SY1753 @ SV211 )
| ~ ( in @ SY1753 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1753 @ ( binunion @ SV506 @ SV954 ) ) ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3003]) ).
thf(3236,plain,
! [SV212: $i] :
( ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
| ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3237,plain,
! [SV212: $i,SV955: $i] :
( ( ~ ~ ( ~ ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) )
| ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
| ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3005]) ).
thf(3238,plain,
! [SV698: $i,SV507: $i,SV213: $i,SV897: $i] :
( ( ( in @ SV897 @ SV213 )
= $false )
| ( ( ( ap @ SV213 @ SV507 @ SV698 @ SV897 )
= ( ap @ SV213 @ SV507 @ SV698 @ SV897 ) )
= $true )
| ( ( in @ SV698 @ ( funcSet @ SV213 @ SV507 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3006]) ).
thf(3239,plain,
! [SV699: $i,SV508: $o,SV214: $i,SV898: $i] :
( ( ( in @ SV898 @ SV214 )
= $false )
| ( ( in @ ( if @ SV214 @ SV508 @ SV699 @ SV898 ) @ ( setadjoin @ SV699 @ ( setadjoin @ SV898 @ emptyset ) ) )
= $true )
| ( ( in @ SV699 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3007]) ).
thf(3240,plain,
! [SV700: $i,SV214: $i,SV899: $i] :
( ( ( in @ SV899 @ SV214 )
= $false )
| ( ( in @ ( if @ SV214 @ $true @ SV700 @ SV899 ) @ ( setadjoin @ SV700 @ ( setadjoin @ SV899 @ emptyset ) ) )
= $true )
| ( ( in @ SV700 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3008]) ).
thf(3241,plain,
! [SV701: $i,SV214: $i,SV900: $i] :
( ( ( in @ SV900 @ SV214 )
= $false )
| ( ( in @ ( if @ SV214 @ $false @ SV701 @ SV900 ) @ ( setadjoin @ SV701 @ ( setadjoin @ SV900 @ emptyset ) ) )
= $true )
| ( ( in @ SV701 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3242,plain,
! [SV215: $i,SV509: $i,SV702: $i > $i > $o] :
( ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3010]) ).
thf(3243,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i] :
( ( ( ! [SY1721: $i] :
~ ~ ( ~ ( in @ SY1721 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SY1721 ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3244,plain,
! [SV705: $i,SV516: $i,SV225: $i,SV901: $i] :
( ( ( in @ SV901 @ SV225 )
= $false )
| ( ( ! [SY1722: $i] :
( ~ ( in @ SY1722 @ SV516 )
| ~ ( in @ ( kpair @ SV901 @ SY1722 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SY1722 ) ) )
= $true )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3012]) ).
thf(3245,plain,
! [SV226: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ omega )
| ~ ( in @ ( sK51_SY601 @ SV226 ) @ SV226 ) )
| ( in @ ( setadjoin @ ( sK51_SY601 @ SV226 ) @ ( sK51_SY601 @ SV226 ) ) @ SV226 ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3013]) ).
thf(3246,plain,
! [SV819: $i,SV227: $i,SV517: $i] :
( ( ( ~ ( subset @ SV517 @ ( setminus @ SV227 @ SV819 ) ) )
= $true )
| ( ( subset @ SV819 @ ( setminus @ SV227 @ SV517 ) )
= $true )
| ( ( in @ SV819 @ ( powerset @ SV227 ) )
= $false )
| ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3247,plain,
! [SV230: $i,SV519: $i] :
( ( ( ~ ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) ) )
= $true )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3248,plain,
! [SV230: $i,SV519: $i] :
( ( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3018]) ).
thf(3249,plain,
! [SV521: $i > $o,SV232: $i,SV902: $i] :
( ( ( in @ SV902 @ SV232 )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( ~ ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3250,plain,
! [SV822: $i,SV523: $i,SV234: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV234 )
| ! [SY1761: $i] :
( ~ ( in @ SY1761 @ SV234 )
| ! [SY1762: $i] :
( ~ ( in @ SY1762 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1762 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1762 @ SY1761 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SY1761 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3020]) ).
thf(3251,plain,
! [SV235: $i,SV524: $i] :
( ( ( ~ ( ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV524 ) ) )
= $true )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3252,plain,
! [SV709: $i > $i > $o,SV238: $i,SV757: $i,SV527: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ SV527 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV757 @ SV923 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SV923 ) )
= $true )
| ( ( in @ SV757 @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3253,plain,
! [SV239: $i,SV710: $i,SV528: $i,SV903: $i] :
( ( ( in @ SV903 @ SV528 )
= $false )
| ( ( in @ ( setadjoin @ SV710 @ ( setadjoin @ SV903 @ emptyset ) ) @ ( powerset @ ( binunion @ SV239 @ SV528 ) ) )
= $true )
| ( ( in @ SV710 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3254,plain,
! [SV711: $i,SV530: $o,SV241: $i,SV904: $i] :
( ( ( in @ SV904 @ SV241 )
= $false )
| ( ( in @ ( if @ SV241 @ SV530 @ SV711 @ SV904 ) @ SV241 )
= $true )
| ( ( in @ SV711 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3255,plain,
! [SV712: $i,SV241: $i,SV905: $i] :
( ( ( in @ SV905 @ SV241 )
= $false )
| ( ( in @ ( if @ SV241 @ $true @ SV712 @ SV905 ) @ SV241 )
= $true )
| ( ( in @ SV712 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3256,plain,
! [SV713: $i,SV241: $i,SV906: $i] :
( ( ( in @ SV906 @ SV241 )
= $false )
| ( ( in @ ( if @ SV241 @ $false @ SV713 @ SV906 ) @ SV241 )
= $true )
| ( ( in @ SV713 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3028]) ).
thf(3257,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3029]) ).
thf(3258,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3259,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
| ~ ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
| ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3030]) ).
thf(3260,plain,
! [SV248: $i,SV537: $i,SV957: $i] :
( ( ( ~ ( in @ SV957 @ SV537 )
| ( in @ SV957 @ SV248 ) )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3031]) ).
thf(3261,plain,
! [SV537: $i,SV248: $i] :
( ( ( ~ ( in @ ( sK52_SY1247 @ SV248 @ SV537 ) @ SV537 )
| ( in @ ( sK52_SY1247 @ SV248 @ SV537 ) @ SV248 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3032]) ).
thf(3262,plain,
! [SV716: $i,SV538: $i,SV250: $i,SV907: $i] :
( ( ( in @ SV907 @ SV250 )
= $false )
| ( ( ! [SY1723: $i] :
( ~ ( in @ SY1723 @ SV538 )
| ~ ( in @ ( kpair @ SV907 @ SY1723 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SY1723 ) ) )
= $true )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3263,plain,
! [SV539: $i,SV824: $i,SV251: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ SV251 )
| ~ ( in @ ( kpair @ SV824 @ SV958 ) @ SV539 )
| ( in @ ( kpair @ SV958 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) )
= $true )
| ( ( in @ SV824 @ SV251 )
= $false )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3034]) ).
thf(3264,plain,
! [SV540: $i,SV825: $i,SV252: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ SV252 )
| ~ ( in @ ( kpair @ SV959 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SV959 ) @ SV540 ) )
= $true )
| ( ( in @ SV825 @ SV252 )
= $false )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3035]) ).
thf(3265,plain,
! [SV826: $i,SV545: $i,SV255: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV255 )
| ! [SY1763: $i] :
( ~ ( in @ SY1763 @ SV255 )
| ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1764: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV545 )
| SY1764 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV826 )
| SY1764 )
| SY1764 ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3036]) ).
thf(3266,plain,
! [SV257: $i,SV719: $i,SV547: $i,SV908: $i] :
( ( ( in @ SV908 @ SV547 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV719 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV719 @ ( setadjoin @ SV908 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV257 @ SV547 ) ) )
= $true )
| ( ( in @ SV719 @ SV257 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3267,plain,
! [SV827: $i,SV548: $i,SV258: $i,SV961: $i] :
( ( ( ~ ( in @ SV961 @ ( powerset @ SV258 ) )
| ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SV961 ) @ ( binunion @ SV827 @ SV961 ) ) ) ) )
= $true )
| ( ( in @ SV827 @ ( powerset @ SV258 ) )
= $false )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3038]) ).
thf(3268,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3269,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
| ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3040]) ).
thf(3270,plain,
! [SV828: $i,SV552: $i,SV263: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ ( powerset @ SV263 ) )
| ~ ( subset @ SV552 @ SV962 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SV962 ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3041]) ).
thf(3271,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ~ ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV264 )
| ! [SY1655: $i] :
( ~ ( in @ SY1655 @ SV264 )
| ~ ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV553 )
| ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV829 ) ) ) )
= $true )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3042]) ).
thf(3272,plain,
! [SV554: $i,SV265: $i,SV721: $i] :
( ( ( in @ SV721 @ ( symdiff @ SV265 @ SV554 ) )
= $false )
| ( ( in @ SV721 @ SV554 )
= $false )
| ( ( in @ SV721 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3043]) ).
thf(3273,plain,
! [SV557: $i,SV268: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) ) )
= $true )
| ( ( in @ SV830 @ SV557 )
= $true )
| ( ( in @ SV830 @ SV268 )
= $false )
| ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3044]) ).
thf(3274,plain,
! [SV558: $i > $o,SV269: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV269 )
| ~ ~ ( SV558 @ SV909 ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3275,plain,
! [SV270: $i,SV559: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ SV559 ) )
= $false )
| ( ( ~ ( in @ SV723 @ SV270 ) )
= $true )
| ( ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3276,plain,
! [SV831: $i,SV560: $i,SV271: $i,SV963: $i] :
( ( ( ~ ( in @ SV963 @ SV271 )
| ~ ( in @ SV963 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SV963 @ ( setminus @ SV271 @ SV831 ) ) )
= $true )
| ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3047]) ).
thf(3277,plain,
! [SV832: $i,SV562: $i,SV274: $i,SV964: $i] :
( ( ( ~ ( in @ SV964 @ SV274 )
| ! [SY1765: $i] :
( ~ ( in @ SY1765 @ SV274 )
| ~ ( in @ ( kpair @ SV964 @ SY1765 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SY1765 ) @ ( binunion @ SV562 @ SV832 ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3048]) ).
thf(3278,plain,
! [SV276: $i,SV564: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ SV564 ) )
= $false )
| ( ( ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true )
| ( ( in @ SV725 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3279,plain,
! [SV278: $i,SV726: $i,SV566: $i,SV910: $i] :
( ( ( in @ SV910 @ SV566 )
= $false )
| ( ( ( kfst @ ( kpair @ SV726 @ SV910 ) )
= SV726 )
= $true )
| ( ( in @ SV726 @ SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3280,plain,
! [SV281: $i] :
( ( ( ~ ( in @ ( sK35_SY742 @ SV281 ) @ SV281 )
| ~ $true )
= $false )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3281,plain,
! [SV911: $i > $o,SV833: $i > $o,SV569: $i,SV283: $i] :
( ( ( ! [SY1724: $i] :
( ~ ( in @ SY1724 @ SV283 )
| ! [SY1725: $i] :
( ~ ( in @ SY1725 @ SV569 )
| ( SY1724 != SY1725 )
| ~ ( ~ ( ~ ( SV833 @ SY1724 )
| ( SV911 @ SY1725 ) )
| ~ ( ~ ( SV911 @ SY1725 )
| ( SV833 @ SY1724 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3282,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV834 ) )
= $true )
| ( ( ~ ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3053]) ).
thf(3283,plain,
! [SV835: $i,SV570: $i,SV285: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ SV285 )
| ~ ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3054]) ).
thf(3284,plain,
! [SV572: $i,SV759: $o,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 )
| SV759 )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3285,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3286,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3287,plain,
! [SV573: $i,SV836: $i,SV288: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ SV288 )
| ! [SY1766: $i] :
( ~ ( in @ SY1766 @ SV288 )
| ~ ( in @ ( kpair @ SV966 @ SY1766 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SY1766 ) @ ( binunion @ SV573 @ SV836 ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3058]) ).
thf(3288,plain,
! [SV731: $i,SV576: $o,SV291: $i,SV912: $i] :
( ( ( in @ SV912 @ SV291 )
= $false )
| ( ( ~ ~ SV576
| ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 ) )
= $true )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3289,plain,
! [SV732: $i,SV291: $i,SV913: $i] :
( ( ( in @ SV913 @ SV291 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 ) )
= $true )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3290,plain,
! [SV733: $i,SV291: $i,SV914: $i] :
( ( ( in @ SV914 @ SV291 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 ) )
= $true )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3291,plain,
! [SV838: $i,SV580: $i,SV296: $i] :
( ( ( ~ ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV296 )
| ~ ( in @ SY1670 @ SV580 )
| ( in @ SY1670 @ SV838 ) ) )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3063]) ).
thf(3292,plain,
! [SV839: $i,SV581: $i,SV297: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV297 )
| ! [SY1767: $i] :
( ~ ( in @ SY1767 @ SV297 )
| ~ ( ( in @ ( kpair @ SV967 @ SY1767 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ ( binunion @ SV581 @ SV839 ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3064]) ).
thf(3293,plain,
! [SV734: $i,SV915: $i,SV582: $i,SV298: $i] :
( ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( ~ ! [SY1728: $i] :
( ~ ( in @ SY1728 @ SV298 )
| ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV582 )
| ~ ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV734 )
| ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV915 ) ) )
| ( subset @ SV734 @ SV915 ) )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3294,plain,
! [SV840: $i,SV583: $i,SV299: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ SV299 )
| ~ ( in @ SV968 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SV968 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3066]) ).
thf(3295,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ SV841 ) )
= $true )
| ( ( ~ ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3067]) ).
thf(3296,plain,
! [SV842: $i,SV584: $i,SV301: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV301 )
| ~ ( in @ SV969 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SV969 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3068]) ).
thf(3297,plain,
! [SV843: $i,SV585: $i,SV302: $i,SV970: $i] :
( ( ( ~ ( in @ SV970 @ SV302 )
| ~ ( in @ SV970 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SV970 @ ( setminus @ SV302 @ SV585 ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3069]) ).
thf(3298,plain,
! [SV305: $i,SV844: $i,SV587: $i,SV971: $i] :
( ( ( ~ ( in @ SV971 @ ( binintersect @ SV587 @ SV844 ) )
| ( in @ SV971 @ SV305 ) )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3071]) ).
thf(3299,plain,
! [SV307: $i,SV589: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ SV589 ) )
= $true )
| ( ( ~ ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) ) )
= $true )
| ( ( in @ SV845 @ SV307 )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3300,plain,
! [SV591: $i,SV916: $o,SV309: $i,SV736: $i] :
( ( ( ( SV736 != SV309 )
| SV916 )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3075]) ).
thf(3301,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ( SV736 != SV309 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3302,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( ( SV736 != SV309 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3303,plain,
! [SV847: $i,SV592: $i,SV310: $i] :
( ( ( ~ ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV310 )
| ~ ( in @ SY1678 @ SV592 )
| ( in @ SY1678 @ SV847 ) ) )
= $true )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3304,plain,
! [SV313: $i,SV738: $i,SV595: $i,SV917: $i] :
( ( ( in @ SV917 @ SV595 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV738 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV738 @ ( setadjoin @ SV917 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV313 @ SV595 ) ) ) )
= $true )
| ( ( in @ SV738 @ SV313 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3305,plain,
! [SV314: $i,SV760: $i,SV739: $i > $i > $o,SV596: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ SV596 ) )
= $true )
| ( ( ~ ( SV739 @ SV760 @ SV924 )
| ( in @ ( kpair @ SV760 @ SV924 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) )
= $true )
| ( ( in @ SV760 @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3306,plain,
! [SV972: $o,SV848: $i,SV597: $i,SV315: $i] :
( ( ( ! [SY1768: $i] :
( ~ ( in @ SY1768 @ SV315 )
| ~ ( in @ SY1768 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SY1768 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SY1768 @ SV848 )
| SV972 )
| SV972 ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3081]) ).
thf(3307,plain,
! [SV848: $i,SV597: $i,SV315: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV315 )
| ~ ( in @ SX0 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SX0 @ SV597 )
| $true )
| ~ ( ~ ( in @ SX0 @ SV848 )
| $true )
| $true ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3081]) ).
thf(3308,plain,
! [SV848: $i,SV597: $i,SV315: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV315 )
| ~ ( in @ SX0 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SX0 @ SV597 )
| $false )
| ~ ( ~ ( in @ SX0 @ SV848 )
| $false )
| $false ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[3081]) ).
thf(3309,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV973: $i] :
( ( ( ~ ( in @ SV973 @ ( powerset @ SV317 ) )
| ! [SY1769: $i] :
( ~ ( in @ SY1769 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SY1769 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SY1769 ) ) ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3082]) ).
thf(3310,plain,
! [SV850: $i,SV600: $i,SV318: $i,SV974: $i] :
( ( ( ~ ( in @ SV974 @ SV318 )
| ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SV974 @ SV850 )
| ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3083]) ).
thf(3311,plain,
! [SV740: $i,SV601: $i,SV319: $i,SV918: $i] :
( ( ( in @ SV918 @ SV319 )
= $false )
| ( ( in @ ( kpair @ SV918 @ ( ap @ SV319 @ SV601 @ SV740 @ SV918 ) ) @ SV740 )
= $true )
| ( ( func @ SV319 @ SV601 @ SV740 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3312,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ( SV323 @ SV852 ) )
= $true )
| ( ( ~ ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3313,plain,
! [SV324: $i,SV743: $i,SV605: $i,SV919: $i] :
( ( ( in @ SV919 @ SV605 )
= $false )
| ( ( ( kpair @ SV743 @ SV919 )
= ( kpair @ SV743 @ SV919 ) )
= $true )
| ( ( in @ SV743 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3314,plain,
! [SV3: $i,SV920: $i] :
( ( ( ! [SY1730: $i] :
( ~ ( in @ SY1730 @ SV920 )
| ( subset @ SY1730 @ SV920 ) ) )
= $false )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3315,plain,
! [SV854: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
| ( subset @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 ) )
= $false )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3092]) ).
thf(3316,plain,
! [SV611: $i,SV332: $i > $o,SV8: $i] :
( ( ( ! [SY1370: $i] :
( ~ ( in @ SY1370 @ SV8 )
| ~ ( SV332 @ SY1370 )
| ( SY1370 = SV611 ) ) )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3317,plain,
! [SV858: $i,SV614: $i,SV335: $i,SV11: $i] :
( ( ( ~ ! [SY1687: $i] :
( ~ ( in @ SY1687 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1687 )
= ( ap @ SV11 @ SV335 @ SV858 @ SY1687 ) ) ) )
= $true )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3098]) ).
thf(3318,plain,
! [SV761: $i,SV340: $i,SV17: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ ( powerset @ SV17 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SV925 ) @ ( binunion @ SV761 @ SV925 ) ) ) )
= $true )
| ( ( in @ SV761 @ ( powerset @ SV17 ) )
= $false )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3100]) ).
thf(3319,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( ~ ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 )
| ! [SY1770: $i] :
( ~ ( in @ SY1770 @ SV342 )
| ~ ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SY1770 ) @ SV618 )
| ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SY1770 ) ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3101]) ).
thf(3320,plain,
! [SV762: $i,SV343: $i,SV20: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV20 ) )
= $true )
| ( ( ~ ~ ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3321,plain,
! [SV763: $i,SV21: $i,SV344: $i] :
( ( ( subset @ SV344 @ ( setminus @ SV21 @ SV763 ) )
= $false )
| ( ( subset @ SV763 @ ( setminus @ SV21 @ SV344 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV21 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV21 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3103]) ).
thf(3322,plain,
! [SV346: $i,SV860: $i,SV24: $i,SV764: $i] :
( ( ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) )
| ~ ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) ) )
= $false )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3104]) ).
thf(3323,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( ~ ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
| ~ ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3324,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3106]) ).
thf(3325,plain,
! [SV348: $i > $o,SV27: $i] :
( ( ( ! [SY902: $i] :
~ ~ ( ~ ( in @ SY902 @ SV27 )
| ~ ( SV348 @ SY902 ) ) )
= $true )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3326,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( SV621 = SV31 )
= $true )
| ( ( in @ SV621 @ SV351 )
= $true )
| ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3327,plain,
! [SV351: $i,SV31: $i,SV621: $i] :
( ( ( SV621 = SV31 )
= $false )
| ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3328,plain,
! [SV31: $i,SV351: $i,SV621: $i] :
( ( ( in @ SV621 @ SV351 )
= $false )
| ( ( in @ SV621 @ ( setadjoin @ SV31 @ SV351 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3329,plain,
! [SV765: $i,SV353: $i,SV34: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV34 ) )
= $true )
| ( ( ~ ~ ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3111]) ).
thf(3330,plain,
! [SV768: $i,SV357: $i,SV40: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV40 ) )
= $true )
| ( ( ! [SY1737: $i] :
( ~ ( in @ SY1737 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1737 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1738: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1738 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1738 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1738 @ SY1737 ) @ SV768 ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3112]) ).
thf(3331,plain,
! [SV769: $i,SV358: $i,SV929: $i,SV41: $i] :
( ( ( ~ ( breln1 @ SV41 @ SV929 ) )
= $true )
| ( ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SV929 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SV929 ) @ ( breln1compset @ SV41 @ SV769 @ SV929 ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV769 )
= $false )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3113]) ).
thf(3332,plain,
! [SV770: $i,SV359: $i,SV42: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ SV42 ) )
= $true )
| ( ( ~ ( in @ SV930 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SV930 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) )
= $true )
| ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3114]) ).
thf(3333,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i,SV921: $i] :
( ( ( ~ ( in @ SV921 @ SV43 )
| ( SV623
!= ( SV360 @ SV921 ) ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3115]) ).
thf(3334,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ SV364 @ ( sK55_SY928 @ SV47 @ SV364 ) )
| ~ ( in @ ( sK55_SY928 @ SV47 @ SV364 ) @ SV47 ) ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3116]) ).
thf(3335,plain,
! [SV47: $i,SV975: $i,SV364: $i] :
( ( ( ~ ~ ( ~ ( in @ SV364 @ SV975 )
| ~ ( in @ SV975 @ SV47 ) ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3117]) ).
thf(3336,plain,
! [SV773: $i,SV367: $i,SV52: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ SV52 ) )
= $true )
| ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3119]) ).
thf(3337,plain,
! [SV53: $i,SV774: $i,SV368: $i] :
( ( ( subset @ SV368 @ SV774 )
= $false )
| ( ( subset @ ( setminus @ SV53 @ SV774 ) @ ( setminus @ SV53 @ SV368 ) )
= $true )
| ( ( in @ SV774 @ ( powerset @ SV53 ) )
= $false )
| ( ( in @ SV368 @ ( powerset @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3338,plain,
! [SV369: $i,SV775: $i,SV54: $i] :
( ( ( subset @ ( setminus @ SV54 @ SV775 ) @ ( setminus @ SV54 @ SV369 ) )
= $false )
| ( ( subset @ SV369 @ SV775 )
= $true )
| ( ( in @ SV775 @ ( powerset @ SV54 ) )
= $false )
| ( ( in @ SV369 @ ( powerset @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3339,plain,
! [SV776: $i,SV55: $i,SV370: $i] :
( ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( ! [SY1586: $i] :
( ~ ( in @ SY1586 @ SV55 )
| ~ ( in @ SY1586 @ SV776 )
| ( in @ SY1586 @ ( setminus @ SV55 @ SV370 ) ) ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3340,plain,
! [SV777: $i,SV372: $i,SV57: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SV932 @ SV372 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3123]) ).
thf(3341,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
| ~ ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3342,plain,
! [SV862: $i,SV376: $i > $o,SV61: $i] :
( ( ( ! [SY945: $i] :
~ ~ ( ~ ( in @ SY945 @ SV61 )
| ~ ~ ( SV376 @ SY945 ) ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3343,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV976: $i] :
( ( ( ~ ( in @ SV976 @ SV62 )
| ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV976 )
= ( SV629 @ SV976 ) ) )
= $true )
| ( ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3126]) ).
thf(3344,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV62 ) )
= $true )
| ( ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV933 )
= ( SV629 @ SV933 ) )
= $true )
| ( ( in @ ( SV629 @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) ) @ SV377 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3127]) ).
thf(3345,plain,
! [SV778: $i,SV380: $i,SV66: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV66 ) )
= $true )
| ( ( ~ ~ ( in @ SV934 @ SV380 )
| ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3128]) ).
thf(3346,plain,
! [SV381: $i,SV863: $i,SV67: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ SV67 ) )
= $true )
| ( ( in @ SV863 @ SV381 )
= $true )
| ( ( SV779 = SV863 )
= $false )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3129]) ).
thf(3347,plain,
! [SV864: $i,SV632: $i,SV70: $i,SV383: $o] :
( ( ( ~ ~ SV383 )
= $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) )
= $true )
| ( ( in @ SV864 @ SV70 )
= $false )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3130]) ).
thf(3348,plain,
! [SV865: $i,SV633: $i,SV70: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) )
= $true )
| ( ( in @ SV865 @ SV70 )
= $false )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3131]) ).
thf(3349,plain,
! [SV866: $i,SV634: $i,SV70: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) )
= $true )
| ( ( in @ SV866 @ SV70 )
= $false )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3350,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ( ~ ( in @ ( sK45_SY168 @ SV780 @ SV73 ) @ SV73 )
| ~ ~ ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3133]) ).
thf(3351,plain,
! [SV781: $i,SV386: $i,SV76: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV76 ) )
= $true )
| ( ( ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SV935 @ SV386 )
| ( in @ SV935 @ SV781 ) )
= $true )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3135]) ).
thf(3352,plain,
! [SV782: $i,SV387: $i,SV77: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV77 ) )
= $true )
| ( ( ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SV936 @ SV782 )
| ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3353,plain,
! [SV784: $i,SV392: $i,SV82: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ SV82 ) )
= $true )
| ( ( ~ ~ ( in @ SV937 @ SV392 )
| ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3138]) ).
thf(3354,plain,
! [SV786: $i,SV402: $i,SV93: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV93 ) )
= $true )
| ( ( ! [SY1741: $i] :
( ~ ( in @ SY1741 @ SV93 )
| ~ ( in @ ( kpair @ SV938 @ SY1741 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV786 ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3144]) ).
thf(3355,plain,
! [SV871: $i,SV94: $i,SV644: $i,SV403: $o] :
( ( ( ~ SV403 ) = $true )
| ( ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1697: $i] :
( ~ ( ~ SV403
| ( SY1697 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1697 != SV871 ) ) ) ) )
= $true )
| ( ( in @ SV871 @ SV94 )
= $false )
| ( ( in @ SV644 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3356,plain,
! [SV872: $i,SV94: $i,SV645: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1698: $i] :
( ~ ( ~ $true
| ( SY1698 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1698 != SV872 ) ) ) ) )
= $true )
| ( ( in @ SV872 @ SV94 )
= $false )
| ( ( in @ SV645 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3146]) ).
thf(3357,plain,
! [SV873: $i,SV94: $i,SV646: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1699: $i] :
( ~ ( ~ $false
| ( SY1699 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1699 != SV873 ) ) ) ) )
= $true )
| ( ( in @ SV873 @ SV94 )
= $false )
| ( ( in @ SV646 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3358,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3359,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3148]) ).
thf(3360,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3149]) ).
thf(3361,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3149]) ).
thf(3362,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3363,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3150]) ).
thf(3364,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ SV99 ) )
= $true )
| ( ( ! [SY1742: $i] :
( ~ ( in @ SY1742 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1742 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1743: $o] :
( ~ ! [SY1744: $i] :
( ~ ( in @ SY1744 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1744 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1744 @ SY1742 ) @ SV787 )
| SY1743 )
| SY1743 ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3151]) ).
thf(3365,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3152]) ).
thf(3366,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3153]) ).
thf(3367,plain,
! [SV788: $i,SV416: $i,SV108: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ ( powerset @ SV108 ) ) )
= $true )
| ( ( ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SV940 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) ) )
= $true )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3154]) ).
thf(3368,plain,
! [SV875: $i,SV651: $i,SV417: $i,SV109: $i] :
( ( ( ~ ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1700 )
= ( ap @ SV109 @ SV417 @ SV875 @ SY1700 ) ) ) )
= $true )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3155]) ).
thf(3369,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( ~ ( in @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SV111 )
| ~ ~ ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3370,plain,
! [SV113: $i] :
( ( ( ~ ( in @ ( sK27_SY275 @ SV113 ) @ SV113 ) )
= $false )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3371,plain,
! [SV113: $i] :
( ( ( ( binintersect @ ( sK27_SY275 @ SV113 ) @ SV113 )
!= emptyset )
= $false )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3157]) ).
thf(3372,plain,
! [SV790: $i,SV424: $i,SV117: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ ( powerset @ SV117 ) ) )
= $true )
| ( ( ! [SY1745: $i] :
( ~ ( in @ SY1745 @ SV117 )
| ~ ( in @ SY1745 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1745 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) ) )
= $true )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3158]) ).
thf(3373,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3159]) ).
thf(3374,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3375,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3376,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
| ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3377,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ~ ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
| ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3378,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ~ ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) )
| ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3379,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3380,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3165]) ).
thf(3381,plain,
( ( in @ sK3_SY2 @ sK2_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3166]) ).
thf(3382,plain,
( ( ~ ( in @ sK3_SY2 @ sK1_X ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3383,plain,
! [SV878: $i,SV657: $i,SV125: $i,SV432: $o] :
( ( ( ~ SV432 ) = $true )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1704: $i] :
( ~ ( ~ SV432
| ( SY1704 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1704 != SV878 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) )
= $true )
| ( ( in @ SV878 @ SV125 )
= $false )
| ( ( in @ SV657 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3169]) ).
thf(3384,plain,
! [SV879: $i,SV658: $i,SV125: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1705: $i] :
( ~ ( ~ $true
| ( SY1705 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1705 != SV879 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) )
= $true )
| ( ( in @ SV879 @ SV125 )
= $false )
| ( ( in @ SV658 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3170]) ).
thf(3385,plain,
! [SV880: $i,SV659: $i,SV125: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1706: $i] :
( ~ ( ~ $false
| ( SY1706 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1706 != SV880 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) )
= $true )
| ( ( in @ SV880 @ SV125 )
= $false )
| ( ( in @ SV659 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3386,plain,
! [SV126: $i,SV791: $o,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) ) )
= $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3387,plain,
! [SV433: $i,SV126: $i,SV791: $o] :
( ( ( ~ ( in @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) @ SV126 )
| SV791 )
= $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3388,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK47_SX0 @ SV126 @ SV433 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3389,plain,
! [SV433: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK47_SX0 @ SV126 @ SV433 ) @ SV126 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3173]) ).
thf(3390,plain,
! [SV126: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ ( sK48_SX0 @ SV126 @ SV433 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3391,plain,
! [SV433: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK48_SX0 @ SV126 @ SV433 ) @ SV126 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3392,plain,
! [SV662: $i,SV438: $i,SV131: $i] :
( ( ( subset @ SV131 @ SV438 )
= $false )
| ( ( in @ SV662 @ SV438 )
= $true )
| ( ( in @ SV662 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3175]) ).
thf(3393,plain,
! [SV793: $i,SV440: $i,SV133: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV133 ) )
= $true )
| ( ( ~ ( in @ SV942 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SV942 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) )
= $true )
| ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3177]) ).
thf(3394,plain,
! [SV794: $i,SV441: $i,SV134: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ! [SY1746: $i] :
( ~ ( in @ SY1746 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SY1746 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SY1746 ) ) ) )
= $true )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3178]) ).
thf(3395,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( SV136 @ SV795 )
= $false )
| ( ( ~ ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) )
= $true )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3396,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( SV138 @ SV796 )
= $false )
| ( ( ~ ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) )
= $true )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3180]) ).
thf(3397,plain,
! [SV881: $i,SV664: $i,SV444: $i,SV139: $i] :
( ( ( ~ ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1707 )
= ( ap @ SV139 @ SV444 @ SV881 @ SY1707 ) ) ) )
= $true )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3181]) ).
thf(3398,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ~ ( ~ ( ~ ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
| ~ ( ~ ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) )
| ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3399,plain,
! [SV445: $i > $i,SV140: $i,SV978: $i] :
( ( ~ ! [SY1774: $i] :
~ ( ~ ( ~ ( in @ SY1774 @ SV978 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1774 @ SV978 ) ) )
| ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3183]) ).
thf(3400,plain,
! [SV448: $i,SV798: $i,SV143: $i,SV944: $i] :
( ( ( ~ ( in @ SV944 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( ~ ( subset @ SV798 @ SV944 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SV944 ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3184]) ).
thf(3401,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( ~ ( in @ ( sK29_SY1085 @ SV449 @ SV144 ) @ SV144 ) )
= $false )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3402,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( ~ ( SV449 @ ( sK29_SY1085 @ SV449 @ SV144 ) ) )
= $false )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3185]) ).
thf(3403,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( ~ ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3404,plain,
! [SV451: $i,SV799: $i > $o,SV146: $i] :
( ( ( ! [SY1747: $i] :
( ~ ( in @ SY1747 @ SV146 )
| ~ ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SY1747 ) @ SV451 )
| ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SY1747 ) ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3405,plain,
! [SV148: $i,SV667: $i,SV453: $i > $i] :
( ( ( ~ ( in @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) @ SV148 )
| ( SV667
!= ( SV453 @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) ) ) )
= $false )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3406,plain,
! [SV800: $i,SV454: $i,SV149: $i] :
( ( ( ! [SY1618: $i] :
( ~ ( in @ SY1618 @ SV149 )
| ~ ( in @ SY1618 @ SV454 )
| ( in @ SY1618 @ SV800 ) ) )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3188]) ).
thf(3407,plain,
! [SV458: $i > $o,SV153: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV153 ) )
= $true )
| ( ( ~ ( SV458 @ SV882 ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3189]) ).
thf(3408,plain,
! [SV801: $i,SV459: $i,SV945: $i,SV154: $i] :
( ( ( ~ ( breln1 @ SV154 @ SV945 ) )
= $true )
| ( ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SV945 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV801 )
= $false )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3190]) ).
thf(3409,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) )
= $true )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3191]) ).
thf(3410,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( ~ ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3411,plain,
! [SV460: $i,SV803: $i > $o,SV156: $i] :
( ( ( ! [SY1748: $i] :
( ~ ( in @ SY1748 @ SV156 )
| ~ ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SY1748 ) @ SV460 )
| ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SY1748 ) ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3412,plain,
! [SV670: $i,SV158: $i,SV884: $i,SV462: $o] :
( ( ( ~ ~ SV462 )
= $true )
| ( ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) )
= $true )
| ( ( in @ SV884 @ SV158 )
= $false )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3194]) ).
thf(3413,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) )
= $true )
| ( ( in @ SV885 @ SV158 )
= $false )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3195]) ).
thf(3414,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) )
= $true )
| ( ( in @ SV886 @ SV158 )
= $false )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3415,plain,
! [SV674: $i,SV464: $i,SV160: $i] :
( ( ( SV160 = SV464 )
= $false )
| ( ( in @ SV674 @ SV464 )
= $true )
| ( ( in @ SV674 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3416,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) ) )
= $false )
| ( ( in @ SV804 @ SV467 )
= $true )
| ( ( in @ SV804 @ SV163 )
= $false )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3417,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY1777: $i] :
( ~ ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
| ~ ( SV166 @ SY1777 )
| ( ( sK56_SY430 @ SV805 @ SV166 )
= SY1777 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3201]) ).
thf(3418,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) )
= $true )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3419,plain,
! [SV887: $i,SV678: $i,SV470: $i,SV168: $i] :
( ( ( ~ ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV168 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SV470 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV678 )
| ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV887 ) ) ) )
= $true )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3203]) ).
thf(3420,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ( ! [SY1460: $i] :
~ ~ ( ~ ( in @ SY1460 @ SV170 )
| ( SV679
!= ( SV472 @ SY1460 ) ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3421,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i] :
( ( ( ! [SY1461: $i] :
~ ~ ( ~ ( in @ SY1461 @ SV170 )
| ( SV679
!= ( SV472 @ SY1461 ) ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3205]) ).
thf(3422,plain,
! [SV473: $i,SV807: $i,SV171: $i,SV946: $i] :
( ( ( ~ ( in @ SV946 @ SV171 ) )
= $true )
| ( ( ~ ~ ( in @ SV946 @ SV807 )
| ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3206]) ).
thf(3423,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV172 )
| ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV979 )
= ( SV680 @ SV979 ) ) )
= $true )
| ( ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3424,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV947: $i] :
( ( ( ~ ( in @ SV947 @ SV172 ) )
= $true )
| ( ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV947 )
= ( SV680 @ SV947 ) )
= $true )
| ( ( in @ ( SV680 @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) ) @ SV474 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3425,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
| ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 ) ) )
= $true )
| ( ( ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3209]) ).
thf(3426,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( ~ ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) ) )
= $true )
| ( ( SV476 @ SV681 )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3427,plain,
! [SV176: $i,SV681: $i,SV476: $i > $o] :
( ( ( ~ ( SV476 @ SV681 ) )
= $true )
| ( ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3212]) ).
thf(3428,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ( in @ ( sK31_SY1142 @ SV478 @ SV178 ) @ SV178 ) )
= $false )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3429,plain,
! [SV178: $i,SV478: $i] :
( ( ( ~ ( in @ SV478 @ ( sK31_SY1142 @ SV478 @ SV178 ) ) )
= $false )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3430,plain,
! [SV810: $i,SV479: $i,SV179: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ ( powerset @ SV179 ) ) )
= $true )
| ( ( ! [SY1750: $i] :
( ~ ( in @ SY1750 @ SV179 )
| ~ ( in @ SY1750 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1750 @ ( binunion @ SV810 @ SV948 ) ) ) )
= $true )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3431,plain,
! [SV889: $i,SV683: $i,SV181: $i,SV480: $o] :
( ( ( ~ SV480 ) = $true )
| ( ( ( if @ SV181 @ SV480 @ SV683 @ SV889 )
= SV683 )
= $true )
| ( ( in @ SV889 @ SV181 )
= $false )
| ( ( in @ SV683 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3215]) ).
thf(3432,plain,
! [SV890: $i,SV684: $i,SV181: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV181 @ $true @ SV684 @ SV890 )
= SV684 )
= $true )
| ( ( in @ SV890 @ SV181 )
= $false )
| ( ( in @ SV684 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3433,plain,
! [SV891: $i,SV685: $i,SV181: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV181 @ $false @ SV685 @ SV891 )
= SV685 )
= $true )
| ( ( in @ SV891 @ SV181 )
= $false )
| ( ( in @ SV685 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3217]) ).
thf(3434,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( ~ ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 )
| ! [SY1779: $i] :
( ~ ( in @ SY1779 @ SV482 )
| ~ ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SY1779 ) @ SV687 )
| ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SY1779 ) ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3219]) ).
thf(3435,plain,
! [SV483: $i,SV184: $i,SV688: $i] :
( ( ( in @ SV688 @ SV184 )
= $false )
| ( ( in @ SV688 @ SV483 )
= $true )
| ( ( subset @ SV184 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3220]) ).
thf(3436,plain,
! [SV812: $i,SV486: $i,SV188: $i,SV949: $i] :
( ( ( ~ ( in @ SV949 @ SV188 ) )
= $true )
| ( ( ~ ( in @ SV949 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SV949 @ ( setminus @ SV188 @ SV486 ) ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3221]) ).
thf(3437,plain,
! [SV813: $i,SV487: $i > $o,SV189: $i,SV950: $i] :
( ( ( ~ ( in @ SV950 @ SV189 ) )
= $true )
| ( ( ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SV950 )
| ( SV813 = SV950 ) )
= $true )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3222]) ).
thf(3438,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ! [SY1780: $i] :
~ ( ~ ( ~ ( in @ SY1780 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1780 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1780 ) )
| ( in @ SY1780 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) ) ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3226]) ).
thf(3439,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
| ~ ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) ) )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3227]) ).
thf(3440,plain,
! [SV814: $i,SV496: $i,SV198: $i,SV952: $i] :
( ( ( ~ ( in @ SV952 @ SV198 ) )
= $true )
| ( ( ~ ( in @ SV952 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SV952 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) )
= $true )
| ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3228]) ).
thf(3441,plain,
! [SV200: $i,SV922: $i] :
( ( ( in @ SV922 @ SV200 )
= $false )
| ( ( subset @ SV922 @ SV200 )
= $true )
| ( ( in @ ( sK9_SY527 @ SV200 ) @ SV200 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3229]) ).
thf(3442,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV980: $i] :
( ( ( ~ ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
| ~ ! [SY1783: $i] :
( ~ ( in @ SY1783 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ SY1783 ) )
= SY1783 ) )
| ( surjective @ SV499 @ SV202 @ SV980 ) )
= $true )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3231]) ).
thf(3443,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) ) )
= $true )
| ( ( ~ ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ SY1752 ) )
= SY1752 ) )
| ( surjective @ SV499 @ SV202 @ SV953 ) )
= $true )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3444,plain,
! [SV205: $i,SV500: $i,SV815: $i] :
( ( ( in @ SV815 @ SV500 )
= $false )
| ( ( in @ SV815 @ ( setminus @ SV205 @ ( setminus @ SV205 @ SV500 ) ) )
= $true )
| ( ( in @ SV815 @ SV205 )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3233]) ).
thf(3445,plain,
! [SV817: $i,SV504: $i,SV209: $i] :
( ( ( ! [SY1638: $i] :
( ~ ( in @ SY1638 @ SV209 )
| ! [SY1639: $i] :
( ~ ( in @ SY1639 @ SV209 )
| ~ ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV504 )
| ( in @ ( kpair @ SY1638 @ SY1639 ) @ SV817 ) ) ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3446,plain,
! [SV818: $i,SV506: $i,SV211: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ ( powerset @ SV211 ) ) )
= $true )
| ( ( ! [SY1753: $i] :
( ~ ( in @ SY1753 @ SV211 )
| ~ ( in @ SY1753 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1753 @ ( binunion @ SV506 @ SV954 ) ) ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3235]) ).
thf(3447,plain,
! [SV212: $i] :
( ( ~ ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3448,plain,
! [SV212: $i] :
( ( ~ ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3236]) ).
thf(3449,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ~ ( ~ ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) )
| ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3237]) ).
thf(3450,plain,
! [SV702: $i > $i > $o,SV215: $i,SV509: $i,SV981: $i] :
( ( ( ~ ( in @ SV981 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SV981 )
| ! [SY1784: $i] :
( ~ ( in @ SY1784 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1785: $i] :
~ ( ~ ( SV702 @ SY1784 @ SY1785 )
| ~ ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SV509 )
| ~ ( SV702 @ SY1784 @ SY1786 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ SV981 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3242]) ).
thf(3451,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i,SV982: $i] :
( ( ( ~ ~ ( ~ ( in @ SV982 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 ) ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3243]) ).
thf(3452,plain,
! [SV225: $i,SV705: $i,SV901: $i,SV516: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV516 )
| ~ ( in @ ( kpair @ SV901 @ SV983 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SV983 ) )
= $true )
| ( ( in @ SV901 @ SV225 )
= $false )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3244]) ).
thf(3453,plain,
! [SV226: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ omega )
| ~ ( in @ ( sK51_SY601 @ SV226 ) @ SV226 ) ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3245]) ).
thf(3454,plain,
! [SV226: $i] :
( ( ( in @ ( setadjoin @ ( sK51_SY601 @ SV226 ) @ ( sK51_SY601 @ SV226 ) ) @ SV226 )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3245]) ).
thf(3455,plain,
! [SV819: $i,SV227: $i,SV517: $i] :
( ( ( subset @ SV517 @ ( setminus @ SV227 @ SV819 ) )
= $false )
| ( ( subset @ SV819 @ ( setminus @ SV227 @ SV517 ) )
= $true )
| ( ( in @ SV819 @ ( powerset @ SV227 ) )
= $false )
| ( ( in @ SV517 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3246]) ).
thf(3456,plain,
! [SV230: $i,SV519: $i] :
( ( ( ! [SY1213: $i] :
( ~ ( in @ SY1213 @ SV519 )
| ( in @ SY1213 @ SV230 ) ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3247]) ).
thf(3457,plain,
! [SV519: $i,SV230: $i] :
( ( ( ~ ( in @ ( sK59_SY1213 @ SV230 @ SV519 ) @ SV519 )
| ( in @ ( sK59_SY1213 @ SV230 @ SV519 ) @ SV230 ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3248]) ).
thf(3458,plain,
! [SV902: $i,SV521: $i > $o,SV232: $i] :
( ( ( ! [SY1215: $i] :
~ ~ ( ~ ( in @ SY1215 @ SV232 )
| ~ ~ ( SV521 @ SY1215 ) ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3459,plain,
! [SV822: $i,SV523: $i,SV234: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV234 ) )
= $true )
| ( ( ! [SY1761: $i] :
( ~ ( in @ SY1761 @ SV234 )
| ! [SY1762: $i] :
( ~ ( in @ SY1762 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1762 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1762 @ SY1761 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SY1761 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3250]) ).
thf(3460,plain,
! [SV235: $i,SV524: $i] :
( ( ( ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV235 )
| ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV524 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3461,plain,
! [SV709: $i > $i > $o,SV238: $i,SV757: $i,SV527: $i,SV923: $i] :
( ( ( in @ SV923 @ SV527 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV757 @ SV923 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
| ( SV709 @ SV757 @ SV923 ) )
= $true )
| ( ( in @ SV757 @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3252]) ).
thf(3462,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3257]) ).
thf(3463,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3258]) ).
thf(3464,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3465,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
| ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3259]) ).
thf(3466,plain,
! [SV248: $i,SV537: $i,SV957: $i] :
( ( ( ~ ( in @ SV957 @ SV537 ) )
= $true )
| ( ( in @ SV957 @ SV248 )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3467,plain,
! [SV537: $i,SV248: $i] :
( ( ( ~ ( in @ ( sK52_SY1247 @ SV248 @ SV537 ) @ SV537 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3468,plain,
! [SV537: $i,SV248: $i] :
( ( ( in @ ( sK52_SY1247 @ SV248 @ SV537 ) @ SV248 )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3261]) ).
thf(3469,plain,
! [SV250: $i,SV716: $i,SV907: $i,SV538: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV538 )
| ~ ( in @ ( kpair @ SV907 @ SV984 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SV984 ) )
= $true )
| ( ( in @ SV907 @ SV250 )
= $false )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3262]) ).
thf(3470,plain,
! [SV539: $i,SV824: $i,SV251: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ SV251 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV824 @ SV958 ) @ SV539 )
| ( in @ ( kpair @ SV958 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) )
= $true )
| ( ( in @ SV824 @ SV251 )
= $false )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3471,plain,
! [SV540: $i,SV825: $i,SV252: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ SV252 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV959 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SV959 ) @ SV540 ) )
= $true )
| ( ( in @ SV825 @ SV252 )
= $false )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3264]) ).
thf(3472,plain,
! [SV826: $i,SV545: $i,SV255: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV255 ) )
= $true )
| ( ( ! [SY1763: $i] :
( ~ ( in @ SY1763 @ SV255 )
| ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1764: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV545 )
| SY1764 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV826 )
| SY1764 )
| SY1764 ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3473,plain,
! [SV827: $i,SV548: $i,SV258: $i,SV961: $i] :
( ( ( ~ ( in @ SV961 @ ( powerset @ SV258 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SV961 ) @ ( binunion @ SV827 @ SV961 ) ) ) )
= $true )
| ( ( in @ SV827 @ ( powerset @ SV258 ) )
= $false )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3474,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3475,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3476,plain,
! [SV828: $i,SV552: $i,SV263: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ ( powerset @ SV263 ) ) )
= $true )
| ( ( ~ ( subset @ SV552 @ SV962 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SV962 ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3270]) ).
thf(3477,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ! [SY1654: $i] :
( ~ ( in @ SY1654 @ SV264 )
| ! [SY1655: $i] :
( ~ ( in @ SY1655 @ SV264 )
| ~ ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV553 )
| ( in @ ( kpair @ SY1654 @ SY1655 ) @ SV829 ) ) ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3271]) ).
thf(3478,plain,
! [SV557: $i,SV268: $i,SV830: $i] :
( ( ( in @ SV830 @ ( setminus @ SV268 @ ( setminus @ SV268 @ SV557 ) ) )
= $false )
| ( ( in @ SV830 @ SV557 )
= $true )
| ( ( in @ SV830 @ SV268 )
= $false )
| ( ( in @ SV557 @ ( powerset @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3479,plain,
! [SV558: $i > $o,SV269: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV269 ) )
= $true )
| ( ( ~ ~ ( SV558 @ SV909 ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3480,plain,
! [SV270: $i,SV559: $i,SV723: $i] :
( ( ( in @ SV723 @ SV559 )
= $true )
| ( ( ~ ( in @ SV723 @ SV270 ) )
= $true )
| ( ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3275]) ).
thf(3481,plain,
! [SV831: $i,SV560: $i,SV271: $i,SV963: $i] :
( ( ( ~ ( in @ SV963 @ SV271 ) )
= $true )
| ( ( ~ ( in @ SV963 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SV963 @ ( setminus @ SV271 @ SV831 ) ) )
= $true )
| ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3276]) ).
thf(3482,plain,
! [SV832: $i,SV562: $i,SV274: $i,SV964: $i] :
( ( ( ~ ( in @ SV964 @ SV274 ) )
= $true )
| ( ( ! [SY1765: $i] :
( ~ ( in @ SY1765 @ SV274 )
| ~ ( in @ ( kpair @ SV964 @ SY1765 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SY1765 ) @ ( binunion @ SV562 @ SV832 ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3277]) ).
thf(3483,plain,
! [SV276: $i,SV564: $i,SV725: $i] :
( ( ( in @ SV725 @ SV564 )
= $true )
| ( ( ~ ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) ) )
= $true )
| ( ( in @ SV725 @ SV276 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3278]) ).
thf(3484,plain,
! [SV281: $i] :
( ( ( ~ ( in @ ( sK35_SY742 @ SV281 ) @ SV281 ) )
= $false )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3485,plain,
! [SV281: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3280]) ).
thf(3486,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( ~ ( in @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) @ SV283 )
| ! [SY1787: $i] :
( ~ ( in @ SY1787 @ SV569 )
| ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
!= SY1787 )
| ~ ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ SY1787 ) )
| ~ ( ~ ( SV911 @ SY1787 )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3281]) ).
thf(3487,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) )
= $true )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3488,plain,
! [SV835: $i,SV570: $i,SV285: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ SV285 ) )
= $true )
| ( ( ~ ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3489,plain,
! [SV759: $o,SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3490,plain,
! [SV287: $i,SV572: $i,SV729: $i,SV759: $o] :
( ( SV759 = $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3284]) ).
thf(3491,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3492,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3493,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV287 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3494,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3286]) ).
thf(3495,plain,
! [SV573: $i,SV836: $i,SV288: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ SV288 ) )
= $true )
| ( ( ! [SY1766: $i] :
( ~ ( in @ SY1766 @ SV288 )
| ~ ( in @ ( kpair @ SV966 @ SY1766 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SY1766 ) @ ( binunion @ SV573 @ SV836 ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3496,plain,
! [SV912: $i,SV731: $i,SV291: $i,SV576: $o] :
( ( ( ~ ~ SV576 )
= $true )
| ( ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 )
= $true )
| ( ( in @ SV912 @ SV291 )
= $false )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3497,plain,
! [SV913: $i,SV732: $i,SV291: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 )
= $true )
| ( ( in @ SV913 @ SV291 )
= $false )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3498,plain,
! [SV914: $i,SV733: $i,SV291: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 )
= $true )
| ( ( in @ SV914 @ SV291 )
= $false )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3499,plain,
! [SV838: $i,SV580: $i,SV296: $i] :
( ( ( ! [SY1670: $i] :
( ~ ( in @ SY1670 @ SV296 )
| ~ ( in @ SY1670 @ SV580 )
| ( in @ SY1670 @ SV838 ) ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3500,plain,
! [SV839: $i,SV581: $i,SV297: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV297 ) )
= $true )
| ( ( ! [SY1767: $i] :
( ~ ( in @ SY1767 @ SV297 )
| ~ ( ( in @ ( kpair @ SV967 @ SY1767 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ ( binunion @ SV581 @ SV839 ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3292]) ).
thf(3501,plain,
! [SV915: $i,SV734: $i,SV582: $i,SV298: $i] :
( ( ( ~ ! [SY1728: $i] :
( ~ ( in @ SY1728 @ SV298 )
| ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV582 )
| ~ ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV734 )
| ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV915 ) ) ) )
= $true )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3502,plain,
! [SV840: $i,SV583: $i,SV299: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ SV299 ) )
= $true )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SV968 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3503,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) )
= $true )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3295]) ).
thf(3504,plain,
! [SV842: $i,SV584: $i,SV301: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV301 ) )
= $true )
| ( ( ~ ( in @ SV969 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SV969 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3505,plain,
! [SV843: $i,SV585: $i,SV302: $i,SV970: $i] :
( ( ( ~ ( in @ SV970 @ SV302 ) )
= $true )
| ( ( ~ ( in @ SV970 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SV970 @ ( setminus @ SV302 @ SV585 ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3297]) ).
thf(3506,plain,
! [SV305: $i,SV844: $i,SV587: $i,SV971: $i] :
( ( ( ~ ( in @ SV971 @ ( binintersect @ SV587 @ SV844 ) ) )
= $true )
| ( ( in @ SV971 @ SV305 )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3507,plain,
! [SV307: $i,SV589: $i,SV845: $i] :
( ( ( in @ SV845 @ SV589 )
= $false )
| ( ( ~ ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) ) )
= $true )
| ( ( in @ SV845 @ SV307 )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3508,plain,
! [SV916: $o,SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 != SV309 )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3509,plain,
! [SV309: $i,SV591: $i,SV736: $i,SV916: $o] :
( ( SV916 = $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3300]) ).
thf(3510,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 != SV309 )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3301]) ).
thf(3511,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3301]) ).
thf(3512,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 != SV309 )
= $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3513,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3514,plain,
! [SV847: $i,SV592: $i,SV310: $i] :
( ( ( ! [SY1678: $i] :
( ~ ( in @ SY1678 @ SV310 )
| ~ ( in @ SY1678 @ SV592 )
| ( in @ SY1678 @ SV847 ) ) )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3303]) ).
thf(3515,plain,
! [SV314: $i,SV760: $i,SV739: $i > $i > $o,SV596: $i,SV924: $i] :
( ( ( in @ SV924 @ SV596 )
= $false )
| ( ( ~ ( SV739 @ SV760 @ SV924 )
| ( in @ ( kpair @ SV760 @ SV924 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) ) )
= $true )
| ( ( in @ SV760 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3305]) ).
thf(3516,plain,
! [SV972: $o,SV848: $i,SV597: $i,SV315: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV315 )
| ~ ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3517,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV315 )
| ~ ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV986 @ SV597 )
| $true )
| ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3307]) ).
thf(3518,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV315 )
| ~ ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV987 @ SV597 )
| $false )
| ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3308]) ).
thf(3519,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV973: $i] :
( ( ( ~ ( in @ SV973 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ! [SY1769: $i] :
( ~ ( in @ SY1769 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SY1769 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SY1769 ) ) ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3309]) ).
thf(3520,plain,
! [SV850: $i,SV600: $i,SV318: $i,SV974: $i] :
( ( ( ~ ( in @ SV974 @ SV318 ) )
= $true )
| ( ( ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SV974 @ SV850 )
| ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3310]) ).
thf(3521,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( SV323 @ SV852 )
= $false )
| ( ( ~ ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) )
= $true )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3522,plain,
! [SV920: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
| ( subset @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 ) )
= $false )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3314]) ).
thf(3523,plain,
! [SV854: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 ) )
= $false )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3315]) ).
thf(3524,plain,
! [SV854: $i,SV3: $i] :
( ( ( subset @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $false )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3315]) ).
thf(3525,plain,
! [SV8: $i,SV332: $i > $o,SV611: $i] :
( ( ( ~ ( in @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) @ SV8 )
| ~ ( SV332 @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) )
| ( ( sK62_SY1370 @ SV611 @ SV332 @ SV8 )
= SV611 ) )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3316]) ).
thf(3526,plain,
! [SV858: $i,SV614: $i,SV335: $i,SV11: $i] :
( ( ( ! [SY1687: $i] :
( ~ ( in @ SY1687 @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ SY1687 )
= ( ap @ SV11 @ SV335 @ SV858 @ SY1687 ) ) ) )
= $false )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3317]) ).
thf(3527,plain,
! [SV761: $i,SV340: $i,SV17: $i,SV925: $i] :
( ( ( in @ SV925 @ ( powerset @ SV17 ) )
= $false )
| ( ( in @ ( binintersect @ SV340 @ SV761 ) @ ( powerset @ ( binintersect @ ( binunion @ SV340 @ SV925 ) @ ( binunion @ SV761 @ SV925 ) ) ) )
= $true )
| ( ( in @ SV761 @ ( powerset @ SV17 ) )
= $false )
| ( ( in @ SV340 @ ( powerset @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3528,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( ~ ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3529,plain,
! [SV19: $i,SV618: $i,SV859: $i > $o,SV342: $i] :
( ( ( ! [SY1770: $i] :
( ~ ( in @ SY1770 @ SV342 )
| ~ ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SY1770 ) @ SV618 )
| ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SY1770 ) ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3530,plain,
! [SV762: $i,SV343: $i,SV20: $i,SV926: $i] :
( ( ( in @ SV926 @ SV20 )
= $false )
| ( ( ~ ~ ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) )
| ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3320]) ).
thf(3531,plain,
! [SV346: $i,SV860: $i,SV24: $i,SV764: $i] :
( ( ( ~ ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) ) )
= $false )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3532,plain,
! [SV24: $i,SV764: $i,SV346: $i,SV860: $i] :
( ( ( ~ ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) ) )
= $false )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3533,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( ~ ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3323]) ).
thf(3534,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( ~ ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) ) )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3323]) ).
thf(3535,plain,
! [SV348: $i > $o,SV27: $i,SV988: $i] :
( ( ( ~ ~ ( ~ ( in @ SV988 @ SV27 )
| ~ ( SV348 @ SV988 ) ) )
= $true )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3324]) ).
thf(3536,plain,
! [SV348: $i > $o,SV27: $i,SV989: $i] :
( ( ( ~ ~ ( ~ ( in @ SV989 @ SV27 )
| ~ ( SV348 @ SV989 ) ) )
= $true )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3325]) ).
thf(3537,plain,
! [SV765: $i,SV353: $i,SV34: $i,SV927: $i] :
( ( ( in @ SV927 @ SV34 )
= $false )
| ( ( ~ ~ ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) )
| ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3538,plain,
! [SV768: $i,SV357: $i,SV40: $i,SV928: $i] :
( ( ( in @ SV928 @ SV40 )
= $false )
| ( ( ! [SY1737: $i] :
( ~ ( in @ SY1737 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1737 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1738: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1738 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1738 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1738 @ SY1737 ) @ SV768 ) ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3539,plain,
! [SV769: $i,SV358: $i,SV929: $i,SV41: $i] :
( ( ( breln1 @ SV41 @ SV929 )
= $false )
| ( ( ( breln1compset @ SV41 @ ( binunion @ SV358 @ SV769 ) @ SV929 )
= ( binunion @ ( breln1compset @ SV41 @ SV358 @ SV929 ) @ ( breln1compset @ SV41 @ SV769 @ SV929 ) ) )
= $true )
| ( ( breln1 @ SV41 @ SV769 )
= $false )
| ( ( breln1 @ SV41 @ SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3540,plain,
! [SV770: $i,SV359: $i,SV42: $i,SV930: $i] :
( ( ( in @ SV930 @ SV42 )
= $false )
| ( ( ~ ( in @ SV930 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
| ( in @ SV930 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) ) )
= $true )
| ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3541,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i,SV921: $i] :
( ( ( ~ ( in @ SV921 @ SV43 ) )
= $true )
| ( ( SV623
!= ( SV360 @ SV921 ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3333]) ).
thf(3542,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ( ~ ( in @ SV364 @ ( sK55_SY928 @ SV47 @ SV364 ) )
| ~ ( in @ ( sK55_SY928 @ SV47 @ SV364 ) @ SV47 ) ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3334]) ).
thf(3543,plain,
! [SV47: $i,SV975: $i,SV364: $i] :
( ( ( ~ ( ~ ( in @ SV364 @ SV975 )
| ~ ( in @ SV975 @ SV47 ) ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3335]) ).
thf(3544,plain,
! [SV773: $i,SV367: $i,SV52: $i,SV931: $i] :
( ( ( in @ SV931 @ SV52 )
= $false )
| ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
| ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3336]) ).
thf(3545,plain,
! [SV370: $i,SV776: $i,SV55: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV55 )
| ~ ( in @ SV990 @ SV776 )
| ( in @ SV990 @ ( setminus @ SV55 @ SV370 ) ) )
= $true )
| ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3339]) ).
thf(3546,plain,
! [SV777: $i,SV372: $i,SV57: $i,SV932: $i] :
( ( ( in @ SV932 @ SV57 )
= $false )
| ( ( ~ ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
| ~ ( in @ SV932 @ SV372 ) )
= $true )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3340]) ).
thf(3547,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3341]) ).
thf(3548,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( ~ ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) ) )
= $false )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3341]) ).
thf(3549,plain,
! [SV61: $i,SV376: $i > $o,SV862: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) @ SV61 )
| ~ ~ ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) ) ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3342]) ).
thf(3550,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV976: $i] :
( ( ( ~ ( in @ SV976 @ SV62 ) )
= $true )
| ( ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV976 )
= ( SV629 @ SV976 ) )
= $true )
| ( ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3343]) ).
thf(3551,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV933: $i] :
( ( ( in @ SV933 @ SV62 )
= $false )
| ( ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV933 )
= ( SV629 @ SV933 ) )
= $true )
| ( ( in @ ( SV629 @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) ) @ SV377 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3552,plain,
! [SV778: $i,SV380: $i,SV66: $i,SV934: $i] :
( ( ( in @ SV934 @ SV66 )
= $false )
| ( ( ~ ~ ( in @ SV934 @ SV380 )
| ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3553,plain,
! [SV381: $i,SV863: $i,SV67: $i,SV779: $i] :
( ( ( in @ SV779 @ SV67 )
= $false )
| ( ( in @ SV863 @ SV381 )
= $true )
| ( ( SV779 = SV863 )
= $false )
| ( ( SV67 = SV381 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3554,plain,
! [SV864: $i,SV632: $i,SV70: $i,SV383: $o] :
( ( ( ~ SV383 ) = $false )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) )
= $true )
| ( ( in @ SV864 @ SV70 )
= $false )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3555,plain,
! [SV865: $i,SV633: $i,SV70: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) )
= $true )
| ( ( in @ SV865 @ SV70 )
= $false )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3556,plain,
! [SV866: $i,SV634: $i,SV70: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) )
= $true )
| ( ( in @ SV866 @ SV70 )
= $false )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3557,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ( in @ ( sK45_SY168 @ SV780 @ SV73 ) @ SV73 )
| ~ ~ ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3350]) ).
thf(3558,plain,
! [SV781: $i,SV386: $i,SV76: $i,SV935: $i] :
( ( ( in @ SV935 @ SV76 )
= $false )
| ( ( ~ ( in @ SV386 @ ( powerset @ SV781 ) )
| ~ ( in @ SV935 @ SV386 )
| ( in @ SV935 @ SV781 ) )
= $true )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3351]) ).
thf(3559,plain,
! [SV782: $i,SV387: $i,SV77: $i,SV936: $i] :
( ( ( in @ SV936 @ SV77 )
= $false )
| ( ( ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
| ~ ( in @ SV936 @ SV782 )
| ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3560,plain,
! [SV784: $i,SV392: $i,SV82: $i,SV937: $i] :
( ( ( in @ SV937 @ SV82 )
= $false )
| ( ( ~ ~ ( in @ SV937 @ SV392 )
| ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3353]) ).
thf(3561,plain,
! [SV786: $i,SV402: $i,SV93: $i,SV938: $i] :
( ( ( in @ SV938 @ SV93 )
= $false )
| ( ( ! [SY1741: $i] :
( ~ ( in @ SY1741 @ SV93 )
| ~ ( in @ ( kpair @ SV938 @ SY1741 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SY1741 ) @ SV786 ) ) )
= $true )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3562,plain,
! [SV871: $i,SV94: $i,SV644: $i,SV403: $o] :
( ( SV403 = $false )
| ( ( in @ SV644
@ ( dsetconstr @ SV94
@ ^ [SY1697: $i] :
( ~ ( ~ SV403
| ( SY1697 != SV644 ) )
| ~ ( ~ ~ SV403
| ( SY1697 != SV871 ) ) ) ) )
= $true )
| ( ( in @ SV871 @ SV94 )
= $false )
| ( ( in @ SV644 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3355]) ).
thf(3563,plain,
! [SV872: $i,SV94: $i,SV645: $i] :
( ( $true = $false )
| ( ( in @ SV645
@ ( dsetconstr @ SV94
@ ^ [SY1698: $i] :
( ~ ( ~ $true
| ( SY1698 != SV645 ) )
| ~ ( ~ ~ $true
| ( SY1698 != SV872 ) ) ) ) )
= $true )
| ( ( in @ SV872 @ SV94 )
= $false )
| ( ( in @ SV645 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3356]) ).
thf(3564,plain,
! [SV873: $i,SV94: $i,SV646: $i] :
( ( $false = $false )
| ( ( in @ SV646
@ ( dsetconstr @ SV94
@ ^ [SY1699: $i] :
( ~ ( ~ $false
| ( SY1699 != SV646 ) )
| ~ ( ~ ~ $false
| ( SY1699 != SV873 ) ) ) ) )
= $true )
| ( ( in @ SV873 @ SV94 )
= $false )
| ( ( in @ SV646 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3565,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3358]) ).
thf(3566,plain,
! [SV874: $o,SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3359]) ).
thf(3567,plain,
! [SV406: $i,SV97: $i,SV647: $i,SV874: $o] :
( ( SV874 = $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3359]) ).
thf(3568,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3360]) ).
thf(3569,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3361]) ).
thf(3570,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3361]) ).
thf(3571,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3572,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3573,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3574,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV939: $i] :
( ( ( in @ SV939 @ SV99 )
= $false )
| ( ( ! [SY1742: $i] :
( ~ ( in @ SY1742 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1742 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1743: $o] :
( ~ ! [SY1744: $i] :
( ~ ( in @ SY1744 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1744 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1744 @ SY1742 ) @ SV787 )
| SY1743 )
| SY1743 ) ) )
= $true )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3575,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3576,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3577,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
| ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
= $false )
| ( ( ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3578,plain,
! [SV788: $i,SV416: $i,SV108: $i,SV940: $i] :
( ( ( in @ SV940 @ ( powerset @ SV108 ) )
= $false )
| ( ( ~ ( subset @ SV416 @ SV788 )
| ~ ( subset @ SV416 @ SV940 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) ) )
= $true )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3579,plain,
! [SV875: $i,SV651: $i,SV417: $i,SV109: $i] :
( ( ( ! [SY1700: $i] :
( ~ ( in @ SY1700 @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ SY1700 )
= ( ap @ SV109 @ SV417 @ SV875 @ SY1700 ) ) ) )
= $false )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3580,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( ~ ( in @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SV111 ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3581,plain,
! [SV111: $i,SV653: $i,SV419: $i] :
( ( ( ~ ~ ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3369]) ).
thf(3582,plain,
! [SV113: $i] :
( ( ( in @ ( sK27_SY275 @ SV113 ) @ SV113 )
= $true )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3370]) ).
thf(3583,plain,
! [SV113: $i] :
( ( ( ( binintersect @ ( sK27_SY275 @ SV113 ) @ SV113 )
= emptyset )
= $true )
| ( ( SV113 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3371]) ).
thf(3584,plain,
! [SV790: $i,SV424: $i,SV117: $i,SV941: $i] :
( ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( ! [SY1745: $i] :
( ~ ( in @ SY1745 @ SV117 )
| ~ ( in @ SY1745 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SY1745 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) ) )
= $true )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3372]) ).
thf(3585,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3373]) ).
thf(3586,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3587,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3375]) ).
thf(3588,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ~ ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3376]) ).
thf(3589,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3376]) ).
thf(3590,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ( ~ ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) ) )
= $true )
| ( ( ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3377]) ).
thf(3591,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ( ~ ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3378]) ).
thf(3592,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) ) )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3379]) ).
thf(3593,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3594,plain,
( ( in @ sK3_SY2 @ sK1_X )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3595,plain,
! [SV878: $i,SV657: $i,SV125: $i,SV432: $o] :
( ( SV432 = $false )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1704: $i] :
( ~ ( ~ SV432
| ( SY1704 != SV657 ) )
| ~ ( ~ ~ SV432
| ( SY1704 != SV878 ) ) ) )
= ( setadjoin @ SV657 @ emptyset ) )
= $true )
| ( ( in @ SV878 @ SV125 )
= $false )
| ( ( in @ SV657 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3383]) ).
thf(3596,plain,
! [SV879: $i,SV658: $i,SV125: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1705: $i] :
( ~ ( ~ $true
| ( SY1705 != SV658 ) )
| ~ ( ~ ~ $true
| ( SY1705 != SV879 ) ) ) )
= ( setadjoin @ SV658 @ emptyset ) )
= $true )
| ( ( in @ SV879 @ SV125 )
= $false )
| ( ( in @ SV658 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3597,plain,
! [SV880: $i,SV659: $i,SV125: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV125
@ ^ [SY1706: $i] :
( ~ ( ~ $false
| ( SY1706 != SV659 ) )
| ~ ( ~ ~ $false
| ( SY1706 != SV880 ) ) ) )
= ( setadjoin @ SV659 @ emptyset ) )
= $true )
| ( ( in @ SV880 @ SV125 )
= $false )
| ( ( in @ SV659 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3598,plain,
! [SV126: $i,SV791: $o,SV433: $i] :
( ( ( in @ SV433 @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) )
= $true )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3386]) ).
thf(3599,plain,
! [SV433: $i,SV126: $i,SV791: $o] :
( ( ( ~ ( in @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) @ SV126 ) )
= $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3600,plain,
! [SV126: $i,SV433: $i,SV791: $o] :
( ( SV791 = $false )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3387]) ).
thf(3601,plain,
! [SV126: $i,SV433: $i] :
( ( ( in @ SV433 @ ( sK47_SX0 @ SV126 @ SV433 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3602,plain,
! [SV433: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK47_SX0 @ SV126 @ SV433 ) @ SV126 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3603,plain,
! [SV126: $i,SV433: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3604,plain,
! [SV126: $i,SV433: $i] :
( ( ( in @ SV433 @ ( sK48_SX0 @ SV126 @ SV433 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3390]) ).
thf(3605,plain,
! [SV433: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK48_SX0 @ SV126 @ SV433 ) @ SV126 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3391]) ).
thf(3606,plain,
! [SV126: $i,SV433: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3391]) ).
thf(3607,plain,
! [SV793: $i,SV440: $i,SV133: $i,SV942: $i] :
( ( ( in @ SV942 @ SV133 )
= $false )
| ( ( ~ ( in @ SV942 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
| ( in @ SV942 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) ) )
= $true )
| ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3608,plain,
! [SV794: $i,SV441: $i,SV134: $i,SV943: $i] :
( ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( ! [SY1746: $i] :
( ~ ( in @ SY1746 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SY1746 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SY1746 ) ) ) )
= $true )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3609,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV795 = SY1610 ) ) )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3610,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ! [SY1611: $i] :
( ~ ( SV138 @ SY1611 )
| ( SV796 = SY1611 ) ) )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3611,plain,
! [SV881: $i,SV664: $i,SV444: $i,SV139: $i] :
( ( ( ! [SY1707: $i] :
( ~ ( in @ SY1707 @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ SY1707 )
= ( ap @ SV139 @ SV444 @ SV881 @ SY1707 ) ) ) )
= $false )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3612,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ~ ( ~ ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
| ~ ( ~ ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) )
| ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3613,plain,
! [SV445: $i > $i,SV140: $i,SV978: $i] :
( ( ( ~ ! [SY1774: $i] :
~ ( ~ ( ~ ( in @ SY1774 @ SV978 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1774 @ SV978 ) ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3399]) ).
thf(3614,plain,
! [SV448: $i,SV798: $i,SV143: $i,SV944: $i] :
( ( ( in @ SV944 @ ( powerset @ SV143 ) )
= $false )
| ( ( ~ ( subset @ SV798 @ SV944 )
| ( subset @ ( binintersect @ SV448 @ SV798 ) @ SV944 ) )
= $true )
| ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3400]) ).
thf(3615,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( in @ ( sK29_SY1085 @ SV449 @ SV144 ) @ SV144 )
= $true )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3401]) ).
thf(3616,plain,
! [SV144: $i,SV449: $i > $o] :
( ( ( SV449 @ ( sK29_SY1085 @ SV449 @ SV144 ) )
= $true )
| ( ( ex1 @ SV144
@ ^ [SY1084: $i] : ( SV449 @ SY1084 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3402]) ).
thf(3617,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3618,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i] :
( ( ( ~ ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 )
| ~ ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
| ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3404]) ).
thf(3619,plain,
! [SV148: $i,SV667: $i,SV453: $i > $i] :
( ( ( ~ ( in @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) @ SV148 ) )
= $false )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3620,plain,
! [SV148: $i,SV453: $i > $i,SV667: $i] :
( ( ( SV667
!= ( SV453 @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) ) )
= $false )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3405]) ).
thf(3621,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( ~ ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
| ~ ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
| ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 ) )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3406]) ).
thf(3622,plain,
! [SV458: $i > $o,SV153: $i,SV882: $i] :
( ( ( in @ SV882 @ SV153 )
= $false )
| ( ( ~ ( SV458 @ SV882 ) )
= $true )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3623,plain,
! [SV801: $i,SV459: $i,SV945: $i,SV154: $i] :
( ( ( breln1 @ SV154 @ SV945 )
= $false )
| ( ( ( breln1compset @ SV154 @ ( binunion @ SV459 @ SV801 ) @ SV945 )
= ( binunion @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV801 ) ) ) @ ( breln1invset @ SV154 @ ( breln1compset @ SV154 @ ( breln1invset @ SV154 @ SV945 ) @ ( breln1invset @ SV154 @ SV459 ) ) ) ) )
= $true )
| ( ( breln1 @ SV154 @ SV801 )
= $false )
| ( ( breln1 @ SV154 @ SV459 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3408]) ).
thf(3624,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ! [SY1621: $i] :
( ~ ( SV155 @ SY1621 )
| ( SV802 = SY1621 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3625,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3410]) ).
thf(3626,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i] :
( ( ( ~ ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 )
| ~ ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
| ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3411]) ).
thf(3627,plain,
! [SV670: $i,SV158: $i,SV884: $i,SV462: $o] :
( ( ( ~ SV462 ) = $false )
| ( ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) )
= $true )
| ( ( in @ SV884 @ SV158 )
= $false )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3628,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) )
= $true )
| ( ( in @ SV885 @ SV158 )
= $false )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3629,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) )
= $true )
| ( ( in @ SV886 @ SV158 )
= $false )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3630,plain,
! [SV467: $i,SV163: $i,SV804: $i] :
( ( ( in @ SV804 @ ( setminus @ SV163 @ SV467 ) )
= $true )
| ( ( in @ SV804 @ SV467 )
= $true )
| ( ( in @ SV804 @ SV163 )
= $false )
| ( ( in @ SV467 @ ( powerset @ SV163 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3416]) ).
thf(3631,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
| ~ ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
| ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3417]) ).
thf(3632,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ! [SY1625: $i] :
( ~ ( SV167 @ SY1625 )
| ( SV806 = SY1625 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3418]) ).
thf(3633,plain,
! [SV887: $i,SV678: $i,SV470: $i,SV168: $i] :
( ( ( ! [SY1711: $i] :
( ~ ( in @ SY1711 @ SV168 )
| ! [SY1712: $i] :
( ~ ( in @ SY1712 @ SV470 )
| ~ ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV678 )
| ( in @ ( kpair @ SY1711 @ SY1712 ) @ SV887 ) ) ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3419]) ).
thf(3634,plain,
! [SV170: $i,SV679: $i,SV472: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) @ SV170 )
| ( SV679
!= ( SV472 @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) ) ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3420]) ).
thf(3635,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i,SV991: $i] :
( ( ( ~ ~ ( ~ ( in @ SV991 @ SV170 )
| ( SV679
!= ( SV472 @ SV991 ) ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3421]) ).
thf(3636,plain,
! [SV473: $i,SV807: $i,SV171: $i,SV946: $i] :
( ( ( in @ SV946 @ SV171 )
= $false )
| ( ( ~ ~ ( in @ SV946 @ SV807 )
| ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3637,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV172 ) )
= $true )
| ( ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV979 )
= ( SV680 @ SV979 ) )
= $true )
| ( ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3423]) ).
thf(3638,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV947: $i] :
( ( ( in @ SV947 @ SV172 )
= $false )
| ( ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV947 )
= ( SV680 @ SV947 ) )
= $true )
| ( ( in @ ( SV680 @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) ) @ SV474 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3639,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
| ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 ) )
= $false )
| ( ( ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3640,plain,
! [SV476: $i > $o,SV176: $i,SV681: $i] :
( ( ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1139: $i] : ( SV476 @ SY1139 ) ) )
= $false )
| ( ( SV476 @ SV681 )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3641,plain,
! [SV176: $i,SV681: $i,SV476: $i > $o] :
( ( ( SV476 @ SV681 )
= $false )
| ( ( in @ SV681
@ ( dsetconstr @ SV176
@ ^ [SY1140: $i] : ( SV476 @ SY1140 ) ) )
= $true )
| ( ( in @ SV681 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3642,plain,
! [SV178: $i,SV478: $i] :
( ( ( in @ ( sK31_SY1142 @ SV478 @ SV178 ) @ SV178 )
= $true )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3643,plain,
! [SV178: $i,SV478: $i] :
( ( ( in @ SV478 @ ( sK31_SY1142 @ SV478 @ SV178 ) )
= $true )
| ( ( in @ SV478 @ ( setunion @ SV178 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3429]) ).
thf(3644,plain,
! [SV810: $i,SV479: $i,SV179: $i,SV948: $i] :
( ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( ! [SY1750: $i] :
( ~ ( in @ SY1750 @ SV179 )
| ~ ( in @ SY1750 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SY1750 @ ( binunion @ SV810 @ SV948 ) ) ) )
= $true )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3430]) ).
thf(3645,plain,
! [SV889: $i,SV683: $i,SV181: $i,SV480: $o] :
( ( SV480 = $false )
| ( ( ( if @ SV181 @ SV480 @ SV683 @ SV889 )
= SV683 )
= $true )
| ( ( in @ SV889 @ SV181 )
= $false )
| ( ( in @ SV683 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3646,plain,
! [SV890: $i,SV684: $i,SV181: $i] :
( ( $true = $false )
| ( ( ( if @ SV181 @ $true @ SV684 @ SV890 )
= SV684 )
= $true )
| ( ( in @ SV890 @ SV181 )
= $false )
| ( ( in @ SV684 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3432]) ).
thf(3647,plain,
! [SV891: $i,SV685: $i,SV181: $i] :
( ( $false = $false )
| ( ( ( if @ SV181 @ $false @ SV685 @ SV891 )
= SV685 )
= $true )
| ( ( in @ SV891 @ SV181 )
= $false )
| ( ( in @ SV685 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3433]) ).
thf(3648,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( ~ ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3434]) ).
thf(3649,plain,
! [SV183: $i,SV687: $i,SV892: $i > $o,SV482: $i] :
( ( ( ! [SY1779: $i] :
( ~ ( in @ SY1779 @ SV482 )
| ~ ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SY1779 ) @ SV687 )
| ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SY1779 ) ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3434]) ).
thf(3650,plain,
! [SV812: $i,SV486: $i,SV188: $i,SV949: $i] :
( ( ( in @ SV949 @ SV188 )
= $false )
| ( ( ~ ( in @ SV949 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
| ( in @ SV949 @ ( setminus @ SV188 @ SV486 ) ) )
= $true )
| ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3651,plain,
! [SV813: $i,SV487: $i > $o,SV189: $i,SV950: $i] :
( ( ( in @ SV950 @ SV189 )
= $false )
| ( ( ~ ( SV487 @ SV813 )
| ~ ( SV487 @ SV950 )
| ( SV813 = SV950 ) )
= $true )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3652,plain,
! [SV489: $i,SV191: $i > $i > $o] :
( ( ( ! [SY1780: $i] :
~ ( ~ ( ~ ( in @ SY1780 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1780 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1780 ) )
| ( in @ SY1780 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3438]) ).
thf(3653,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
| ~ ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3439]) ).
thf(3654,plain,
! [SV814: $i,SV496: $i,SV198: $i,SV952: $i] :
( ( ( in @ SV952 @ SV198 )
= $false )
| ( ( ~ ( in @ SV952 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
| ( in @ SV952 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) ) )
= $true )
| ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3655,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV980: $i] :
( ( ( ~ ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) ) )
= $true )
| ( ( ~ ! [SY1783: $i] :
( ~ ( in @ SY1783 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ SY1783 ) )
= SY1783 ) )
| ( surjective @ SV499 @ SV202 @ SV980 ) )
= $true )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3656,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV953: $i] :
( ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( ~ ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ SY1752 ) )
= SY1752 ) )
| ( surjective @ SV499 @ SV202 @ SV953 ) )
= $true )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3443]) ).
thf(3657,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( ~ ( in @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SV209 )
| ! [SY1788: $i] :
( ~ ( in @ SY1788 @ SV209 )
| ~ ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SY1788 ) @ SV504 )
| ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SY1788 ) @ SV817 ) ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3445]) ).
thf(3658,plain,
! [SV818: $i,SV506: $i,SV211: $i,SV954: $i] :
( ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( ! [SY1753: $i] :
( ~ ( in @ SY1753 @ SV211 )
| ~ ( in @ SY1753 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SY1753 @ ( binunion @ SV506 @ SV954 ) ) ) )
= $true )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3446]) ).
thf(3659,plain,
! [SV212: $i] :
( ( ~ ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3447]) ).
thf(3660,plain,
! [SV212: $i] :
( ( ! [SY1494: $i,SY1495: $i] :
( ~ ~ ( ~ ( in @ SY1494 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1495 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1494 )
| ( in @ SX4 @ SY1495 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY1495 )
| ( in @ SX4 @ SY1494 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3661,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ( ~ ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) )
| ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) ) )
= $false )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3449]) ).
thf(3662,plain,
! [SV702: $i > $i > $o,SV215: $i,SV509: $i,SV981: $i] :
( ( ( ~ ( in @ SV981 @ ( breln1Set @ SV509 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV509 @ SV981 )
| ! [SY1784: $i] :
( ~ ( in @ SY1784 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1785: $i] :
~ ( ~ ( SV702 @ SY1784 @ SY1785 )
| ~ ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SV509 )
| ~ ( SV702 @ SY1784 @ SY1786 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ SV981 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3663,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i,SV982: $i] :
( ( ( ~ ( ~ ( in @ SV982 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 ) ) )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3664,plain,
! [SV225: $i,SV705: $i,SV901: $i,SV516: $i,SV983: $i] :
( ( ( ~ ( in @ SV983 @ SV516 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV901 @ SV983 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SV983 ) )
= $true )
| ( ( in @ SV901 @ SV225 )
= $false )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3452]) ).
thf(3665,plain,
! [SV226: $i] :
( ( ( ~ ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ omega )
| ~ ( in @ ( sK51_SY601 @ SV226 ) @ SV226 ) ) )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3453]) ).
thf(3666,plain,
! [SV226: $i,SV992: $i] :
( ( ( ~ ( in @ SV992 @ omega )
| ( in @ SV992 @ SV226 ) )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( setadjoin @ ( sK51_SY601 @ SV226 ) @ ( sK51_SY601 @ SV226 ) ) @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3454]) ).
thf(3667,plain,
! [SV519: $i,SV230: $i] :
( ( ( ~ ( in @ ( sK70_SY1213 @ SV230 @ SV519 ) @ SV519 )
| ( in @ ( sK70_SY1213 @ SV230 @ SV519 ) @ SV230 ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3456]) ).
thf(3668,plain,
! [SV519: $i,SV230: $i] :
( ( ( ~ ( in @ ( sK59_SY1213 @ SV230 @ SV519 ) @ SV519 ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3669,plain,
! [SV519: $i,SV230: $i] :
( ( ( in @ ( sK59_SY1213 @ SV230 @ SV519 ) @ SV230 )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3670,plain,
! [SV232: $i,SV521: $i > $o,SV902: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) @ SV232 )
| ~ ~ ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) ) ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3458]) ).
thf(3671,plain,
! [SV822: $i,SV523: $i,SV234: $i,SV956: $i] :
( ( ( in @ SV956 @ SV234 )
= $false )
| ( ( ! [SY1761: $i] :
( ~ ( in @ SY1761 @ SV234 )
| ! [SY1762: $i] :
( ~ ( in @ SY1762 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1762 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1762 @ SY1761 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SY1761 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) ) )
= $true )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3459]) ).
thf(3672,plain,
! [SV235: $i,SV524: $i] :
( ( ( ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV235 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3673,plain,
! [SV235: $i,SV524: $i] :
( ( ( ~ ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV524 ) )
= $false )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3674,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i,SV923: $i,SV757: $i] :
( ( ( ~ ( in @ ( kpair @ SV757 @ SV923 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) ) )
= $true )
| ( ( SV709 @ SV757 @ SV923 )
= $true )
| ( ( in @ SV923 @ SV527 )
= $false )
| ( ( in @ SV757 @ SV238 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3461]) ).
thf(3675,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3462]) ).
thf(3676,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3463]) ).
thf(3677,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3464]) ).
thf(3678,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ~ ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3465]) ).
thf(3679,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3465]) ).
thf(3680,plain,
! [SV248: $i,SV537: $i,SV957: $i] :
( ( ( in @ SV957 @ SV537 )
= $false )
| ( ( in @ SV957 @ SV248 )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3466]) ).
thf(3681,plain,
! [SV537: $i,SV248: $i] :
( ( ( in @ ( sK52_SY1247 @ SV248 @ SV537 ) @ SV537 )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV248 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3467]) ).
thf(3682,plain,
! [SV250: $i,SV716: $i,SV907: $i,SV538: $i,SV984: $i] :
( ( ( ~ ( in @ SV984 @ SV538 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV907 @ SV984 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SV984 ) )
= $true )
| ( ( in @ SV907 @ SV250 )
= $false )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3469]) ).
thf(3683,plain,
! [SV539: $i,SV824: $i,SV251: $i,SV958: $i] :
( ( ( in @ SV958 @ SV251 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV824 @ SV958 ) @ SV539 )
| ( in @ ( kpair @ SV958 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) ) )
= $true )
| ( ( in @ SV824 @ SV251 )
= $false )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3470]) ).
thf(3684,plain,
! [SV540: $i,SV825: $i,SV252: $i,SV959: $i] :
( ( ( in @ SV959 @ SV252 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV959 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
| ( in @ ( kpair @ SV825 @ SV959 ) @ SV540 ) )
= $true )
| ( ( in @ SV825 @ SV252 )
= $false )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3471]) ).
thf(3685,plain,
! [SV826: $i,SV545: $i,SV255: $i,SV960: $i] :
( ( ( in @ SV960 @ SV255 )
= $false )
| ( ( ! [SY1763: $i] :
( ~ ( in @ SY1763 @ SV255 )
| ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1764: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV545 )
| SY1764 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SY1763 ) @ SV826 )
| SY1764 )
| SY1764 ) ) )
= $true )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3686,plain,
! [SV827: $i,SV548: $i,SV258: $i,SV961: $i] :
( ( ( in @ SV961 @ ( powerset @ SV258 ) )
= $false )
| ( ( in @ ( binintersect @ SV548 @ SV827 ) @ ( powerset @ ( binintersect @ ( binunion @ SV548 @ SV961 ) @ ( binunion @ SV827 @ SV961 ) ) ) )
= $true )
| ( ( in @ SV827 @ ( powerset @ SV258 ) )
= $false )
| ( ( in @ SV548 @ ( powerset @ SV258 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3687,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3688,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
| ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
= $false )
| ( ( ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3689,plain,
! [SV828: $i,SV552: $i,SV263: $i,SV962: $i] :
( ( ( in @ SV962 @ ( powerset @ SV263 ) )
= $false )
| ( ( ~ ( subset @ SV552 @ SV962 )
| ( subset @ ( binintersect @ SV552 @ SV828 ) @ SV962 ) )
= $true )
| ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3690,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
| ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SV264 )
| ~ ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SY1789 ) @ SV553 )
| ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SY1789 ) @ SV829 ) ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3477]) ).
thf(3691,plain,
! [SV558: $i > $o,SV269: $i,SV909: $i] :
( ( ( in @ SV909 @ SV269 )
= $false )
| ( ( ~ ~ ( SV558 @ SV909 ) )
= $true )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3692,plain,
! [SV559: $i,SV270: $i,SV723: $i] :
( ( ( in @ SV723 @ SV270 )
= $false )
| ( ( in @ SV723 @ SV559 )
= $true )
| ( ( in @ SV723 @ ( setminus @ SV270 @ SV559 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3480]) ).
thf(3693,plain,
! [SV831: $i,SV560: $i,SV271: $i,SV963: $i] :
( ( ( in @ SV963 @ SV271 )
= $false )
| ( ( ~ ( in @ SV963 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
| ( in @ SV963 @ ( setminus @ SV271 @ SV831 ) ) )
= $true )
| ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3694,plain,
! [SV832: $i,SV562: $i,SV274: $i,SV964: $i] :
( ( ( in @ SV964 @ SV274 )
= $false )
| ( ( ! [SY1765: $i] :
( ~ ( in @ SY1765 @ SV274 )
| ~ ( in @ ( kpair @ SV964 @ SY1765 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SY1765 ) @ ( binunion @ SV562 @ SV832 ) ) ) )
= $true )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3695,plain,
! [SV564: $i,SV276: $i,SV725: $i] :
( ( ( in @ SV725 @ ( symdiff @ SV276 @ SV564 ) )
= $false )
| ( ( in @ SV725 @ SV564 )
= $true )
| ( ( in @ SV725 @ SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3483]) ).
thf(3696,plain,
! [SV281: $i] :
( ( ( in @ ( sK35_SY742 @ SV281 ) @ SV281 )
= $true )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3484]) ).
thf(3697,plain,
! [SV281: $i] :
( ( $true = $true )
| ( ( SV281 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3485]) ).
thf(3698,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( ~ ( in @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) @ SV283 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3699,plain,
! [SV283: $i,SV833: $i > $o,SV911: $i > $o,SV569: $i] :
( ( ( ! [SY1787: $i] :
( ~ ( in @ SY1787 @ SV569 )
| ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
!= SY1787 )
| ~ ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ SY1787 ) )
| ~ ( ~ ( SV911 @ SY1787 )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3486]) ).
thf(3700,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ! [SY1666: $i] :
( ~ ( SV284 @ SY1666 )
| ( SV834 = SY1666 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3487]) ).
thf(3701,plain,
! [SV835: $i,SV570: $i,SV285: $i,SV965: $i] :
( ( ( in @ SV965 @ SV285 )
= $false )
| ( ( ~ ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) )
| ~ ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) ) )
= $true )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3702,plain,
! [SV759: $o,SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ SV287 )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 )
| SV759 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3489]) ).
thf(3703,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 ) )
= $true )
| ( SV759 = $true )
| ( SV759 = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3490]) ).
thf(3704,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ SV287 )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true )
| $true )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3491]) ).
thf(3705,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3706,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( ( in @ SV729 @ SV287 )
= $true )
| ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false )
| $false )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3493]) ).
thf(3707,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(3708,plain,
! [SV573: $i,SV836: $i,SV288: $i,SV966: $i] :
( ( ( in @ SV966 @ SV288 )
= $false )
| ( ( ! [SY1766: $i] :
( ~ ( in @ SY1766 @ SV288 )
| ~ ( in @ ( kpair @ SV966 @ SY1766 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SY1766 ) @ ( binunion @ SV573 @ SV836 ) ) ) )
= $true )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3495]) ).
thf(3709,plain,
! [SV912: $i,SV731: $i,SV291: $i,SV576: $o] :
( ( ( ~ SV576 ) = $false )
| ( ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 )
= $true )
| ( ( in @ SV912 @ SV291 )
= $false )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3496]) ).
thf(3710,plain,
! [SV913: $i,SV732: $i,SV291: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 )
= $true )
| ( ( in @ SV913 @ SV291 )
= $false )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3711,plain,
! [SV914: $i,SV733: $i,SV291: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 )
= $true )
| ( ( in @ SV914 @ SV291 )
= $false )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3712,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( ~ ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV296 )
| ~ ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV580 )
| ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV838 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3499]) ).
thf(3713,plain,
! [SV839: $i,SV581: $i,SV297: $i,SV967: $i] :
( ( ( in @ SV967 @ SV297 )
= $false )
| ( ( ! [SY1767: $i] :
( ~ ( in @ SY1767 @ SV297 )
| ~ ( ( in @ ( kpair @ SV967 @ SY1767 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SY1767 ) @ ( binunion @ SV581 @ SV839 ) ) ) )
= $true )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3500]) ).
thf(3714,plain,
! [SV915: $i,SV734: $i,SV582: $i,SV298: $i] :
( ( ( ! [SY1728: $i] :
( ~ ( in @ SY1728 @ SV298 )
| ! [SY1729: $i] :
( ~ ( in @ SY1729 @ SV582 )
| ~ ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV734 )
| ( in @ ( kpair @ SY1728 @ SY1729 ) @ SV915 ) ) ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3715,plain,
! [SV840: $i,SV583: $i,SV299: $i,SV968: $i] :
( ( ( in @ SV968 @ SV299 )
= $false )
| ( ( ~ ( in @ SV968 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
| ( in @ SV968 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) ) )
= $true )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3716,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ! [SY1674: $i] :
( ~ ( SV300 @ SY1674 )
| ( SV841 = SY1674 ) ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3717,plain,
! [SV842: $i,SV584: $i,SV301: $i,SV969: $i] :
( ( ( in @ SV969 @ SV301 )
= $false )
| ( ( ~ ( in @ SV969 @ ( setminus @ SV301 @ SV584 ) )
| ( in @ SV969 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) ) )
= $true )
| ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3504]) ).
thf(3718,plain,
! [SV843: $i,SV585: $i,SV302: $i,SV970: $i] :
( ( ( in @ SV970 @ SV302 )
= $false )
| ( ( ~ ( in @ SV970 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
| ( in @ SV970 @ ( setminus @ SV302 @ SV585 ) ) )
= $true )
| ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3505]) ).
thf(3719,plain,
! [SV305: $i,SV844: $i,SV587: $i,SV971: $i] :
( ( ( in @ SV971 @ ( binintersect @ SV587 @ SV844 ) )
= $false )
| ( ( in @ SV971 @ SV305 )
= $true )
| ( ( in @ SV844 @ ( powerset @ SV305 ) )
= $false )
| ( ( in @ SV587 @ ( powerset @ SV305 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3720,plain,
! [SV589: $i,SV307: $i,SV845: $i] :
( ( ( in @ SV845 @ ( setminus @ SV307 @ SV589 ) )
= $false )
| ( ( in @ SV845 @ SV589 )
= $false )
| ( ( in @ SV845 @ SV307 )
= $false )
| ( ( in @ SV589 @ ( powerset @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3721,plain,
! [SV916: $o,SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 = SV309 )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 )
| SV916 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3508]) ).
thf(3722,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 ) )
= $true )
| ( SV916 = $true )
| ( SV916 = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3723,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 = SV309 )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true )
| $true )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3510]) ).
thf(3724,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3725,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( ( SV736 = SV309 )
= $true )
| ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false )
| $false )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3512]) ).
thf(3726,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3513]) ).
thf(3727,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( ~ ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV310 )
| ~ ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV592 )
| ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV847 ) )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3514]) ).
thf(3728,plain,
! [SV596: $i,SV314: $i,SV924: $i,SV760: $i,SV739: $i > $i > $o] :
( ( ( ~ ( SV739 @ SV760 @ SV924 ) )
= $true )
| ( ( in @ ( kpair @ SV760 @ SV924 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) )
= $true )
| ( ( in @ SV924 @ SV596 )
= $false )
| ( ( in @ SV760 @ SV314 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3515]) ).
thf(3729,plain,
! [SV972: $o,SV848: $i,SV597: $i,SV315: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV315 ) )
= $true )
| ( ( ~ ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3516]) ).
thf(3730,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV315 ) )
= $true )
| ( ( ~ ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV986 @ SV597 )
| $true )
| ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3517]) ).
thf(3731,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV315 ) )
= $true )
| ( ( ~ ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV987 @ SV597 )
| $false )
| ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3518]) ).
thf(3732,plain,
! [SV849: $i,SV599: $i,SV317: $i,SV973: $i] :
( ( ( in @ SV973 @ ( powerset @ SV317 ) )
= $false )
| ( ( ! [SY1769: $i] :
( ~ ( in @ SY1769 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SY1769 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SY1769 ) ) ) ) ) )
= $true )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3733,plain,
! [SV850: $i,SV600: $i,SV318: $i,SV974: $i] :
( ( ( in @ SV974 @ SV318 )
= $false )
| ( ( ~ ( subset @ SV600 @ SV850 )
| ~ ~ ( in @ SV974 @ SV850 )
| ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3520]) ).
thf(3734,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ! [SY1684: $i] :
( ~ ( SV323 @ SY1684 )
| ( SV852 = SY1684 ) ) )
= $false )
| ( ( SV323 @ SV852 )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3735,plain,
! [SV920: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 ) )
= $false )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3736,plain,
! [SV920: $i,SV3: $i] :
( ( ( subset @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $false )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3522]) ).
thf(3737,plain,
! [SV854: $i,SV3: $i] :
( ( ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $true )
| ( ( ! [SY1686: $i] :
( ~ ( in @ SY1686 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SY1686 @ ( binintersect @ SV3 @ SV854 ) ) ) )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3523]) ).
thf(3738,plain,
! [SV854: $i,SV3: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SV993 @ ( binintersect @ SV3 @ SV854 ) ) )
= $true )
| ( ( subset @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $false )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3524]) ).
thf(3739,plain,
! [SV8: $i,SV332: $i > $o,SV611: $i] :
( ( ( ~ ( in @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) @ SV8 ) )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3740,plain,
! [SV8: $i,SV611: $i,SV332: $i > $o] :
( ( ( ~ ( SV332 @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) )
| ( ( sK62_SY1370 @ SV611 @ SV332 @ SV8 )
= SV611 ) )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3525]) ).
thf(3741,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i] :
( ( ( ~ ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
| ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) ) )
= $false )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3526]) ).
thf(3742,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 )
= $true )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3743,plain,
! [SV342: $i,SV859: $i > $o,SV618: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 )
| ~ ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
| ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3529]) ).
thf(3744,plain,
! [SV20: $i,SV762: $i,SV343: $i,SV926: $i] :
( ( ( ~ ~ ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) ) )
= $true )
| ( ( ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV926 @ SV20 )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3530]) ).
thf(3745,plain,
! [SV346: $i,SV860: $i,SV24: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV24 )
| ( in @ SV860 @ SV346 ) )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3531]) ).
thf(3746,plain,
! [SV24: $i,SV764: $i,SV346: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ SV346 )
| ( in @ SV764 @ SV24 ) )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3747,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3533]) ).
thf(3748,plain,
! [SV26: $i,SV347: $i > $o] :
( ( ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( in @ SY900 @ SV26 )
| ~ ( SV347 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3534]) ).
thf(3749,plain,
! [SV348: $i > $o,SV27: $i,SV988: $i] :
( ( ( ~ ( ~ ( in @ SV988 @ SV27 )
| ~ ( SV348 @ SV988 ) ) )
= $false )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3535]) ).
thf(3750,plain,
! [SV348: $i > $o,SV27: $i,SV989: $i] :
( ( ( ~ ( ~ ( in @ SV989 @ SV27 )
| ~ ( SV348 @ SV989 ) ) )
= $false )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3751,plain,
! [SV34: $i,SV765: $i,SV353: $i,SV927: $i] :
( ( ( ~ ~ ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) ) )
= $true )
| ( ( ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV927 @ SV34 )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3537]) ).
thf(3752,plain,
! [SV768: $i,SV357: $i,SV928: $i,SV40: $i,SV994: $i] :
( ( ( ~ ( in @ SV994 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3538]) ).
thf(3753,plain,
! [SV770: $i,SV359: $i,SV42: $i,SV930: $i] :
( ( ( ~ ( in @ SV930 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) ) )
= $true )
| ( ( in @ SV930 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) )
= $true )
| ( ( in @ SV930 @ SV42 )
= $false )
| ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3540]) ).
thf(3754,plain,
! [SV360: $i > $i,SV623: $i,SV43: $i,SV921: $i] :
( ( ( in @ SV921 @ SV43 )
= $false )
| ( ( SV623
!= ( SV360 @ SV921 ) )
= $true )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3541]) ).
thf(3755,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ ( sK55_SY928 @ SV47 @ SV364 ) )
| ~ ( in @ ( sK55_SY928 @ SV47 @ SV364 ) @ SV47 ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3756,plain,
! [SV47: $i,SV975: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV975 )
| ~ ( in @ SV975 @ SV47 ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3543]) ).
thf(3757,plain,
! [SV773: $i,SV367: $i,SV52: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) ) )
= $true )
| ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV931 @ SV52 )
= $false )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3544]) ).
thf(3758,plain,
! [SV370: $i,SV776: $i,SV55: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV55 ) )
= $true )
| ( ( ~ ( in @ SV990 @ SV776 )
| ( in @ SV990 @ ( setminus @ SV55 @ SV370 ) ) )
= $true )
| ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3545]) ).
thf(3759,plain,
! [SV777: $i,SV372: $i,SV57: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) ) )
= $true )
| ( ( ~ ( in @ SV932 @ SV372 ) )
= $true )
| ( ( in @ SV932 @ SV57 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3546]) ).
thf(3760,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
= $true )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3547]) ).
thf(3761,plain,
! [SV58: $i,SV373: $i > $o] :
( ( ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) )
= $true )
| ( ( ! [SY941: $i] :
( ~ ( in @ SY941 @ SV58 )
| ~ ( SV373 @ SY941 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3548]) ).
thf(3762,plain,
! [SV61: $i,SV376: $i > $o,SV862: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) @ SV61 )
| ~ ~ ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) ) ) )
= $true )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3549]) ).
thf(3763,plain,
! [SV629: $i > $i,SV377: $i,SV62: $i,SV976: $i] :
( ( ( in @ SV976 @ SV62 )
= $false )
| ( ( ( ap @ SV62 @ SV377
@ ( lam @ SV62 @ SV377
@ ^ [SY1392: $i] : ( SV629 @ SY1392 ) )
@ SV976 )
= ( SV629 @ SV976 ) )
= $true )
| ( ( in @ ( sK24_SY1390 @ SV377 @ SV629 @ SV62 ) @ SV62 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3764,plain,
! [SV66: $i,SV778: $i,SV380: $i,SV934: $i] :
( ( ( ~ ~ ( in @ SV934 @ SV380 ) )
= $true )
| ( ( ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3552]) ).
thf(3765,plain,
! [SV864: $i,SV632: $i,SV70: $i,SV383: $o] :
( ( SV383 = $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1693: $i] :
( ~ ( ~ SV383
| ( SY1693 != SV632 ) )
| ~ ( ~ ~ SV383
| ( SY1693 != SV864 ) ) ) )
= ( setadjoin @ SV864 @ emptyset ) )
= $true )
| ( ( in @ SV864 @ SV70 )
= $false )
| ( ( in @ SV632 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(3766,plain,
! [SV865: $i,SV633: $i,SV70: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1694: $i] :
( ~ ( ~ $true
| ( SY1694 != SV633 ) )
| ~ ( ~ ~ $true
| ( SY1694 != SV865 ) ) ) )
= ( setadjoin @ SV865 @ emptyset ) )
= $true )
| ( ( in @ SV865 @ SV70 )
= $false )
| ( ( in @ SV633 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3555]) ).
thf(3767,plain,
! [SV866: $i,SV634: $i,SV70: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV70
@ ^ [SY1695: $i] :
( ~ ( ~ $false
| ( SY1695 != SV634 ) )
| ~ ( ~ ~ $false
| ( SY1695 != SV866 ) ) ) )
= ( setadjoin @ SV866 @ emptyset ) )
= $true )
| ( ( in @ SV866 @ SV70 )
= $false )
| ( ( in @ SV634 @ SV70 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3556]) ).
thf(3768,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ( in @ ( sK45_SY168 @ SV780 @ SV73 ) @ SV73 ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3769,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ~ ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3557]) ).
thf(3770,plain,
! [SV76: $i,SV935: $i,SV781: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( powerset @ SV781 ) ) )
= $true )
| ( ( ~ ( in @ SV935 @ SV386 )
| ( in @ SV935 @ SV781 ) )
= $true )
| ( ( in @ SV935 @ SV76 )
= $false )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3558]) ).
thf(3771,plain,
! [SV936: $i,SV782: $i,SV77: $i,SV387: $i] :
( ( ( ~ ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) ) )
= $true )
| ( ( ~ ( in @ SV936 @ SV782 )
| ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( in @ SV936 @ SV77 )
= $false )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3559]) ).
thf(3772,plain,
! [SV82: $i,SV784: $i,SV392: $i,SV937: $i] :
( ( ( ~ ~ ( in @ SV937 @ SV392 ) )
= $true )
| ( ( ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV937 @ SV82 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3560]) ).
thf(3773,plain,
! [SV786: $i,SV402: $i,SV938: $i,SV93: $i,SV995: $i] :
( ( ( ~ ( in @ SV995 @ SV93 )
| ~ ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 ) )
= $true )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3561]) ).
thf(3774,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 ) )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3565]) ).
thf(3775,plain,
! [SV874: $o,SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3566]) ).
thf(3776,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 ) )
= $true )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3567]) ).
thf(3777,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3568]) ).
thf(3778,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3779,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(3780,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3571]) ).
thf(3781,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3572]) ).
thf(3782,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(3783,plain,
! [SV787: $i,SV408: $i,SV939: $i,SV99: $i,SV996: $i] :
( ( ( ~ ( in @ SV996 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1791: $o] :
( ~ ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1792 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1792 @ SV996 ) @ SV787 )
| SY1791 )
| SY1791 ) )
= $true )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3574]) ).
thf(3784,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3575]) ).
thf(3785,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3576]) ).
thf(3786,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) )
= $false )
| ( ( ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3787,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3788,plain,
! [SV108: $i,SV940: $i,SV788: $i,SV416: $i] :
( ( ( ~ ( subset @ SV416 @ SV788 ) )
= $true )
| ( ( ~ ( subset @ SV416 @ SV940 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) ) )
= $true )
| ( ( in @ SV940 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3578]) ).
thf(3789,plain,
! [SV109: $i,SV417: $i,SV651: $i,SV875: $i] :
( ( ( ~ ( in @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) @ SV109 )
| ( ( ap @ SV109 @ SV417 @ SV651 @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) )
= ( ap @ SV109 @ SV417 @ SV875 @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) ) ) )
= $false )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3579]) ).
thf(3790,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( in @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3580]) ).
thf(3791,plain,
! [SV111: $i,SV653: $i,SV419: $i] :
( ( ( ~ ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3581]) ).
thf(3792,plain,
! [SV941: $i,SV790: $i,SV424: $i,SV117: $i,SV997: $i] :
( ( ( ~ ( in @ SV997 @ SV117 )
| ~ ( in @ SV997 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SV997 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) )
= $true )
| ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3584]) ).
thf(3793,plain,
! [SV425: $i > $o,SV118: $i,SV998: $i] :
( ( ( ~ ~ ( ~ ( in @ SV998 @ SV118 )
| ~ ( SV425 @ SV998 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3794,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3586]) ).
thf(3795,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3587]) ).
thf(3796,plain,
! [SV118: $i,SV425: $i > $o] :
( ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true )
| ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) )
| ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3588]) ).
thf(3797,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3589]) ).
thf(3798,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false )
| ( ( ~ ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3799,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ( ~ ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3800,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
| ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 ) )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3592]) ).
thf(3801,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3802,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3593]) ).
thf(3803,plain,
! [SV433: $i,SV126: $i,SV791: $o] :
( ( ( in @ ( sK46_SY1606 @ SV791 @ SV126 @ SV433 ) @ SV126 )
= $true )
| ( SV791 = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3599]) ).
thf(3804,plain,
! [SV433: $i,SV126: $i] :
( ( ( in @ ( sK47_SX0 @ SV126 @ SV433 ) @ SV126 )
= $true )
| ( $true = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3805,plain,
! [SV433: $i,SV126: $i] :
( ( ( in @ ( sK48_SX0 @ SV126 @ SV433 ) @ SV126 )
= $true )
| ( $false = $true )
| ( ( in @ SV433 @ ( setunion @ SV126 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3806,plain,
! [SV793: $i,SV440: $i,SV133: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) ) )
= $true )
| ( ( in @ SV942 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) )
= $true )
| ( ( in @ SV942 @ SV133 )
= $false )
| ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3607]) ).
thf(3807,plain,
! [SV794: $i,SV943: $i,SV441: $i,SV134: $i,SV999: $i] :
( ( ( ~ ( in @ SV999 @ ( powerset @ SV134 ) )
| ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SV999 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3608]) ).
thf(3808,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
| ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) ) )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3609]) ).
thf(3809,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
| ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) ) )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3610]) ).
thf(3810,plain,
! [SV139: $i,SV444: $i,SV664: $i,SV881: $i] :
( ( ( ~ ( in @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) @ SV139 )
| ( ( ap @ SV139 @ SV444 @ SV664 @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) )
= ( ap @ SV139 @ SV444 @ SV881 @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) ) ) )
= $false )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3611]) ).
thf(3811,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ~ ( ~ ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3612]) ).
thf(3812,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ~ ( ~ ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) )
| ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3612]) ).
thf(3813,plain,
! [SV445: $i > $i,SV140: $i,SV978: $i] :
( ( ( ! [SY1774: $i] :
~ ( ~ ( ~ ( in @ SY1774 @ SV978 )
| ~ ! [SY1073: $i] :
~ ~ ( ~ ( in @ SY1073 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1073 ) ) ) )
| ~ ( ~ ~ ! [SY1074: $i] :
~ ~ ( ~ ( in @ SY1074 @ SV140 )
| ( SY1774
!= ( SV445 @ SY1074 ) ) )
| ( in @ SY1774 @ SV978 ) ) ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3814,plain,
! [SV143: $i,SV448: $i,SV944: $i,SV798: $i] :
( ( ( ~ ( subset @ SV798 @ SV944 ) )
= $true )
| ( ( subset @ ( binintersect @ SV448 @ SV798 ) @ SV944 )
= $true )
| ( ( in @ SV944 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3614]) ).
thf(3815,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1000: $i] :
( ( ( ~ ( in @ SV1000 @ SV451 )
| ( SV799 @ SV1000 ) )
= $true )
| ( ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3617]) ).
thf(3816,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i] :
( ( ( ~ ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3618]) ).
thf(3817,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
| ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3618]) ).
thf(3818,plain,
! [SV148: $i,SV667: $i,SV453: $i > $i] :
( ( ( in @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) @ SV148 )
= $true )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3619]) ).
thf(3819,plain,
! [SV148: $i,SV453: $i > $i,SV667: $i] :
( ( ( SV667
= ( SV453 @ ( sK41_SY1445 @ SV453 @ SV667 @ SV148 ) ) )
= $true )
| ( ( in @ SV667
@ ( image1 @ SV148
@ ^ [SY1092: $i] : ( SV453 @ SY1092 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3620]) ).
thf(3820,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( ~ ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 ) )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3621]) ).
thf(3821,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( ~ ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
| ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 ) )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3621]) ).
thf(3822,plain,
! [SV153: $i,SV882: $i,SV458: $i > $o] :
( ( ( SV458 @ SV882 )
= $false )
| ( ( in @ SV882 @ SV153 )
= $false )
| ( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3622]) ).
thf(3823,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
| ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3624]) ).
thf(3824,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1001: $i] :
( ( ( ~ ( in @ SV1001 @ SV460 )
| ( SV803 @ SV1001 ) )
= $true )
| ( ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3625]) ).
thf(3825,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i] :
( ( ( ~ ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(3826,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
| ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3626]) ).
thf(3827,plain,
! [SV670: $i,SV158: $i,SV884: $i,SV462: $o] :
( ( SV462 = $true )
| ( ( in @ SV884
@ ( dsetconstr @ SV158
@ ^ [SY1708: $i] :
( ~ ( ~ SV462
| ( SY1708 != SV670 ) )
| ~ ( ~ ~ SV462
| ( SY1708 != SV884 ) ) ) ) )
= $true )
| ( ( in @ SV884 @ SV158 )
= $false )
| ( ( in @ SV670 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3627]) ).
thf(3828,plain,
! [SV671: $i,SV158: $i,SV885: $i] :
( ( $true = $true )
| ( ( in @ SV885
@ ( dsetconstr @ SV158
@ ^ [SY1709: $i] :
( ~ ( ~ $true
| ( SY1709 != SV671 ) )
| ~ ( ~ ~ $true
| ( SY1709 != SV885 ) ) ) ) )
= $true )
| ( ( in @ SV885 @ SV158 )
= $false )
| ( ( in @ SV671 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3628]) ).
thf(3829,plain,
! [SV672: $i,SV158: $i,SV886: $i] :
( ( $false = $true )
| ( ( in @ SV886
@ ( dsetconstr @ SV158
@ ^ [SY1710: $i] :
( ~ ( ~ $false
| ( SY1710 != SV672 ) )
| ~ ( ~ ~ $false
| ( SY1710 != SV886 ) ) ) ) )
= $true )
| ( ( in @ SV886 @ SV158 )
= $false )
| ( ( in @ SV672 @ SV158 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3629]) ).
thf(3830,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3831,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
| ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3631]) ).
thf(3832,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
| ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3632]) ).
thf(3833,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( ~ ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
| ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV470 )
| ~ ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SY1793 ) @ SV678 )
| ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SY1793 ) @ SV887 ) ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3633]) ).
thf(3834,plain,
! [SV170: $i,SV679: $i,SV472: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) @ SV170 )
| ( SV679
!= ( SV472 @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) ) ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3634]) ).
thf(3835,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i,SV991: $i] :
( ( ( ~ ( ~ ( in @ SV991 @ SV170 )
| ( SV679
!= ( SV472 @ SV991 ) ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3635]) ).
thf(3836,plain,
! [SV171: $i,SV473: $i,SV807: $i,SV946: $i] :
( ( ( ~ ~ ( in @ SV946 @ SV807 ) )
= $true )
| ( ( ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV946 @ SV171 )
= $false )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3636]) ).
thf(3837,plain,
! [SV680: $i > $i,SV474: $i,SV172: $i,SV979: $i] :
( ( ( in @ SV979 @ SV172 )
= $false )
| ( ( ( ap @ SV172 @ SV474
@ ( lam @ SV172 @ SV474
@ ^ [SY1465: $i] : ( SV680 @ SY1465 ) )
@ SV979 )
= ( SV680 @ SV979 ) )
= $true )
| ( ( in @ ( sK30_SY1463 @ SV474 @ SV680 @ SV172 ) @ SV172 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3637]) ).
thf(3838,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) )
= $false )
| ( ( ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3639]) ).
thf(3839,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3639]) ).
thf(3840,plain,
! [SV948: $i,SV810: $i,SV479: $i,SV179: $i,SV1002: $i] :
( ( ( ~ ( in @ SV1002 @ SV179 )
| ~ ( in @ SV1002 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SV1002 @ ( binunion @ SV810 @ SV948 ) ) )
= $true )
| ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3644]) ).
thf(3841,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3648]) ).
thf(3842,plain,
! [SV482: $i,SV892: $i > $o,SV687: $i,SV183: $i] :
( ( ( ~ ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 )
| ~ ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
| ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3649]) ).
thf(3843,plain,
! [SV812: $i,SV486: $i,SV188: $i,SV949: $i] :
( ( ( ~ ( in @ SV949 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) ) )
= $true )
| ( ( in @ SV949 @ ( setminus @ SV188 @ SV486 ) )
= $true )
| ( ( in @ SV949 @ SV188 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3650]) ).
thf(3844,plain,
! [SV189: $i,SV950: $i,SV813: $i,SV487: $i > $o] :
( ( ( ~ ( SV487 @ SV813 ) )
= $true )
| ( ( ~ ( SV487 @ SV950 )
| ( SV813 = SV950 ) )
= $true )
| ( ( in @ SV950 @ SV189 )
= $false )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3651]) ).
thf(3845,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
| ~ ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) )
| ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3652]) ).
thf(3846,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 ) )
= $true )
| ( ( ~ ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3653]) ).
thf(3847,plain,
! [SV814: $i,SV496: $i,SV198: $i,SV952: $i] :
( ( ( ~ ( in @ SV952 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) ) )
= $true )
| ( ( in @ SV952 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) )
= $true )
| ( ( in @ SV952 @ SV198 )
= $false )
| ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3654]) ).
thf(3848,plain,
! [SV695: $i > $i,SV202: $i,SV499: $i,SV980: $i] :
( ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( ~ ! [SY1783: $i] :
( ~ ( in @ SY1783 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ SY1783 ) )
= SY1783 ) )
| ( surjective @ SV499 @ SV202 @ SV980 ) )
= $true )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3849,plain,
! [SV695: $i > $i,SV953: $i,SV499: $i,SV202: $i] :
( ( ( ~ ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ SY1752 ) )
= SY1752 ) ) )
= $true )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3850,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( ~ ( in @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SV209 ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3657]) ).
thf(3851,plain,
! [SV504: $i,SV817: $i,SV209: $i] :
( ( ( ! [SY1788: $i] :
( ~ ( in @ SY1788 @ SV209 )
| ~ ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SY1788 ) @ SV504 )
| ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SY1788 ) @ SV817 ) ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3657]) ).
thf(3852,plain,
! [SV954: $i,SV818: $i,SV506: $i,SV211: $i,SV1004: $i] :
( ( ( ~ ( in @ SV1004 @ SV211 )
| ~ ( in @ SV1004 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SV1004 @ ( binunion @ SV506 @ SV954 ) ) )
= $true )
| ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3658]) ).
thf(3853,plain,
! [SV212: $i] :
( ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) )
| ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3854,plain,
! [SV212: $i,SV1005: $i] :
( ( ! [SY1796: $i] :
( ~ ~ ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1796 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SY1797: $i] :
( ~ ( in @ SY1797 @ SV1005 )
| ( in @ SY1797 @ SY1796 ) )
| ! [SY1798: $i] :
( ~ ( in @ SY1798 @ SY1796 )
| ( in @ SY1798 @ SV1005 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3660]) ).
thf(3855,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) )
| ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(3856,plain,
! [SV702: $i > $i > $o,SV215: $i,SV509: $i,SV981: $i] :
( ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV509 @ SV981 )
| ! [SY1784: $i] :
( ~ ( in @ SY1784 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1785: $i] :
~ ( ~ ( SV702 @ SY1784 @ SY1785 )
| ~ ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SV509 )
| ~ ( SV702 @ SY1784 @ SY1786 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ SV981 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(3857,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV509 )
| ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3663]) ).
thf(3858,plain,
! [SV225: $i,SV705: $i,SV901: $i,SV516: $i,SV983: $i] :
( ( ( in @ SV983 @ SV516 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV901 @ SV983 ) @ SV705 )
| ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SV983 ) )
= $true )
| ( ( in @ SV901 @ SV225 )
= $false )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3664]) ).
thf(3859,plain,
! [SV226: $i] :
( ( ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ omega )
| ~ ( in @ ( sK51_SY601 @ SV226 ) @ SV226 ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3665]) ).
thf(3860,plain,
! [SV226: $i,SV992: $i] :
( ( ( ~ ( in @ SV992 @ omega ) )
= $true )
| ( ( in @ SV992 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( setadjoin @ ( sK51_SY601 @ SV226 ) @ ( sK51_SY601 @ SV226 ) ) @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3666]) ).
thf(3861,plain,
! [SV519: $i,SV230: $i] :
( ( ( ~ ( in @ ( sK70_SY1213 @ SV230 @ SV519 ) @ SV519 ) )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3667]) ).
thf(3862,plain,
! [SV519: $i,SV230: $i] :
( ( ( in @ ( sK70_SY1213 @ SV230 @ SV519 ) @ SV230 )
= $false )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3667]) ).
thf(3863,plain,
! [SV519: $i,SV230: $i] :
( ( ( in @ ( sK59_SY1213 @ SV230 @ SV519 ) @ SV519 )
= $true )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV519 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3668]) ).
thf(3864,plain,
! [SV232: $i,SV521: $i > $o,SV902: $i] :
( ( ( ~ ( ~ ( in @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) @ SV232 )
| ~ ~ ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) ) ) )
= $true )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3670]) ).
thf(3865,plain,
! [SV822: $i,SV523: $i,SV956: $i,SV234: $i,SV1006: $i] :
( ( ( ~ ( in @ SV1006 @ SV234 )
| ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1799 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1799 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) )
= $true )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3671]) ).
thf(3866,plain,
! [SV235: $i,SV524: $i] :
( ( ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV235 )
= $true )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3672]) ).
thf(3867,plain,
! [SV235: $i,SV524: $i] :
( ( ( in @ ( sK43_SY1221 @ SV524 @ SV235 ) @ SV524 )
= $true )
| ( ( ( binintersect @ SV235 @ SV524 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(3868,plain,
! [SV709: $i > $i > $o,SV527: $i,SV238: $i,SV923: $i,SV757: $i] :
( ( ( in @ ( kpair @ SV757 @ SV923 )
@ ( dpsetconstr @ SV238 @ SV527
@ ^ [SY1521: $i,SY1522: $i] : ( SV709 @ SY1521 @ SY1522 ) ) )
= $false )
| ( ( SV709 @ SV757 @ SV923 )
= $true )
| ( ( in @ SV923 @ SV527 )
= $false )
| ( ( in @ SV757 @ SV238 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(3869,plain,
! [SV534: $i > $o,SV245: $i,SV1007: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1007 @ SV245 )
| ~ ( SV534 @ SV1007 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3675]) ).
thf(3870,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3676]) ).
thf(3871,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3677]) ).
thf(3872,plain,
! [SV245: $i,SV534: $i > $o] :
( ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true )
| ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) )
| ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3873,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3679]) ).
thf(3874,plain,
! [SV250: $i,SV716: $i,SV907: $i,SV538: $i,SV984: $i] :
( ( ( in @ SV984 @ SV538 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV907 @ SV984 ) @ SV716 )
| ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SV984 ) )
= $true )
| ( ( in @ SV907 @ SV250 )
= $false )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3682]) ).
thf(3875,plain,
! [SV251: $i,SV539: $i,SV958: $i,SV824: $i] :
( ( ( ~ ( in @ ( kpair @ SV824 @ SV958 ) @ SV539 ) )
= $true )
| ( ( in @ ( kpair @ SV958 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) )
= $true )
| ( ( in @ SV958 @ SV251 )
= $false )
| ( ( in @ SV824 @ SV251 )
= $false )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3876,plain,
! [SV540: $i,SV252: $i,SV825: $i,SV959: $i] :
( ( ( ~ ( in @ ( kpair @ SV959 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) ) )
= $true )
| ( ( in @ ( kpair @ SV825 @ SV959 ) @ SV540 )
= $true )
| ( ( in @ SV959 @ SV252 )
= $false )
| ( ( in @ SV825 @ SV252 )
= $false )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3684]) ).
thf(3877,plain,
! [SV826: $i,SV545: $i,SV960: $i,SV255: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV255 )
| ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1800: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SY1800 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SY1800 )
| SY1800 ) )
= $true )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3685]) ).
thf(3878,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3879,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) )
= $false )
| ( ( ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3688]) ).
thf(3880,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3688]) ).
thf(3881,plain,
! [SV263: $i,SV828: $i,SV962: $i,SV552: $i] :
( ( ( ~ ( subset @ SV552 @ SV962 ) )
= $true )
| ( ( subset @ ( binintersect @ SV552 @ SV828 ) @ SV962 )
= $true )
| ( ( in @ SV962 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3689]) ).
thf(3882,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3690]) ).
thf(3883,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ! [SY1789: $i] :
( ~ ( in @ SY1789 @ SV264 )
| ~ ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SY1789 ) @ SV553 )
| ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SY1789 ) @ SV829 ) ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3690]) ).
thf(3884,plain,
! [SV269: $i,SV909: $i,SV558: $i > $o] :
( ( ( ~ ( SV558 @ SV909 ) )
= $false )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(3885,plain,
! [SV831: $i,SV560: $i,SV271: $i,SV963: $i] :
( ( ( ~ ( in @ SV963 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) ) )
= $true )
| ( ( in @ SV963 @ ( setminus @ SV271 @ SV831 ) )
= $true )
| ( ( in @ SV963 @ SV271 )
= $false )
| ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3693]) ).
thf(3886,plain,
! [SV832: $i,SV562: $i,SV964: $i,SV274: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ SV274 )
| ~ ( in @ ( kpair @ SV964 @ SV1009 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SV1009 ) @ ( binunion @ SV562 @ SV832 ) ) )
= $true )
| ( ( in @ SV964 @ SV274 )
= $false )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3694]) ).
thf(3887,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( in @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) @ SV283 )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3698]) ).
thf(3888,plain,
! [SV569: $i,SV911: $i > $o,SV833: $i > $o,SV283: $i] :
( ( ( ~ ( in @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) @ SV569 )
| ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
!= ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ~ ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
| ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3699]) ).
thf(3889,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
| ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3700]) ).
thf(3890,plain,
! [SV835: $i,SV570: $i,SV285: $i,SV965: $i] :
( ( ( ~ ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) ) )
= $true )
| ( ( ~ ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) ) )
= $true )
| ( ( in @ SV965 @ SV285 )
= $false )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3891,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| SV759 ) )
= $true )
| ( SV759 = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3702]) ).
thf(3892,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| SV759 )
= $false )
| ( SV759 = $true )
| ( SV759 = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3703]) ).
thf(3893,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3704]) ).
thf(3894,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3705]) ).
thf(3895,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( ~ ( in @ SV729 @ SV572 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3706]) ).
thf(3896,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3707]) ).
thf(3897,plain,
! [SV573: $i,SV836: $i,SV966: $i,SV288: $i,SV1010: $i] :
( ( ( ~ ( in @ SV1010 @ SV288 )
| ~ ( in @ ( kpair @ SV966 @ SV1010 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SV1010 ) @ ( binunion @ SV573 @ SV836 ) ) )
= $true )
| ( ( in @ SV966 @ SV288 )
= $false )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3708]) ).
thf(3898,plain,
! [SV912: $i,SV731: $i,SV291: $i,SV576: $o] :
( ( SV576 = $true )
| ( ( ( if @ SV291 @ SV576 @ SV731 @ SV912 )
= SV912 )
= $true )
| ( ( in @ SV912 @ SV291 )
= $false )
| ( ( in @ SV731 @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3709]) ).
thf(3899,plain,
! [SV913: $i,SV732: $i,SV291: $i] :
( ( $true = $true )
| ( ( ( if @ SV291 @ $true @ SV732 @ SV913 )
= SV913 )
= $true )
| ( ( in @ SV913 @ SV291 )
= $false )
| ( ( in @ SV732 @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3710]) ).
thf(3900,plain,
! [SV914: $i,SV733: $i,SV291: $i] :
( ( $false = $true )
| ( ( ( if @ SV291 @ $false @ SV733 @ SV914 )
= SV914 )
= $true )
| ( ( in @ SV914 @ SV291 )
= $false )
| ( ( in @ SV733 @ SV291 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3711]) ).
thf(3901,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( ~ ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3902,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( ~ ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV580 )
| ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV838 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3903,plain,
! [SV839: $i,SV581: $i,SV967: $i,SV297: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ SV297 )
| ~ ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) ) )
= $true )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3713]) ).
thf(3904,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( ~ ( in @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SV298 )
| ! [SY1801: $i] :
( ~ ( in @ SY1801 @ SV582 )
| ~ ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SY1801 ) @ SV734 )
| ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SY1801 ) @ SV915 ) ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3714]) ).
thf(3905,plain,
! [SV840: $i,SV583: $i,SV299: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) ) )
= $true )
| ( ( in @ SV968 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) )
= $true )
| ( ( in @ SV968 @ SV299 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3715]) ).
thf(3906,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) )
| ( SV841
= ( sK88_SY1674 @ SV841 @ SV300 ) ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3716]) ).
thf(3907,plain,
! [SV842: $i,SV584: $i,SV301: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ ( setminus @ SV301 @ SV584 ) ) )
= $true )
| ( ( in @ SV969 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) )
= $true )
| ( ( in @ SV969 @ SV301 )
= $false )
| ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3717]) ).
thf(3908,plain,
! [SV843: $i,SV585: $i,SV302: $i,SV970: $i] :
( ( ( ~ ( in @ SV970 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) ) )
= $true )
| ( ( in @ SV970 @ ( setminus @ SV302 @ SV585 ) )
= $true )
| ( ( in @ SV970 @ SV302 )
= $false )
| ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3718]) ).
thf(3909,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| SV916 ) )
= $true )
| ( SV916 = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3721]) ).
thf(3910,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| SV916 )
= $false )
| ( SV916 = $true )
| ( SV916 = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3911,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3723]) ).
thf(3912,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3724]) ).
thf(3913,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( ~ ( in @ SV736 @ SV591 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3725]) ).
thf(3914,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3726]) ).
thf(3915,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( ~ ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV310 ) )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3916,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( ~ ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV592 )
| ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV847 ) )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3727]) ).
thf(3917,plain,
! [SV596: $i,SV314: $i,SV924: $i,SV760: $i,SV739: $i > $i > $o] :
( ( ( SV739 @ SV760 @ SV924 )
= $false )
| ( ( in @ ( kpair @ SV760 @ SV924 )
@ ( dpsetconstr @ SV314 @ SV596
@ ^ [SY1547: $i,SY1548: $i] : ( SV739 @ SY1547 @ SY1548 ) ) )
= $true )
| ( ( in @ SV924 @ SV596 )
= $false )
| ( ( in @ SV760 @ SV314 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3728]) ).
thf(3918,plain,
! [SV972: $o,SV848: $i,SV597: $i,SV315: $i,SV985: $i] :
( ( ( in @ SV985 @ SV315 )
= $false )
| ( ( ~ ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3729]) ).
thf(3919,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV986: $i] :
( ( ( in @ SV986 @ SV315 )
= $false )
| ( ( ~ ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV986 @ SV597 )
| $true )
| ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3730]) ).
thf(3920,plain,
! [SV848: $i,SV597: $i,SV315: $i,SV987: $i] :
( ( ( in @ SV987 @ SV315 )
= $false )
| ( ( ~ ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
| ~ ( ~ ( in @ SV987 @ SV597 )
| $false )
| ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3731]) ).
thf(3921,plain,
! [SV973: $i,SV849: $i,SV599: $i,SV317: $i,SV1012: $i] :
( ( ( ~ ( in @ SV1012 @ ( powerset @ SV317 ) )
| ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SV1012 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SV1012 ) ) ) ) )
= $true )
| ( ( in @ SV973 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3732]) ).
thf(3922,plain,
! [SV318: $i,SV974: $i,SV850: $i,SV600: $i] :
( ( ( ~ ( subset @ SV600 @ SV850 ) )
= $true )
| ( ( ~ ~ ( in @ SV974 @ SV850 )
| ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3733]) ).
thf(3923,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ( SV323 @ ( sK89_SY1684 @ SV852 @ SV323 ) )
| ( SV852
= ( sK89_SY1684 @ SV852 @ SV323 ) ) )
= $false )
| ( ( SV323 @ SV852 )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3734]) ).
thf(3924,plain,
! [SV920: $i,SV3: $i] :
( ( ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $true )
| ( ( ! [SY1731: $i] :
( ~ ( in @ SY1731 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SY1731 @ ( binintersect @ SV3 @ SV920 ) ) ) )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3735]) ).
thf(3925,plain,
! [SV920: $i,SV3: $i,SV1013: $i] :
( ( ( ~ ( in @ SV1013 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SV1013 @ ( binintersect @ SV3 @ SV920 ) ) )
= $true )
| ( ( subset @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $false )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3736]) ).
thf(3926,plain,
! [SV854: $i,SV3: $i,SV1014: $i] :
( ( ( ~ ( in @ SV1014 @ ( binintersect @ SV3 @ SV854 ) )
| ( subset @ SV1014 @ ( binintersect @ SV3 @ SV854 ) ) )
= $true )
| ( ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3737]) ).
thf(3927,plain,
! [SV854: $i,SV3: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( binintersect @ SV3 @ SV854 ) ) )
= $true )
| ( ( subset @ SV993 @ ( binintersect @ SV3 @ SV854 ) )
= $true )
| ( ( subset @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $false )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3738]) ).
thf(3928,plain,
! [SV8: $i,SV332: $i > $o,SV611: $i] :
( ( ( in @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) @ SV8 )
= $true )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3739]) ).
thf(3929,plain,
! [SV8: $i,SV611: $i,SV332: $i > $o] :
( ( ( ~ ( SV332 @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) ) )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3930,plain,
! [SV8: $i,SV332: $i > $o,SV611: $i] :
( ( ( ( sK62_SY1370 @ SV611 @ SV332 @ SV8 )
= SV611 )
= $false )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3740]) ).
thf(3931,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i] :
( ( ( ~ ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 ) )
= $false )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3932,plain,
! [SV858: $i,SV614: $i,SV335: $i,SV11: $i] :
( ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3741]) ).
thf(3933,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1015: $i] :
( ( ( ~ ( in @ SV1015 @ SV618 )
| ( SV859 @ SV1015 ) )
= $true )
| ( ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3742]) ).
thf(3934,plain,
! [SV342: $i,SV859: $i > $o,SV618: $i,SV19: $i] :
( ( ( ~ ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3743]) ).
thf(3935,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
| ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3743]) ).
thf(3936,plain,
! [SV20: $i,SV762: $i,SV343: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) ) )
= $false )
| ( ( ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV926 @ SV20 )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3744]) ).
thf(3937,plain,
! [SV346: $i,SV860: $i,SV24: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV24 ) )
= $true )
| ( ( in @ SV860 @ SV346 )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3745]) ).
thf(3938,plain,
! [SV24: $i,SV764: $i,SV346: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ SV346 ) )
= $true )
| ( ( in @ SV764 @ SV24 )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3746]) ).
thf(3939,plain,
! [SV347: $i > $o,SV26: $i,SV1016: $i] :
( ( ( ~ ( in @ SV1016 @ SV26 )
| ~ ( SV347 @ SV1016 ) )
= $true )
| ( ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3747]) ).
thf(3940,plain,
! [SV347: $i > $o,SV26: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ SV26 )
| ~ ( SV347 @ SV1017 ) )
= $true )
| ( ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3748]) ).
thf(3941,plain,
! [SV348: $i > $o,SV27: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV27 )
| ~ ( SV348 @ SV988 ) )
= $true )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3942,plain,
! [SV348: $i > $o,SV27: $i,SV989: $i] :
( ( ( ~ ( in @ SV989 @ SV27 )
| ~ ( SV348 @ SV989 ) )
= $true )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3750]) ).
thf(3943,plain,
! [SV34: $i,SV765: $i,SV353: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) ) )
= $false )
| ( ( ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV927 @ SV34 )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3944,plain,
! [SV768: $i,SV357: $i,SV928: $i,SV40: $i,SV994: $i] :
( ( ( ~ ( in @ SV994 @ SV40 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3752]) ).
thf(3945,plain,
! [SV770: $i,SV359: $i,SV42: $i,SV930: $i] :
( ( ( in @ SV930 @ ( binunion @ ( setminus @ SV42 @ SV359 ) @ ( setminus @ SV42 @ SV770 ) ) )
= $false )
| ( ( in @ SV930 @ ( setminus @ SV42 @ ( binintersect @ SV359 @ SV770 ) ) )
= $true )
| ( ( in @ SV930 @ SV42 )
= $false )
| ( ( in @ SV770 @ ( powerset @ SV42 ) )
= $false )
| ( ( in @ SV359 @ ( powerset @ SV42 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3946,plain,
! [SV43: $i,SV921: $i,SV360: $i > $i,SV623: $i] :
( ( ( SV623
= ( SV360 @ SV921 ) )
= $false )
| ( ( in @ SV921 @ SV43 )
= $false )
| ( ( in @ SV623
@ ( image1 @ SV43
@ ^ [SY923: $i] : ( SV360 @ SY923 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3754]) ).
thf(3947,plain,
! [SV47: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ ( sK55_SY928 @ SV47 @ SV364 ) ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3948,plain,
! [SV364: $i,SV47: $i] :
( ( ( ~ ( in @ ( sK55_SY928 @ SV47 @ SV364 ) @ SV47 ) )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3949,plain,
! [SV47: $i,SV975: $i,SV364: $i] :
( ( ( ~ ( in @ SV364 @ SV975 ) )
= $true )
| ( ( ~ ( in @ SV975 @ SV47 ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3756]) ).
thf(3950,plain,
! [SV773: $i,SV367: $i,SV52: $i,SV931: $i] :
( ( ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
= $false )
| ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
| ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV931 @ SV52 )
= $false )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(3951,plain,
! [SV370: $i,SV776: $i,SV55: $i,SV990: $i] :
( ( ( in @ SV990 @ SV55 )
= $false )
| ( ( ~ ( in @ SV990 @ SV776 )
| ( in @ SV990 @ ( setminus @ SV55 @ SV370 ) ) )
= $true )
| ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3758]) ).
thf(3952,plain,
! [SV777: $i,SV372: $i,SV57: $i,SV932: $i] :
( ( ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
= $false )
| ( ( ~ ( in @ SV932 @ SV372 ) )
= $true )
| ( ( in @ SV932 @ SV57 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3759]) ).
thf(3953,plain,
! [SV373: $i > $o,SV58: $i,SV1018: $i] :
( ( ( ~ ( in @ SV1018 @ SV58 )
| ~ ( SV373 @ SV1018 ) )
= $true )
| ( ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3760]) ).
thf(3954,plain,
! [SV373: $i > $o,SV58: $i,SV1019: $i] :
( ( ( ~ ( in @ SV1019 @ SV58 )
| ~ ( SV373 @ SV1019 ) )
= $true )
| ( ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3761]) ).
thf(3955,plain,
! [SV61: $i,SV376: $i > $o,SV862: $i] :
( ( ( ~ ( in @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) @ SV61 )
| ~ ~ ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3762]) ).
thf(3956,plain,
! [SV66: $i,SV778: $i,SV380: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV380 ) )
= $false )
| ( ( ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3957,plain,
! [SV73: $i,SV780: $i] :
( ( ( in @ ( sK45_SY168 @ SV780 @ SV73 ) @ SV73 )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3768]) ).
thf(3958,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3769]) ).
thf(3959,plain,
! [SV76: $i,SV935: $i,SV781: $i,SV386: $i] :
( ( ( in @ SV386 @ ( powerset @ SV781 ) )
= $false )
| ( ( ~ ( in @ SV935 @ SV386 )
| ( in @ SV935 @ SV781 ) )
= $true )
| ( ( in @ SV935 @ SV76 )
= $false )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3960,plain,
! [SV936: $i,SV782: $i,SV77: $i,SV387: $i] :
( ( ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
= $false )
| ( ( ~ ( in @ SV936 @ SV782 )
| ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( in @ SV936 @ SV77 )
= $false )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3961,plain,
! [SV82: $i,SV784: $i,SV392: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ SV392 ) )
= $false )
| ( ( ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV937 @ SV82 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(3962,plain,
! [SV786: $i,SV402: $i,SV938: $i,SV93: $i,SV995: $i] :
( ( ( ~ ( in @ SV995 @ SV93 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 ) )
= $true )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3773]) ).
thf(3963,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3774]) ).
thf(3964,plain,
! [SV874: $o,SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
| SV874 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3965,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3966,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(3967,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
| $true )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3968,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3969,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3780]) ).
thf(3970,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
| $false )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3781]) ).
thf(3971,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3782]) ).
thf(3972,plain,
! [SV787: $i,SV408: $i,SV939: $i,SV99: $i,SV996: $i] :
( ( ( ~ ( in @ SV996 @ SV99 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1791: $o] :
( ~ ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1792 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1792 @ SV996 ) @ SV787 )
| SY1791 )
| SY1791 ) )
= $true )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3783]) ).
thf(3973,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3784]) ).
thf(3974,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3785]) ).
thf(3975,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3786]) ).
thf(3976,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3787]) ).
thf(3977,plain,
! [SV108: $i,SV940: $i,SV788: $i,SV416: $i] :
( ( ( subset @ SV416 @ SV788 )
= $false )
| ( ( ~ ( subset @ SV416 @ SV940 )
| ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) ) )
= $true )
| ( ( in @ SV940 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3788]) ).
thf(3978,plain,
! [SV109: $i,SV417: $i,SV651: $i,SV875: $i] :
( ( ( ~ ( in @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) @ SV109 ) )
= $false )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3979,plain,
! [SV875: $i,SV651: $i,SV417: $i,SV109: $i] :
( ( ( ( ap @ SV109 @ SV417 @ SV651 @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) )
= ( ap @ SV109 @ SV417 @ SV875 @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) ) )
= $false )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3789]) ).
thf(3980,plain,
! [SV111: $i,SV653: $i,SV419: $i] :
( ( ( ! [SY1732: $i] :
~ ~ ( ~ ( in @ SY1732 @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ SY1732 ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3791]) ).
thf(3981,plain,
! [SV941: $i,SV790: $i,SV424: $i,SV117: $i,SV997: $i] :
( ( ( ~ ( in @ SV997 @ SV117 ) )
= $true )
| ( ( ~ ( in @ SV997 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SV997 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) )
= $true )
| ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3982,plain,
! [SV425: $i > $o,SV118: $i,SV998: $i] :
( ( ( ~ ( ~ ( in @ SV998 @ SV118 )
| ~ ( SV425 @ SV998 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3983,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3794]) ).
thf(3984,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3795]) ).
thf(3985,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3986,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3797]) ).
thf(3987,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ( ! [SY1701: $i] :
~ ~ ( ~ ( in @ SY1701 @ SV119 )
| ( SV876
!= ( SV426 @ SY1701 ) ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3798]) ).
thf(3988,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i] :
( ( ( ! [SY1702: $i] :
~ ~ ( ~ ( in @ SY1702 @ SV119 )
| ( SV876
!= ( SV426 @ SY1702 ) ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3799]) ).
thf(3989,plain,
! [SV121: $i,SV428: $i] :
( ( ( ~ ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 ) )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(3990,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $false )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3800]) ).
thf(3991,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $true )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $false )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3801]) ).
thf(3992,plain,
! [SV793: $i,SV440: $i,SV133: $i,SV942: $i] :
( ( ( in @ SV942 @ ( setminus @ SV133 @ ( binintersect @ SV440 @ SV793 ) ) )
= $false )
| ( ( in @ SV942 @ ( binunion @ ( setminus @ SV133 @ SV440 ) @ ( setminus @ SV133 @ SV793 ) ) )
= $true )
| ( ( in @ SV942 @ SV133 )
= $false )
| ( ( in @ SV793 @ ( powerset @ SV133 ) )
= $false )
| ( ( in @ SV440 @ ( powerset @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3993,plain,
! [SV794: $i,SV943: $i,SV441: $i,SV134: $i,SV999: $i] :
( ( ( ~ ( in @ SV999 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SV999 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3807]) ).
thf(3994,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) ) )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3995,plain,
! [SV136: $i > $o,SV795: $i] :
( ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3808]) ).
thf(3996,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) ) )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3997,plain,
! [SV138: $i > $o,SV796: $i] :
( ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3809]) ).
thf(3998,plain,
! [SV139: $i,SV444: $i,SV664: $i,SV881: $i] :
( ( ( ~ ( in @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) @ SV139 ) )
= $false )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(3999,plain,
! [SV881: $i,SV664: $i,SV444: $i,SV139: $i] :
( ( ( ( ap @ SV139 @ SV444 @ SV664 @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) )
= ( ap @ SV139 @ SV444 @ SV881 @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) ) )
= $false )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3810]) ).
thf(4000,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ~ ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
| ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3811]) ).
thf(4001,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ~ ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) )
| ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3812]) ).
thf(4002,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
| ~ ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) )
| ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3813]) ).
thf(4003,plain,
! [SV143: $i,SV448: $i,SV944: $i,SV798: $i] :
( ( ( subset @ SV798 @ SV944 )
= $false )
| ( ( subset @ ( binintersect @ SV448 @ SV798 ) @ SV944 )
= $true )
| ( ( in @ SV944 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV798 @ ( powerset @ SV143 ) )
= $false )
| ( ( in @ SV448 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3814]) ).
thf(4004,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1000: $i] :
( ( ( ~ ( in @ SV1000 @ SV451 ) )
= $true )
| ( ( SV799 @ SV1000 )
= $true )
| ( ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3815]) ).
thf(4005,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i] :
( ( ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3816]) ).
thf(4006,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3817]) ).
thf(4007,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3817]) ).
thf(4008,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3820]) ).
thf(4009,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( ~ ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 ) )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3821]) ).
thf(4010,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3821]) ).
thf(4011,plain,
! [SV882: $i,SV458: $i > $o,SV153: $i] :
( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV882 @ SV153 )
= $false )
| ( ( SV458 @ SV882 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3822]) ).
thf(4012,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3823]) ).
thf(4013,plain,
! [SV155: $i > $o,SV802: $i] :
( ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3823]) ).
thf(4014,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1001: $i] :
( ( ( ~ ( in @ SV1001 @ SV460 ) )
= $true )
| ( ( SV803 @ SV1001 )
= $true )
| ( ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3824]) ).
thf(4015,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i] :
( ( ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3825]) ).
thf(4016,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3826]) ).
thf(4017,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) )
= $false )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3826]) ).
thf(4018,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3830]) ).
thf(4019,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(4020,plain,
! [SV166: $i > $o,SV805: $i] :
( ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3831]) ).
thf(4021,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3832]) ).
thf(4022,plain,
! [SV167: $i > $o,SV806: $i] :
( ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3832]) ).
thf(4023,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( ~ ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(4024,plain,
! [SV168: $i,SV678: $i,SV887: $i,SV470: $i] :
( ( ( ! [SY1793: $i] :
( ~ ( in @ SY1793 @ SV470 )
| ~ ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SY1793 ) @ SV678 )
| ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SY1793 ) @ SV887 ) ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3833]) ).
thf(4025,plain,
! [SV170: $i,SV679: $i,SV472: $i > $i] :
( ( ( ~ ( in @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) @ SV170 )
| ( SV679
!= ( SV472 @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3834]) ).
thf(4026,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i,SV991: $i] :
( ( ( ~ ( in @ SV991 @ SV170 )
| ( SV679
!= ( SV472 @ SV991 ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3835]) ).
thf(4027,plain,
! [SV171: $i,SV473: $i,SV807: $i,SV946: $i] :
( ( ( ~ ( in @ SV946 @ SV807 ) )
= $false )
| ( ( ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV946 @ SV171 )
= $false )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3836]) ).
thf(4028,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ~ ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3838]) ).
thf(4029,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3839]) ).
thf(4030,plain,
! [SV948: $i,SV810: $i,SV479: $i,SV179: $i,SV1002: $i] :
( ( ( ~ ( in @ SV1002 @ SV179 ) )
= $true )
| ( ( ~ ( in @ SV1002 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SV1002 @ ( binunion @ SV810 @ SV948 ) ) )
= $true )
| ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(4031,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1020: $i] :
( ( ( ~ ( in @ SV1020 @ SV687 )
| ( SV892 @ SV1020 ) )
= $true )
| ( ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3841]) ).
thf(4032,plain,
! [SV482: $i,SV892: $i > $o,SV687: $i,SV183: $i] :
( ( ( ~ ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3842]) ).
thf(4033,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
| ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3842]) ).
thf(4034,plain,
! [SV812: $i,SV486: $i,SV188: $i,SV949: $i] :
( ( ( in @ SV949 @ ( setminus @ SV188 @ ( binunion @ SV486 @ SV812 ) ) )
= $false )
| ( ( in @ SV949 @ ( setminus @ SV188 @ SV486 ) )
= $true )
| ( ( in @ SV949 @ SV188 )
= $false )
| ( ( in @ SV812 @ ( powerset @ SV188 ) )
= $false )
| ( ( in @ SV486 @ ( powerset @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(4035,plain,
! [SV189: $i,SV950: $i,SV813: $i,SV487: $i > $o] :
( ( ( SV487 @ SV813 )
= $false )
| ( ( ~ ( SV487 @ SV950 )
| ( SV813 = SV950 ) )
= $true )
| ( ( in @ SV950 @ SV189 )
= $false )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(4036,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
| ~ ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) )
| ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3845]) ).
thf(4037,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) )
= $true )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(4038,plain,
! [SV814: $i,SV496: $i,SV198: $i,SV952: $i] :
( ( ( in @ SV952 @ ( binintersect @ ( setminus @ SV198 @ SV496 ) @ ( setminus @ SV198 @ SV814 ) ) )
= $false )
| ( ( in @ SV952 @ ( setminus @ SV198 @ ( binunion @ SV496 @ SV814 ) ) )
= $true )
| ( ( in @ SV952 @ SV198 )
= $false )
| ( ( in @ SV814 @ ( powerset @ SV198 ) )
= $false )
| ( ( in @ SV496 @ ( powerset @ SV198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3847]) ).
thf(4039,plain,
! [SV695: $i > $i,SV980: $i,SV499: $i,SV202: $i] :
( ( ( ~ ! [SY1783: $i] :
( ~ ( in @ SY1783 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ SY1783 ) )
= SY1783 ) ) )
= $true )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3848]) ).
thf(4040,plain,
! [SV695: $i > $i,SV953: $i,SV499: $i,SV202: $i] :
( ( ( ! [SY1752: $i] :
( ~ ( in @ SY1752 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ SY1752 ) )
= SY1752 ) ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(4041,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( in @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ SV209 )
= $true )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3850]) ).
thf(4042,plain,
! [SV209: $i,SV817: $i,SV504: $i] :
( ( ( ~ ( in @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) @ SV209 )
| ~ ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV504 )
| ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV817 ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3851]) ).
thf(4043,plain,
! [SV954: $i,SV818: $i,SV506: $i,SV211: $i,SV1004: $i] :
( ( ( ~ ( in @ SV1004 @ SV211 ) )
= $true )
| ( ( ~ ( in @ SV1004 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SV1004 @ ( binunion @ SV506 @ SV954 ) ) )
= $true )
| ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3852]) ).
thf(4044,plain,
! [SV212: $i] :
( ( ~ ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3853]) ).
thf(4045,plain,
! [SV212: $i] :
( ( ~ ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3853]) ).
thf(4046,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ~ ~ ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) )
| ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3854]) ).
thf(4047,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) ) )
= $true )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3855]) ).
thf(4048,plain,
! [SV702: $i > $i > $o,SV215: $i,SV981: $i,SV509: $i] :
( ( ( ~ ( reflwellordering @ SV509 @ SV981 ) )
= $true )
| ( ( ! [SY1784: $i] :
( ~ ( in @ SY1784 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1785: $i] :
~ ( ~ ( SV702 @ SY1784 @ SY1785 )
| ~ ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SV509 )
| ~ ( SV702 @ SY1784 @ SY1786 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ SV981 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3856]) ).
thf(4049,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i,SV982: $i] :
( ( ( ~ ( in @ SV982 @ SV509 ) )
= $true )
| ( ( ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3857]) ).
thf(4050,plain,
! [SV516: $i,SV225: $i,SV705: $i,SV983: $i,SV901: $i] :
( ( ( ~ ( in @ ( kpair @ SV901 @ SV983 ) @ SV705 ) )
= $true )
| ( ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SV983 )
= $true )
| ( ( in @ SV983 @ SV516 )
= $false )
| ( ( in @ SV901 @ SV225 )
= $false )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3858]) ).
thf(4051,plain,
! [SV226: $i] :
( ( ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(4052,plain,
! [SV226: $i] :
( ( ( ~ ( in @ ( sK51_SY601 @ SV226 ) @ SV226 ) )
= $false )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3859]) ).
thf(4053,plain,
! [SV226: $i,SV992: $i] :
( ( ( in @ SV992 @ omega )
= $false )
| ( ( in @ SV992 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( setadjoin @ ( sK51_SY601 @ SV226 ) @ ( sK51_SY601 @ SV226 ) ) @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4054,plain,
! [SV519: $i,SV230: $i] :
( ( ( in @ ( sK70_SY1213 @ SV230 @ SV519 ) @ SV519 )
= $true )
| ( ( SV230 = SV519 )
= $true )
| ( ( in @ ( sK19_SY1212 @ SV519 @ SV230 ) @ SV230 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3861]) ).
thf(4055,plain,
! [SV232: $i,SV521: $i > $o,SV902: $i] :
( ( ( ~ ( in @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) @ SV232 )
| ~ ~ ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(4056,plain,
! [SV822: $i,SV523: $i,SV956: $i,SV234: $i,SV1006: $i] :
( ( ( ~ ( in @ SV1006 @ SV234 ) )
= $true )
| ( ( ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1799 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1799 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) )
= $true )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3865]) ).
thf(4057,plain,
! [SV534: $i > $o,SV245: $i,SV1007: $i] :
( ( ( ~ ( ~ ( in @ SV1007 @ SV245 )
| ~ ( SV534 @ SV1007 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(4058,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3870]) ).
thf(4059,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3871]) ).
thf(4060,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4061,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3873]) ).
thf(4062,plain,
! [SV538: $i,SV250: $i,SV716: $i,SV984: $i,SV907: $i] :
( ( ( ~ ( in @ ( kpair @ SV907 @ SV984 ) @ SV716 ) )
= $true )
| ( ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SV984 )
= $true )
| ( ( in @ SV984 @ SV538 )
= $false )
| ( ( in @ SV907 @ SV250 )
= $false )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3874]) ).
thf(4063,plain,
! [SV251: $i,SV539: $i,SV958: $i,SV824: $i] :
( ( ( in @ ( kpair @ SV824 @ SV958 ) @ SV539 )
= $false )
| ( ( in @ ( kpair @ SV958 @ SV824 ) @ ( breln1invset @ SV251 @ SV539 ) )
= $true )
| ( ( in @ SV958 @ SV251 )
= $false )
| ( ( in @ SV824 @ SV251 )
= $false )
| ( ( breln1 @ SV251 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3875]) ).
thf(4064,plain,
! [SV540: $i,SV252: $i,SV825: $i,SV959: $i] :
( ( ( in @ ( kpair @ SV959 @ SV825 ) @ ( breln1invset @ SV252 @ SV540 ) )
= $false )
| ( ( in @ ( kpair @ SV825 @ SV959 ) @ SV540 )
= $true )
| ( ( in @ SV959 @ SV252 )
= $false )
| ( ( in @ SV825 @ SV252 )
= $false )
| ( ( breln1 @ SV252 @ SV540 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3876]) ).
thf(4065,plain,
! [SV826: $i,SV545: $i,SV960: $i,SV255: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV255 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1800: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SY1800 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SY1800 )
| SY1800 ) )
= $true )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(4066,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( ~ ~ ( ~ ( SV260 @ SV1022 )
| ~ ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3878]) ).
thf(4067,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( ~ ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3879]) ).
thf(4068,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3880]) ).
thf(4069,plain,
! [SV263: $i,SV828: $i,SV962: $i,SV552: $i] :
( ( ( subset @ SV552 @ SV962 )
= $false )
| ( ( subset @ ( binintersect @ SV552 @ SV828 ) @ SV962 )
= $true )
| ( ( in @ SV962 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV828 @ ( powerset @ SV263 ) )
= $false )
| ( ( in @ SV552 @ ( powerset @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3881]) ).
thf(4070,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3882]) ).
thf(4071,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
| ~ ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
| ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3883]) ).
thf(4072,plain,
! [SV269: $i,SV909: $i,SV558: $i > $o] :
( ( ( SV558 @ SV909 )
= $true )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( ~ ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3884]) ).
thf(4073,plain,
! [SV831: $i,SV560: $i,SV271: $i,SV963: $i] :
( ( ( in @ SV963 @ ( setminus @ SV271 @ ( binunion @ SV560 @ SV831 ) ) )
= $false )
| ( ( in @ SV963 @ ( setminus @ SV271 @ SV831 ) )
= $true )
| ( ( in @ SV963 @ SV271 )
= $false )
| ( ( in @ SV831 @ ( powerset @ SV271 ) )
= $false )
| ( ( in @ SV560 @ ( powerset @ SV271 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3885]) ).
thf(4074,plain,
! [SV832: $i,SV562: $i,SV964: $i,SV274: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ SV274 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV964 @ SV1009 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SV1009 ) @ ( binunion @ SV562 @ SV832 ) ) )
= $true )
| ( ( in @ SV964 @ SV274 )
= $false )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3886]) ).
thf(4075,plain,
! [SV569: $i,SV911: $i > $o,SV833: $i > $o,SV283: $i] :
( ( ( ~ ( in @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3888]) ).
thf(4076,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
!= ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ~ ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
| ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3888]) ).
thf(4077,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3889]) ).
thf(4078,plain,
! [SV284: $i > $o,SV834: $i] :
( ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3889]) ).
thf(4079,plain,
! [SV835: $i,SV570: $i,SV285: $i,SV965: $i] :
( ( ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) )
= $false )
| ( ( ~ ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) ) )
= $true )
| ( ( in @ SV965 @ SV285 )
= $false )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3890]) ).
thf(4080,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| SV759 )
= $false )
| ( SV759 = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(4081,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( SV759 = $true )
| ( SV759 = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(4082,plain,
! [SV572: $i,SV287: $i,SV729: $i,SV759: $o] :
( ( SV759 = $false )
| ( SV759 = $true )
| ( SV759 = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3892]) ).
thf(4083,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3893]) ).
thf(4084,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3894]) ).
thf(4085,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3894]) ).
thf(4086,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(4087,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3896]) ).
thf(4088,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3896]) ).
thf(4089,plain,
! [SV573: $i,SV836: $i,SV966: $i,SV288: $i,SV1010: $i] :
( ( ( ~ ( in @ SV1010 @ SV288 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV966 @ SV1010 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SV1010 ) @ ( binunion @ SV573 @ SV836 ) ) )
= $true )
| ( ( in @ SV966 @ SV288 )
= $false )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3897]) ).
thf(4090,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV296 )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3901]) ).
thf(4091,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( ~ ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV580 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3902]) ).
thf(4092,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV838 )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3902]) ).
thf(4093,plain,
! [SV839: $i,SV581: $i,SV967: $i,SV297: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ SV297 ) )
= $true )
| ( ( ~ ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) ) )
= $true )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3903]) ).
thf(4094,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( ~ ( in @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SV298 ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(4095,plain,
! [SV298: $i,SV734: $i,SV915: $i,SV582: $i] :
( ( ( ! [SY1801: $i] :
( ~ ( in @ SY1801 @ SV582 )
| ~ ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SY1801 ) @ SV734 )
| ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SY1801 ) @ SV915 ) ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3904]) ).
thf(4096,plain,
! [SV840: $i,SV583: $i,SV299: $i,SV968: $i] :
( ( ( in @ SV968 @ ( setminus @ SV299 @ ( binunion @ SV583 @ SV840 ) ) )
= $false )
| ( ( in @ SV968 @ ( binintersect @ ( setminus @ SV299 @ SV583 ) @ ( setminus @ SV299 @ SV840 ) ) )
= $true )
| ( ( in @ SV968 @ SV299 )
= $false )
| ( ( in @ SV840 @ ( powerset @ SV299 ) )
= $false )
| ( ( in @ SV583 @ ( powerset @ SV299 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3905]) ).
thf(4097,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3906]) ).
thf(4098,plain,
! [SV300: $i > $o,SV841: $i] :
( ( ( SV841
= ( sK88_SY1674 @ SV841 @ SV300 ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3906]) ).
thf(4099,plain,
! [SV842: $i,SV584: $i,SV301: $i,SV969: $i] :
( ( ( in @ SV969 @ ( setminus @ SV301 @ SV584 ) )
= $false )
| ( ( in @ SV969 @ ( setminus @ SV301 @ ( binintersect @ SV584 @ SV842 ) ) )
= $true )
| ( ( in @ SV969 @ SV301 )
= $false )
| ( ( in @ SV842 @ ( powerset @ SV301 ) )
= $false )
| ( ( in @ SV584 @ ( powerset @ SV301 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3907]) ).
thf(4100,plain,
! [SV843: $i,SV585: $i,SV302: $i,SV970: $i] :
( ( ( in @ SV970 @ ( setminus @ SV302 @ ( binunion @ SV585 @ SV843 ) ) )
= $false )
| ( ( in @ SV970 @ ( setminus @ SV302 @ SV585 ) )
= $true )
| ( ( in @ SV970 @ SV302 )
= $false )
| ( ( in @ SV843 @ ( powerset @ SV302 ) )
= $false )
| ( ( in @ SV585 @ ( powerset @ SV302 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3908]) ).
thf(4101,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| SV916 )
= $false )
| ( SV916 = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4102,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( SV916 = $true )
| ( SV916 = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3910]) ).
thf(4103,plain,
! [SV591: $i,SV309: $i,SV736: $i,SV916: $o] :
( ( SV916 = $false )
| ( SV916 = $true )
| ( SV916 = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3910]) ).
thf(4104,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3911]) ).
thf(4105,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4106,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4107,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3913]) ).
thf(4108,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4109,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3914]) ).
thf(4110,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV310 )
= $true )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3915]) ).
thf(4111,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( ~ ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV592 ) )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4112,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV847 )
= $false )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3916]) ).
thf(4113,plain,
! [SV315: $i,SV972: $o,SV848: $i,SV597: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3918]) ).
thf(4114,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV986 @ SV597 )
| $true )
| ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3919]) ).
thf(4115,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV987 @ SV597 )
| $false )
| ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3920]) ).
thf(4116,plain,
! [SV973: $i,SV849: $i,SV599: $i,SV317: $i,SV1012: $i] :
( ( ( ~ ( in @ SV1012 @ ( powerset @ SV317 ) ) )
= $true )
| ( ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SV1012 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SV1012 ) ) ) )
= $true )
| ( ( in @ SV973 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4117,plain,
! [SV318: $i,SV974: $i,SV850: $i,SV600: $i] :
( ( ( subset @ SV600 @ SV850 )
= $false )
| ( ( ~ ~ ( in @ SV974 @ SV850 )
| ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3922]) ).
thf(4118,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( ~ ( SV323 @ ( sK89_SY1684 @ SV852 @ SV323 ) ) )
= $false )
| ( ( SV323 @ SV852 )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3923]) ).
thf(4119,plain,
! [SV323: $i > $o,SV852: $i] :
( ( ( SV852
= ( sK89_SY1684 @ SV852 @ SV323 ) )
= $false )
| ( ( SV323 @ SV852 )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3923]) ).
thf(4120,plain,
! [SV920: $i,SV3: $i,SV1023: $i] :
( ( ( ~ ( in @ SV1023 @ ( binintersect @ SV3 @ SV920 ) )
| ( subset @ SV1023 @ ( binintersect @ SV3 @ SV920 ) ) )
= $true )
| ( ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3924]) ).
thf(4121,plain,
! [SV920: $i,SV3: $i,SV1013: $i] :
( ( ( ~ ( in @ SV1013 @ ( binintersect @ SV3 @ SV920 ) ) )
= $true )
| ( ( subset @ SV1013 @ ( binintersect @ SV3 @ SV920 ) )
= $true )
| ( ( subset @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $false )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3925]) ).
thf(4122,plain,
! [SV854: $i,SV3: $i,SV1014: $i] :
( ( ( ~ ( in @ SV1014 @ ( binintersect @ SV3 @ SV854 ) ) )
= $true )
| ( ( subset @ SV1014 @ ( binintersect @ SV3 @ SV854 ) )
= $true )
| ( ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3926]) ).
thf(4123,plain,
! [SV854: $i,SV3: $i,SV993: $i] :
( ( ( in @ SV993 @ ( binintersect @ SV3 @ SV854 ) )
= $false )
| ( ( subset @ SV993 @ ( binintersect @ SV3 @ SV854 ) )
= $true )
| ( ( subset @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $false )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3927]) ).
thf(4124,plain,
! [SV8: $i,SV611: $i,SV332: $i > $o] :
( ( ( SV332 @ ( sK62_SY1370 @ SV611 @ SV332 @ SV8 ) )
= $true )
| ( ( ex1 @ SV8
@ ^ [SY871: $i] : ( SV332 @ SY871 ) )
= $true )
| ( ( SV332 @ SV611 )
= $false )
| ( ( in @ SV611 @ SV8 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3929]) ).
thf(4125,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i] :
( ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( ! [SY1688: $i] :
( ~ ( in @ SY1688 @ SV11 )
| ! [SY1689: $i] :
( ~ ( in @ SY1689 @ SV335 )
| ~ ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV858 )
| ( in @ ( kpair @ SY1688 @ SY1689 ) @ SV614 ) ) ) )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3931]) ).
thf(4126,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV11 )
| ! [SY1807: $i] :
( ~ ( in @ SY1807 @ SV335 )
| ~ ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV614 ) ) )
= $true )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3932]) ).
thf(4127,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1015: $i] :
( ( ( ~ ( in @ SV1015 @ SV618 ) )
= $true )
| ( ( SV859 @ SV1015 )
= $true )
| ( ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3933]) ).
thf(4128,plain,
! [SV342: $i,SV859: $i > $o,SV618: $i,SV19: $i] :
( ( ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 )
= $true )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3934]) ).
thf(4129,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4130,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) )
= $false )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3935]) ).
thf(4131,plain,
! [SV20: $i,SV762: $i,SV343: $i,SV926: $i] :
( ( ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) )
= $true )
| ( ( ~ ( in @ SV926 @ SV762 ) )
= $true )
| ( ( in @ SV926 @ SV20 )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3936]) ).
thf(4132,plain,
! [SV346: $i,SV860: $i,SV24: $i,SV764: $i] :
( ( ( in @ SV764 @ SV24 )
= $false )
| ( ( in @ SV860 @ SV346 )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(4133,plain,
! [SV24: $i,SV764: $i,SV346: $i,SV860: $i] :
( ( ( in @ SV860 @ SV346 )
= $false )
| ( ( in @ SV764 @ SV24 )
= $true )
| ( ( SV764 = SV860 )
= $false )
| ( ( SV24 = SV346 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4134,plain,
! [SV347: $i > $o,SV26: $i,SV1016: $i] :
( ( ( ~ ( in @ SV1016 @ SV26 ) )
= $true )
| ( ( ~ ( SV347 @ SV1016 ) )
= $true )
| ( ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3939]) ).
thf(4135,plain,
! [SV347: $i > $o,SV26: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ SV26 ) )
= $true )
| ( ( ~ ( SV347 @ SV1017 ) )
= $true )
| ( ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3940]) ).
thf(4136,plain,
! [SV348: $i > $o,SV27: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV27 ) )
= $true )
| ( ( ~ ( SV348 @ SV988 ) )
= $true )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4137,plain,
! [SV348: $i > $o,SV27: $i,SV989: $i] :
( ( ( ~ ( in @ SV989 @ SV27 ) )
= $true )
| ( ( ~ ( SV348 @ SV989 ) )
= $true )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3942]) ).
thf(4138,plain,
! [SV34: $i,SV765: $i,SV353: $i,SV927: $i] :
( ( ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) )
= $true )
| ( ( ~ ( in @ SV927 @ SV353 ) )
= $true )
| ( ( in @ SV927 @ SV34 )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3943]) ).
thf(4139,plain,
! [SV768: $i,SV357: $i,SV928: $i,SV40: $i,SV994: $i] :
( ( ( in @ SV994 @ SV40 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
| ~ ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3944]) ).
thf(4140,plain,
! [SV47: $i,SV364: $i] :
( ( ( in @ SV364 @ ( sK55_SY928 @ SV47 @ SV364 ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3947]) ).
thf(4141,plain,
! [SV364: $i,SV47: $i] :
( ( ( in @ ( sK55_SY928 @ SV47 @ SV364 ) @ SV47 )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3948]) ).
thf(4142,plain,
! [SV47: $i,SV975: $i,SV364: $i] :
( ( ( in @ SV364 @ SV975 )
= $false )
| ( ( ~ ( in @ SV975 @ SV47 ) )
= $true )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3949]) ).
thf(4143,plain,
! [SV367: $i,SV773: $i,SV52: $i,SV931: $i] :
( ( ( ~ ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) ) )
= $true )
| ( ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) )
= $true )
| ( ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
= $false )
| ( ( in @ SV931 @ SV52 )
= $false )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3950]) ).
thf(4144,plain,
! [SV370: $i,SV55: $i,SV776: $i,SV990: $i] :
( ( ( ~ ( in @ SV990 @ SV776 ) )
= $true )
| ( ( in @ SV990 @ ( setminus @ SV55 @ SV370 ) )
= $true )
| ( ( in @ SV990 @ SV55 )
= $false )
| ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3951]) ).
thf(4145,plain,
! [SV777: $i,SV57: $i,SV372: $i,SV932: $i] :
( ( ( in @ SV932 @ SV372 )
= $false )
| ( ( in @ SV932 @ ( setminus @ SV57 @ ( binunion @ SV372 @ SV777 ) ) )
= $false )
| ( ( in @ SV932 @ SV57 )
= $false )
| ( ( in @ SV777 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV372 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4146,plain,
! [SV373: $i > $o,SV58: $i,SV1018: $i] :
( ( ( ~ ( in @ SV1018 @ SV58 ) )
= $true )
| ( ( ~ ( SV373 @ SV1018 ) )
= $true )
| ( ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3953]) ).
thf(4147,plain,
! [SV373: $i > $o,SV58: $i,SV1019: $i] :
( ( ( ~ ( in @ SV1019 @ SV58 ) )
= $true )
| ( ( ~ ( SV373 @ SV1019 ) )
= $true )
| ( ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3954]) ).
thf(4148,plain,
! [SV61: $i,SV376: $i > $o,SV862: $i] :
( ( ( ~ ( in @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) @ SV61 ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3955]) ).
thf(4149,plain,
! [SV61: $i,SV862: $i,SV376: $i > $o] :
( ( ( ~ ~ ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3955]) ).
thf(4150,plain,
! [SV66: $i,SV778: $i,SV380: $i,SV934: $i] :
( ( ( in @ SV934 @ SV380 )
= $true )
| ( ( ~ ~ ( in @ SV934 @ SV778 )
| ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3956]) ).
thf(4151,plain,
! [SV73: $i,SV780: $i] :
( ( ( ~ ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4152,plain,
! [SV76: $i,SV781: $i,SV386: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV386 ) )
= $true )
| ( ( in @ SV935 @ SV781 )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV781 ) )
= $false )
| ( ( in @ SV935 @ SV76 )
= $false )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3959]) ).
thf(4153,plain,
! [SV77: $i,SV387: $i,SV782: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV782 ) )
= $true )
| ( ( ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
= $false )
| ( ( in @ SV936 @ SV77 )
= $false )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3960]) ).
thf(4154,plain,
! [SV82: $i,SV784: $i,SV392: $i,SV937: $i] :
( ( ( in @ SV937 @ SV392 )
= $true )
| ( ( ~ ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) ) )
= $true )
| ( ( in @ SV937 @ SV82 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3961]) ).
thf(4155,plain,
! [SV786: $i,SV402: $i,SV938: $i,SV93: $i,SV995: $i] :
( ( ( in @ SV995 @ SV93 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 ) )
= $true )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4156,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3963]) ).
thf(4157,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3963]) ).
thf(4158,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 ) )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3964]) ).
thf(4159,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3965]) ).
thf(4160,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3965]) ).
thf(4161,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4162,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3966]) ).
thf(4163,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4164,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3968]) ).
thf(4165,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3968]) ).
thf(4166,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4167,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4168,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3970]) ).
thf(4169,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4170,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3971]) ).
thf(4171,plain,
! [SV787: $i,SV408: $i,SV939: $i,SV99: $i,SV996: $i] :
( ( ( in @ SV996 @ SV99 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
| ! [SY1791: $o] :
( ~ ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1792 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1792 @ SV996 ) @ SV787 )
| SY1791 )
| SY1791 ) )
= $true )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3972]) ).
thf(4172,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3973]) ).
thf(4173,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3974]) ).
thf(4174,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
| ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3975]) ).
thf(4175,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3976]) ).
thf(4176,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3976]) ).
thf(4177,plain,
! [SV108: $i,SV788: $i,SV940: $i,SV416: $i] :
( ( ( ~ ( subset @ SV416 @ SV940 ) )
= $true )
| ( ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) )
= $true )
| ( ( subset @ SV416 @ SV788 )
= $false )
| ( ( in @ SV940 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3977]) ).
thf(4178,plain,
! [SV109: $i,SV417: $i,SV651: $i,SV875: $i] :
( ( ( in @ ( sK77_SY1700 @ SV875 @ SV651 @ SV417 @ SV109 ) @ SV109 )
= $true )
| ( ( SV651 = SV875 )
= $true )
| ( ( in @ SV875 @ ( funcSet @ SV109 @ SV417 ) )
= $false )
| ( ( in @ SV651 @ ( funcSet @ SV109 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3978]) ).
thf(4179,plain,
! [SV419: $i,SV653: $i,SV111: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3980]) ).
thf(4180,plain,
! [SV941: $i,SV790: $i,SV424: $i,SV117: $i,SV997: $i] :
( ( ( in @ SV997 @ SV117 )
= $false )
| ( ( ~ ( in @ SV997 @ ( binintersect @ SV424 @ SV790 ) )
| ( in @ SV997 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) ) )
= $true )
| ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3981]) ).
thf(4181,plain,
! [SV425: $i > $o,SV118: $i,SV998: $i] :
( ( ( ~ ( in @ SV998 @ SV118 )
| ~ ( SV425 @ SV998 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3982]) ).
thf(4182,plain,
! [SV425: $i > $o,SV118: $i,SV1025: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1025 @ SV118 )
| ~ ( SV425 @ SV1025 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3983]) ).
thf(4183,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3984]) ).
thf(4184,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ~ ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3985]) ).
thf(4185,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3986]) ).
thf(4186,plain,
! [SV119: $i,SV876: $i,SV426: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) @ SV119 )
| ( SV876
!= ( SV426 @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) ) ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3987]) ).
thf(4187,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i,SV1026: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1026 @ SV119 )
| ( SV876
!= ( SV426 @ SV1026 ) ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3988]) ).
thf(4188,plain,
! [SV121: $i,SV428: $i] :
( ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV428 )
= $true )
| ( ( in @ ( sK15_SY1043 @ SV428 @ SV121 ) @ SV121 )
= $true )
| ( ( SV121 = SV428 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3989]) ).
thf(4189,plain,
! [SV794: $i,SV943: $i,SV441: $i,SV134: $i,SV999: $i] :
( ( ( in @ SV999 @ ( powerset @ SV134 ) )
= $false )
| ( ( ~ ( subset @ SV441 @ SV943 )
| ~ ( subset @ SV794 @ SV999 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) ) )
= $true )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4190,plain,
! [SV795: $i,SV136: $i > $o] :
( ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( ! [SY337: $i,SY338: $i] :
( ~ ( SV136 @ SY337 )
| ~ ( SV136 @ SY338 )
| ( SY337 = SY338 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3994]) ).
thf(4191,plain,
! [SV795: $i,SV1027: $i,SV136: $i > $o] :
( ( ( ! [SY1808: $i] :
( ~ ( SV136 @ SV1027 )
| ~ ( SV136 @ SY1808 )
| ( SV1027 = SY1808 ) ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3995]) ).
thf(4192,plain,
! [SV796: $i,SV138: $i > $o] :
( ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( ! [SY342: $i,SY343: $i] :
( ~ ( SV138 @ SY342 )
| ~ ( SV138 @ SY343 )
| ( SY342 = SY343 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3996]) ).
thf(4193,plain,
! [SV796: $i,SV1028: $i,SV138: $i > $o] :
( ( ( ! [SY1809: $i] :
( ~ ( SV138 @ SV1028 )
| ~ ( SV138 @ SY1809 )
| ( SV1028 = SY1809 ) ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3997]) ).
thf(4194,plain,
! [SV139: $i,SV444: $i,SV664: $i,SV881: $i] :
( ( ( in @ ( sK80_SY1707 @ SV881 @ SV664 @ SV444 @ SV139 ) @ SV139 )
= $true )
| ( ( SV664 = SV881 )
= $true )
| ( ( func @ SV139 @ SV444 @ SV881 )
= $false )
| ( ( func @ SV139 @ SV444 @ SV664 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3998]) ).
thf(4195,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ( ~ ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) ) )
= $true )
| ( ( ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4000]) ).
thf(4196,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ( ~ ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4001]) ).
thf(4197,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
| ~ ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) )
| ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4002]) ).
thf(4198,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1000: $i] :
( ( ( in @ SV1000 @ SV451 )
= $false )
| ( ( SV799 @ SV1000 )
= $true )
| ( ( in @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4004]) ).
thf(4199,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV451 )
| ( SV799 @ SV1029 ) )
= $true )
| ( ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4005]) ).
thf(4200,plain,
! [SV146: $i,SV451: $i,SV799: $i > $o] :
( ( ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV451 )
| ( SV799 @ SY1617 ) ) )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4006]) ).
thf(4201,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1030: $i] :
( ( ( ~ ( in @ SV1030 @ SV451 )
| ( SV799 @ SV1030 ) )
= $true )
| ( ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) )
= $false )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4007]) ).
thf(4202,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4203,plain,
! [SV149: $i,SV454: $i,SV800: $i] :
( ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) )
| ( SV454 = SV800 ) )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4009]) ).
thf(4204,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4010]) ).
thf(4205,plain,
! [SV882: $i,SV458: $i > $o,SV153: $i] :
( ( ( ( dsetconstr @ SV153
@ ^ [SY1100: $i] : ( SV458 @ SY1100 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV882 @ SV153 )
= $false )
| ( ( SV458 @ SV882 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4011]) ).
thf(4206,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( ~ ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4012]) ).
thf(4207,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4013]) ).
thf(4208,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1001: $i] :
( ( ( in @ SV1001 @ SV460 )
= $false )
| ( ( SV803 @ SV1001 )
= $true )
| ( ( in @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4014]) ).
thf(4209,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1031: $i] :
( ( ( ~ ( in @ SV1031 @ SV460 )
| ( SV803 @ SV1031 ) )
= $true )
| ( ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4015]) ).
thf(4210,plain,
! [SV156: $i,SV460: $i,SV803: $i > $o] :
( ( ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
= $true )
| ( ( ! [SY1624: $i] :
( ~ ( in @ SY1624 @ SV460 )
| ( SV803 @ SY1624 ) ) )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4016]) ).
thf(4211,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ SV460 )
| ( SV803 @ SV1032 ) )
= $true )
| ( ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) )
= $false )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4017]) ).
thf(4212,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $false )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4213,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( ~ ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4019]) ).
thf(4214,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $false )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4020]) ).
thf(4215,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( ~ ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4021]) ).
thf(4216,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4022]) ).
thf(4217,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4023]) ).
thf(4218,plain,
! [SV470: $i,SV887: $i,SV678: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
| ~ ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
| ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4024]) ).
thf(4219,plain,
! [SV170: $i,SV679: $i,SV472: $i > $i] :
( ( ( ~ ( in @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) @ SV170 ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4025]) ).
thf(4220,plain,
! [SV170: $i,SV472: $i > $i,SV679: $i] :
( ( ( SV679
!= ( SV472 @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) ) )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4025]) ).
thf(4221,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i,SV991: $i] :
( ( ( ~ ( in @ SV991 @ SV170 ) )
= $true )
| ( ( SV679
!= ( SV472 @ SV991 ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4026]) ).
thf(4222,plain,
! [SV171: $i,SV473: $i,SV807: $i,SV946: $i] :
( ( ( in @ SV946 @ SV807 )
= $true )
| ( ( ~ ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) ) )
= $true )
| ( ( in @ SV946 @ SV171 )
= $false )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4027]) ).
thf(4223,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
| ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4028]) ).
thf(4224,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4225,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4029]) ).
thf(4226,plain,
! [SV948: $i,SV810: $i,SV479: $i,SV179: $i,SV1002: $i] :
( ( ( in @ SV1002 @ SV179 )
= $false )
| ( ( ~ ( in @ SV1002 @ ( binintersect @ SV479 @ SV810 ) )
| ( in @ SV1002 @ ( binunion @ SV810 @ SV948 ) ) )
= $true )
| ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4227,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1020: $i] :
( ( ( ~ ( in @ SV1020 @ SV687 ) )
= $true )
| ( ( SV892 @ SV1020 )
= $true )
| ( ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4031]) ).
thf(4228,plain,
! [SV482: $i,SV892: $i > $o,SV687: $i,SV183: $i] :
( ( ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4032]) ).
thf(4229,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4230,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) )
= $false )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4231,plain,
! [SV189: $i,SV813: $i,SV950: $i,SV487: $i > $o] :
( ( ( ~ ( SV487 @ SV950 ) )
= $true )
| ( ( SV813 = SV950 )
= $true )
| ( ( SV487 @ SV813 )
= $false )
| ( ( in @ SV950 @ SV189 )
= $false )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4035]) ).
thf(4232,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4036]) ).
thf(4233,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) )
| ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4036]) ).
thf(4234,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ! [SY1751: $i] :
( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SY1751 )
| ( SV951 = SY1751 ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4037]) ).
thf(4235,plain,
! [SV695: $i > $i,SV980: $i,SV499: $i,SV202: $i] :
( ( ( ! [SY1783: $i] :
( ~ ( in @ SY1783 @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ SY1783 ) )
= SY1783 ) ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4039]) ).
thf(4236,plain,
! [SV202: $i,SV499: $i,SV953: $i,SV695: $i > $i] :
( ( ( ~ ( in @ ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) ) )
= ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4040]) ).
thf(4237,plain,
! [SV209: $i,SV817: $i,SV504: $i] :
( ( ( ~ ( in @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) @ SV209 ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4238,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV504 )
| ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV817 ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4042]) ).
thf(4239,plain,
! [SV954: $i,SV818: $i,SV506: $i,SV211: $i,SV1004: $i] :
( ( ( in @ SV1004 @ SV211 )
= $false )
| ( ( ~ ( in @ SV1004 @ ( binintersect @ SV506 @ SV818 ) )
| ( in @ SV1004 @ ( binunion @ SV506 @ SV954 ) ) )
= $true )
| ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4043]) ).
thf(4240,plain,
! [SV212: $i] :
( ( ! [SY1489: $i] :
( ~ ( in @ SY1489 @ ( sK4_SY557 @ SV212 ) )
| ! [SY559: $i] :
( ~ ( in @ SY559 @ SY1489 )
| ( in @ SY559 @ SV212 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4044]) ).
thf(4241,plain,
! [SV212: $i] :
( ( ! [SY1491: $i,SY1492: $i] :
( ~ ~ ( ~ ( in @ SY1491 @ SV212 )
| ~ ( in @ SY1492 @ SV212 ) )
| ~ ! [SY1493: $i] :
( ~ ( in @ SY1493 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SY1491 @ SY1493 )
| ( in @ SY1492 @ SY1493 ) )
| ~ ( ~ ( in @ SY1492 @ SY1493 )
| ( in @ SY1491 @ SY1493 ) ) ) )
| ( SY1491 = SY1492 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[4045]) ).
thf(4242,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) ) )
= $true )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4046]) ).
thf(4243,plain,
! [SV212: $i,SV955: $i] :
( ( ( ! [SY1754: $i] :
( ~ ( in @ SY1754 @ SV955 )
| ( in @ SY1754 @ SV212 ) ) )
= $false )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4047]) ).
thf(4244,plain,
! [SV702: $i > $i > $o,SV215: $i,SV981: $i,SV509: $i] :
( ( ( reflwellordering @ SV509 @ SV981 )
= $false )
| ( ( ! [SY1784: $i] :
( ~ ( in @ SY1784 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1785: $i] :
~ ( ~ ( SV702 @ SY1784 @ SY1785 )
| ~ ! [SY1786: $i] :
( ~ ( in @ SY1786 @ SV509 )
| ~ ( SV702 @ SY1784 @ SY1786 )
| ( in @ ( kpair @ SY1785 @ SY1786 ) @ SV981 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4048]) ).
thf(4245,plain,
! [SV215: $i,SV702: $i > $i > $o,SV509: $i,SV982: $i] :
( ( ( in @ SV982 @ SV509 )
= $false )
| ( ( ~ ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 ) )
= $true )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4049]) ).
thf(4246,plain,
! [SV516: $i,SV225: $i,SV705: $i,SV983: $i,SV901: $i] :
( ( ( in @ ( kpair @ SV901 @ SV983 ) @ SV705 )
= $false )
| ( ( ( ap @ SV225 @ SV516 @ SV705 @ SV901 )
= SV983 )
= $true )
| ( ( in @ SV983 @ SV516 )
= $false )
| ( ( in @ SV901 @ SV225 )
= $false )
| ( ( func @ SV225 @ SV516 @ SV705 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4050]) ).
thf(4247,plain,
! [SV226: $i] :
( ( ( in @ ( sK51_SY601 @ SV226 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4051]) ).
thf(4248,plain,
! [SV226: $i] :
( ( ( in @ ( sK51_SY601 @ SV226 ) @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ omega )
| ( in @ SY602 @ SV226 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4052]) ).
thf(4249,plain,
! [SV232: $i,SV521: $i > $o,SV902: $i] :
( ( ( ~ ( in @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) @ SV232 ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4055]) ).
thf(4250,plain,
! [SV232: $i,SV902: $i,SV521: $i > $o] :
( ( ( ~ ~ ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4055]) ).
thf(4251,plain,
! [SV822: $i,SV523: $i,SV956: $i,SV234: $i,SV1006: $i] :
( ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( ! [SY1799: $i] :
( ~ ( in @ SY1799 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SY1799 ) @ SV523 )
| ~ ( in @ ( kpair @ SY1799 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) ) )
= $true )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4252,plain,
! [SV534: $i > $o,SV245: $i,SV1007: $i] :
( ( ( ~ ( in @ SV1007 @ SV245 )
| ~ ( SV534 @ SV1007 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4057]) ).
thf(4253,plain,
! [SV534: $i > $o,SV245: $i,SV1033: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1033 @ SV245 )
| ~ ( SV534 @ SV1033 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4058]) ).
thf(4254,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4059]) ).
thf(4255,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ~ ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4060]) ).
thf(4256,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4061]) ).
thf(4257,plain,
! [SV538: $i,SV250: $i,SV716: $i,SV984: $i,SV907: $i] :
( ( ( in @ ( kpair @ SV907 @ SV984 ) @ SV716 )
= $false )
| ( ( ( ap @ SV250 @ SV538 @ SV716 @ SV907 )
= SV984 )
= $true )
| ( ( in @ SV984 @ SV538 )
= $false )
| ( ( in @ SV907 @ SV250 )
= $false )
| ( ( in @ SV716 @ ( funcSet @ SV250 @ SV538 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4062]) ).
thf(4258,plain,
! [SV826: $i,SV545: $i,SV960: $i,SV255: $i,SV1008: $i] :
( ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
| ! [SY1800: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SY1800 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SY1800 )
| SY1800 ) )
= $true )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4065]) ).
thf(4259,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ SV1022 )
| ~ ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4066]) ).
thf(4260,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
| ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4261,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4068]) ).
thf(4262,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4068]) ).
thf(4263,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4070]) ).
thf(4264,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4071]) ).
thf(4265,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
| ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4071]) ).
thf(4266,plain,
! [SV909: $i,SV558: $i > $o,SV269: $i] :
( ( ( ! [SY1285: $i] :
( ~ ( in @ SY1285 @ SV269 )
| ( SV558 @ SY1285 ) ) )
= $false )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( SV558 @ SV909 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4072]) ).
thf(4267,plain,
! [SV832: $i,SV562: $i,SV964: $i,SV274: $i,SV1009: $i] :
( ( ( in @ SV1009 @ SV274 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV964 @ SV1009 ) @ SV562 )
| ( in @ ( kpair @ SV964 @ SV1009 ) @ ( binunion @ SV562 @ SV832 ) ) )
= $true )
| ( ( in @ SV964 @ SV274 )
= $false )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4074]) ).
thf(4268,plain,
! [SV569: $i,SV911: $i > $o,SV833: $i > $o,SV283: $i] :
( ( ( in @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) @ SV569 )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4075]) ).
thf(4269,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
!= ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4076]) ).
thf(4270,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
| ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4076]) ).
thf(4271,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( ~ ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4077]) ).
thf(4272,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4273,plain,
! [SV285: $i,SV835: $i,SV570: $i,SV965: $i] :
( ( ( in @ SV965 @ ( binintersect @ SV570 @ SV835 ) )
= $false )
| ( ( in @ SV965 @ ( setminus @ SV285 @ SV570 ) )
= $false )
| ( ( in @ SV965 @ SV285 )
= $false )
| ( ( in @ SV835 @ ( powerset @ SV285 ) )
= $false )
| ( ( in @ SV570 @ ( powerset @ SV285 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4079]) ).
thf(4274,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( SV759 = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4080]) ).
thf(4275,plain,
! [SV572: $i,SV287: $i,SV729: $i,SV759: $o] :
( ( SV759 = $false )
| ( SV759 = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4080]) ).
thf(4276,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( SV759 = $true )
| ( SV759 = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4081]) ).
thf(4277,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4083]) ).
thf(4278,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4083]) ).
thf(4279,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4084]) ).
thf(4280,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ SV572 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4086]) ).
thf(4281,plain,
! [SV572: $i,SV287: $i,SV729: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4086]) ).
thf(4282,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4087]) ).
thf(4283,plain,
! [SV573: $i,SV836: $i,SV966: $i,SV288: $i,SV1010: $i] :
( ( ( in @ SV1010 @ SV288 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV966 @ SV1010 ) @ SV836 )
| ( in @ ( kpair @ SV966 @ SV1010 ) @ ( binunion @ SV573 @ SV836 ) ) )
= $true )
| ( ( in @ SV966 @ SV288 )
= $false )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4089]) ).
thf(4284,plain,
! [SV296: $i,SV580: $i,SV838: $i] :
( ( ( in @ ( sK73_SY1670 @ SV838 @ SV580 @ SV296 ) @ SV580 )
= $true )
| ( ( in @ SV580 @ ( powerset @ SV838 ) )
= $true )
| ( ( in @ SV838 @ ( powerset @ SV296 ) )
= $false )
| ( ( in @ SV580 @ ( powerset @ SV296 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4091]) ).
thf(4285,plain,
! [SV839: $i,SV581: $i,SV967: $i,SV297: $i,SV1011: $i] :
( ( ( in @ SV1011 @ SV297 )
= $false )
| ( ( ~ ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 ) )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) ) )
= $true )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4093]) ).
thf(4286,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( in @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ SV298 )
= $true )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4094]) ).
thf(4287,plain,
! [SV582: $i,SV915: $i,SV734: $i,SV298: $i] :
( ( ( ~ ( in @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) @ SV582 )
| ~ ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV734 )
| ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV915 ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4095]) ).
thf(4288,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) )
= $true )
| ( ( SV300 @ SV841 )
= $false )
| ( ( ~ ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4097]) ).
thf(4289,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV841
= ( sK88_SY1674 @ SV841 @ SV300 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4098]) ).
thf(4290,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( SV916 = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4101]) ).
thf(4291,plain,
! [SV591: $i,SV309: $i,SV736: $i,SV916: $o] :
( ( SV916 = $false )
| ( SV916 = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4101]) ).
thf(4292,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( SV916 = $true )
| ( SV916 = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4102]) ).
thf(4293,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( $true = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4104]) ).
thf(4294,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4104]) ).
thf(4295,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4105]) ).
thf(4296,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ SV591 ) )
= $false )
| ( $false = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4107]) ).
thf(4297,plain,
! [SV591: $i,SV309: $i,SV736: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4107]) ).
thf(4298,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4108]) ).
thf(4299,plain,
! [SV310: $i,SV592: $i,SV847: $i] :
( ( ( in @ ( sK74_SY1678 @ SV847 @ SV592 @ SV310 ) @ SV592 )
= $true )
| ( ( subset @ SV592 @ SV847 )
= $true )
| ( ( in @ SV847 @ ( powerset @ SV310 ) )
= $false )
| ( ( in @ SV592 @ ( powerset @ SV310 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4111]) ).
thf(4300,plain,
! [SV315: $i,SV972: $o,SV848: $i,SV597: $i,SV985: $i] :
( ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 )
| ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4113]) ).
thf(4301,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV986 @ SV597 )
| $true )
| ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4114]) ).
thf(4302,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV987 @ SV597 )
| $false )
| ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4115]) ).
thf(4303,plain,
! [SV973: $i,SV849: $i,SV599: $i,SV317: $i,SV1012: $i] :
( ( ( in @ SV1012 @ ( powerset @ SV317 ) )
= $false )
| ( ( ( setminus @ SV317 @ ( binintersect @ ( binunion @ SV599 @ SV849 ) @ ( binunion @ SV973 @ SV1012 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV317 @ SV599 ) @ ( setminus @ SV317 @ SV849 ) ) @ ( binintersect @ ( setminus @ SV317 @ SV973 ) @ ( setminus @ SV317 @ SV1012 ) ) ) )
= $true )
| ( ( in @ SV973 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV849 @ ( powerset @ SV317 ) )
= $false )
| ( ( in @ SV599 @ ( powerset @ SV317 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4116]) ).
thf(4304,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV974: $i] :
( ( ( ~ ~ ( in @ SV974 @ SV850 ) )
= $true )
| ( ( ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( subset @ SV600 @ SV850 )
= $false )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4117]) ).
thf(4305,plain,
! [SV852: $i,SV323: $i > $o] :
( ( ( SV323 @ ( sK89_SY1684 @ SV852 @ SV323 ) )
= $true )
| ( ( SV323 @ SV852 )
= $false )
| ( ( SV323
@ ( descr
@ ^ [SY855: $i] : ( SV323 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4118]) ).
thf(4306,plain,
! [SV920: $i,SV3: $i,SV1023: $i] :
( ( ( ~ ( in @ SV1023 @ ( binintersect @ SV3 @ SV920 ) ) )
= $true )
| ( ( subset @ SV1023 @ ( binintersect @ SV3 @ SV920 ) )
= $true )
| ( ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4120]) ).
thf(4307,plain,
! [SV920: $i,SV3: $i,SV1013: $i] :
( ( ( in @ SV1013 @ ( binintersect @ SV3 @ SV920 ) )
= $false )
| ( ( subset @ SV1013 @ ( binintersect @ SV3 @ SV920 ) )
= $true )
| ( ( subset @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $false )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4121]) ).
thf(4308,plain,
! [SV854: $i,SV3: $i,SV1014: $i] :
( ( ( in @ SV1014 @ ( binintersect @ SV3 @ SV854 ) )
= $false )
| ( ( subset @ SV1014 @ ( binintersect @ SV3 @ SV854 ) )
= $true )
| ( ( in @ ( sK53_SY1685 @ SV3 @ SV854 ) @ SV854 )
= $true )
| ( ( subset @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4122]) ).
thf(4309,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1034: $i] :
( ( ( ~ ( in @ SV1034 @ SV11 )
| ! [SY1810: $i] :
( ~ ( in @ SY1810 @ SV335 )
| ~ ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV614 ) ) )
= $true )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4125]) ).
thf(4310,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV11 ) )
= $true )
| ( ( ! [SY1807: $i] :
( ~ ( in @ SY1807 @ SV335 )
| ~ ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV614 ) ) )
= $true )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4311,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1015: $i] :
( ( ( in @ SV1015 @ SV618 )
= $false )
| ( ( SV859 @ SV1015 )
= $true )
| ( ( in @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ SV19 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4127]) ).
thf(4312,plain,
! [SV342: $i,SV19: $i,SV859: $i > $o,SV618: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV618 )
| ( SV859 @ SV1035 ) )
= $true )
| ( ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4128]) ).
thf(4313,plain,
! [SV19: $i,SV342: $i,SV618: $i,SV859: $i > $o] :
( ( ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
= $true )
| ( ( ! [SY1692: $i] :
( ~ ( in @ SY1692 @ SV618 )
| ( SV859 @ SY1692 ) ) )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4129]) ).
thf(4314,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV618 )
| ( SV859 @ SV1036 ) )
= $true )
| ( ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) )
= $false )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4130]) ).
thf(4315,plain,
! [SV20: $i,SV343: $i,SV762: $i,SV926: $i] :
( ( ( in @ SV926 @ SV762 )
= $false )
| ( ( in @ SV926 @ ( binunion @ SV343 @ SV762 ) )
= $true )
| ( ( in @ SV926 @ SV20 )
= $false )
| ( ( in @ SV762 @ ( powerset @ SV20 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV20 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4131]) ).
thf(4316,plain,
! [SV347: $i > $o,SV26: $i,SV1016: $i] :
( ( ( in @ SV1016 @ SV26 )
= $false )
| ( ( ~ ( SV347 @ SV1016 ) )
= $true )
| ( ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4317,plain,
! [SV347: $i > $o,SV26: $i,SV1017: $i] :
( ( ( in @ SV1017 @ SV26 )
= $false )
| ( ( ~ ( SV347 @ SV1017 ) )
= $true )
| ( ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4135]) ).
thf(4318,plain,
! [SV348: $i > $o,SV27: $i,SV988: $i] :
( ( ( in @ SV988 @ SV27 )
= $false )
| ( ( ~ ( SV348 @ SV988 ) )
= $true )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4136]) ).
thf(4319,plain,
! [SV348: $i > $o,SV27: $i,SV989: $i] :
( ( ( in @ SV989 @ SV27 )
= $false )
| ( ( ~ ( SV348 @ SV989 ) )
= $true )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4137]) ).
thf(4320,plain,
! [SV34: $i,SV765: $i,SV353: $i,SV927: $i] :
( ( ( in @ SV927 @ SV353 )
= $false )
| ( ( in @ SV927 @ ( binunion @ SV353 @ SV765 ) )
= $true )
| ( ( in @ SV927 @ SV34 )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV34 ) )
= $false )
| ( ( in @ SV353 @ ( powerset @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4138]) ).
thf(4321,plain,
! [SV768: $i,SV357: $i,SV40: $i,SV994: $i,SV928: $i] :
( ( ( ~ ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) ) )
= $true )
| ( ( ~ ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4139]) ).
thf(4322,plain,
! [SV364: $i,SV47: $i,SV975: $i] :
( ( ( in @ SV975 @ SV47 )
= $false )
| ( ( in @ SV364 @ SV975 )
= $false )
| ( ( in @ SV364 @ ( setunion @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4142]) ).
thf(4323,plain,
! [SV367: $i,SV773: $i,SV52: $i,SV931: $i] :
( ( ( in @ SV931 @ ( setminus @ SV52 @ SV773 ) )
= $false )
| ( ( in @ SV931 @ ( setminus @ SV52 @ ( binunion @ SV367 @ SV773 ) ) )
= $true )
| ( ( in @ SV931 @ ( setminus @ SV52 @ SV367 ) )
= $false )
| ( ( in @ SV931 @ SV52 )
= $false )
| ( ( in @ SV773 @ ( powerset @ SV52 ) )
= $false )
| ( ( in @ SV367 @ ( powerset @ SV52 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4143]) ).
thf(4324,plain,
! [SV370: $i,SV55: $i,SV776: $i,SV990: $i] :
( ( ( in @ SV990 @ SV776 )
= $false )
| ( ( in @ SV990 @ ( setminus @ SV55 @ SV370 ) )
= $true )
| ( ( in @ SV990 @ SV55 )
= $false )
| ( ( subset @ SV370 @ ( setminus @ SV55 @ SV776 ) )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV55 ) )
= $false )
| ( ( in @ SV370 @ ( powerset @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4144]) ).
thf(4325,plain,
! [SV373: $i > $o,SV58: $i,SV1018: $i] :
( ( ( in @ SV1018 @ SV58 )
= $false )
| ( ( ~ ( SV373 @ SV1018 ) )
= $true )
| ( ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4146]) ).
thf(4326,plain,
! [SV373: $i > $o,SV58: $i,SV1019: $i] :
( ( ( in @ SV1019 @ SV58 )
= $false )
| ( ( ~ ( SV373 @ SV1019 ) )
= $true )
| ( ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4147]) ).
thf(4327,plain,
! [SV61: $i,SV376: $i > $o,SV862: $i] :
( ( ( in @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) @ SV61 )
= $true )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4148]) ).
thf(4328,plain,
! [SV61: $i,SV862: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) ) )
= $true )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4149]) ).
thf(4329,plain,
! [SV66: $i,SV380: $i,SV778: $i,SV934: $i] :
( ( ( ~ ~ ( in @ SV934 @ SV778 ) )
= $true )
| ( ( ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV380 )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4150]) ).
thf(4330,plain,
! [SV73: $i,SV780: $i] :
( ( ( ! [SY1740: $i] :
~ ~ ( ~ ( in @ SY1740 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SY1740 @ SV73 ) ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4151]) ).
thf(4331,plain,
! [SV76: $i,SV781: $i,SV386: $i,SV935: $i] :
( ( ( in @ SV935 @ SV386 )
= $false )
| ( ( in @ SV935 @ SV781 )
= $true )
| ( ( in @ SV386 @ ( powerset @ SV781 ) )
= $false )
| ( ( in @ SV935 @ SV76 )
= $false )
| ( ( in @ SV781 @ ( powerset @ SV76 ) )
= $false )
| ( ( in @ SV386 @ ( powerset @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4152]) ).
thf(4332,plain,
! [SV77: $i,SV387: $i,SV782: $i,SV936: $i] :
( ( ( in @ SV936 @ SV782 )
= $false )
| ( ( ~ ( in @ SV936 @ SV387 ) )
= $true )
| ( ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
= $false )
| ( ( in @ SV936 @ SV77 )
= $false )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4153]) ).
thf(4333,plain,
! [SV82: $i,SV784: $i,SV392: $i,SV937: $i] :
( ( ( in @ SV937 @ ( binintersect @ SV392 @ SV784 ) )
= $false )
| ( ( in @ SV937 @ SV392 )
= $true )
| ( ( in @ SV937 @ SV82 )
= $false )
| ( ( in @ SV784 @ ( powerset @ SV82 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4154]) ).
thf(4334,plain,
! [SV93: $i,SV786: $i,SV402: $i,SV995: $i,SV938: $i] :
( ( ( ~ ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) ) )
= $true )
| ( ( ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 ) )
= $true )
| ( ( in @ SV995 @ SV93 )
= $false )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4155]) ).
thf(4335,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4156]) ).
thf(4336,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4157]) ).
thf(4337,plain,
! [SV406: $i,SV97: $i,SV647: $i,SV874: $o] :
( ( SV874 = $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4157]) ).
thf(4338,plain,
! [SV874: $o,SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4158]) ).
thf(4339,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4159]) ).
thf(4340,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4341,plain,
! [SV406: $i,SV97: $i,SV647: $i,SV874: $o] :
( ( SV874 = $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4160]) ).
thf(4342,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4161]) ).
thf(4343,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4162]) ).
thf(4344,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4162]) ).
thf(4345,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4163]) ).
thf(4346,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4164]) ).
thf(4347,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4165]) ).
thf(4348,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4165]) ).
thf(4349,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4350,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4167]) ).
thf(4351,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4167]) ).
thf(4352,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 )
| ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4168]) ).
thf(4353,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4169]) ).
thf(4354,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4170]) ).
thf(4355,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4170]) ).
thf(4356,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV996: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) ) )
= $true )
| ( ( ! [SY1791: $o] :
( ~ ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1792 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1792 @ SV996 ) @ SV787 )
| SY1791 )
| SY1791 ) )
= $true )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4171]) ).
thf(4357,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4172]) ).
thf(4358,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4173]) ).
thf(4359,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4360,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4361,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4175]) ).
thf(4362,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4176]) ).
thf(4363,plain,
! [SV108: $i,SV788: $i,SV940: $i,SV416: $i] :
( ( ( subset @ SV416 @ SV940 )
= $false )
| ( ( subset @ SV416 @ ( binintersect @ SV788 @ SV940 ) )
= $true )
| ( ( subset @ SV416 @ SV788 )
= $false )
| ( ( in @ SV940 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV788 @ ( powerset @ SV108 ) )
= $false )
| ( ( in @ SV416 @ ( powerset @ SV108 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4364,plain,
! [SV419: $i,SV653: $i,SV111: $i] :
( ( ( ~ ( ~ ( in @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) ) ) ) )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4179]) ).
thf(4365,plain,
! [SV117: $i,SV941: $i,SV790: $i,SV424: $i,SV997: $i] :
( ( ( ~ ( in @ SV997 @ ( binintersect @ SV424 @ SV790 ) ) )
= $true )
| ( ( in @ SV997 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) )
= $true )
| ( ( in @ SV997 @ SV117 )
= $false )
| ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4180]) ).
thf(4366,plain,
! [SV425: $i > $o,SV118: $i,SV998: $i] :
( ( ( ~ ( in @ SV998 @ SV118 ) )
= $true )
| ( ( ~ ( SV425 @ SV998 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4181]) ).
thf(4367,plain,
! [SV425: $i > $o,SV118: $i,SV1025: $i] :
( ( ( ~ ( ~ ( in @ SV1025 @ SV118 )
| ~ ( SV425 @ SV1025 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4182]) ).
thf(4368,plain,
! [SV425: $i > $o,SV118: $i,SV1037: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1037 @ SV118 )
| ~ ( SV425 @ SV1037 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4183]) ).
thf(4369,plain,
! [SV425: $i > $o,SV118: $i] :
( ( ( ! [SY1034: $i] :
~ ~ ( ~ ( in @ SY1034 @ SV118 )
| ~ ( SV425 @ SY1034 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4184]) ).
thf(4370,plain,
! [SV425: $i > $o,SV118: $i,SV1038: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1038 @ SV118 )
| ~ ( SV425 @ SV1038 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4185]) ).
thf(4371,plain,
! [SV119: $i,SV876: $i,SV426: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) @ SV119 )
| ( SV876
!= ( SV426 @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) ) ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4186]) ).
thf(4372,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i,SV1026: $i] :
( ( ( ~ ( ~ ( in @ SV1026 @ SV119 )
| ( SV876
!= ( SV426 @ SV1026 ) ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4373,plain,
! [SV134: $i,SV999: $i,SV794: $i,SV943: $i,SV441: $i] :
( ( ( ~ ( subset @ SV441 @ SV943 ) )
= $true )
| ( ( ~ ( subset @ SV794 @ SV999 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) ) )
= $true )
| ( ( in @ SV999 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4189]) ).
thf(4374,plain,
! [SV795: $i,SV1039: $i,SV136: $i > $o] :
( ( ( ! [SY1811: $i] :
( ~ ( SV136 @ SV1039 )
| ~ ( SV136 @ SY1811 )
| ( SV1039 = SY1811 ) ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4190]) ).
thf(4375,plain,
! [SV795: $i,SV1040: $i,SV1027: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1027 )
| ~ ( SV136 @ SV1040 )
| ( SV1027 = SV1040 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4191]) ).
thf(4376,plain,
! [SV796: $i,SV1041: $i,SV138: $i > $o] :
( ( ( ! [SY1812: $i] :
( ~ ( SV138 @ SV1041 )
| ~ ( SV138 @ SY1812 )
| ( SV1041 = SY1812 ) ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4192]) ).
thf(4377,plain,
! [SV796: $i,SV1042: $i,SV1028: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1028 )
| ~ ( SV138 @ SV1042 )
| ( SV1028 = SV1042 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4193]) ).
thf(4378,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false )
| ( ( ~ ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4195]) ).
thf(4379,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ( ~ ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4380,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
| ~ ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4197]) ).
thf(4381,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ SV451 ) )
= $true )
| ( ( SV799 @ SV1029 )
= $true )
| ( ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4199]) ).
thf(4382,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV451 )
| ( SV799 @ SV1043 ) )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4200]) ).
thf(4383,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1030: $i] :
( ( ( ~ ( in @ SV1030 @ SV451 ) )
= $true )
| ( ( SV799 @ SV1030 )
= $true )
| ( ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) )
= $false )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4201]) ).
thf(4384,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4202]) ).
thf(4385,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ~ ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4203]) ).
thf(4386,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4204]) ).
thf(4387,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ! [SY401: $i] :
~ ~ ( ~ ( SV155 @ SY401 )
| ~ ! [SY402: $i] :
( ~ ( SV155 @ SY402 )
| ( SY401 = SY402 ) ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4206]) ).
thf(4388,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ~ ( ~ ( SV155 @ ( sK98_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1813: $i] :
( ~ ( SV155 @ SY1813 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SY1813 ) ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4207]) ).
thf(4389,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1031: $i] :
( ( ( ~ ( in @ SV1031 @ SV460 ) )
= $true )
| ( ( SV803 @ SV1031 )
= $true )
| ( ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4390,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1044: $i] :
( ( ( ~ ( in @ SV1044 @ SV460 )
| ( SV803 @ SV1044 ) )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4210]) ).
thf(4391,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1032: $i] :
( ( ( ~ ( in @ SV1032 @ SV460 ) )
= $true )
| ( ( SV803 @ SV1032 )
= $true )
| ( ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) )
= $false )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4211]) ).
thf(4392,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ~ ( ~ ( SV166 @ ( sK99_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1814: $i] :
( ~ ( SV166 @ SY1814 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SY1814 ) ) ) )
= $false )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4212]) ).
thf(4393,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY432: $i] :
~ ~ ( ~ ( SV166 @ SY432 )
| ~ ! [SY433: $i] :
( ~ ( SV166 @ SY433 )
| ( SY432 = SY433 ) ) ) )
= $false )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4213]) ).
thf(4394,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ~ ( ~ ( SV166 @ ( sK100_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1815: $i] :
( ~ ( SV166 @ SY1815 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SY1815 ) ) ) )
= $false )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4214]) ).
thf(4395,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ! [SY436: $i] :
~ ! [SY437: $i] :
~ ( ~ ( ~ ( SV167 @ SY437 )
| ( SY437 = SY436 ) )
| ~ ( ( SY437 != SY436 )
| ( SV167 @ SY437 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4396,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ! [SY1816: $i] :
~ ( ~ ( ~ ( SV167 @ SY1816 )
| ( SY1816
= ( sK101_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SY1816
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SY1816 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4216]) ).
thf(4397,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4217]) ).
thf(4398,plain,
! [SV470: $i,SV887: $i,SV678: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4218]) ).
thf(4399,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
| ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4218]) ).
thf(4400,plain,
! [SV170: $i,SV679: $i,SV472: $i > $i] :
( ( ( in @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) @ SV170 )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4219]) ).
thf(4401,plain,
! [SV170: $i,SV472: $i > $i,SV679: $i] :
( ( ( SV679
= ( SV472 @ ( sK68_SY1460 @ SV472 @ SV679 @ SV170 ) ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1126: $i] : ( SV472 @ SY1126 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4220]) ).
thf(4402,plain,
! [SV472: $i > $i,SV679: $i,SV170: $i,SV991: $i] :
( ( ( in @ SV991 @ SV170 )
= $false )
| ( ( SV679
!= ( SV472 @ SV991 ) )
= $true )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4403,plain,
! [SV171: $i,SV807: $i,SV473: $i,SV946: $i] :
( ( ( in @ SV946 @ ( binintersect @ SV473 @ SV807 ) )
= $false )
| ( ( in @ SV946 @ SV807 )
= $true )
| ( ( in @ SV946 @ SV171 )
= $false )
| ( ( in @ SV807 @ ( powerset @ SV171 ) )
= $false )
| ( ( in @ SV473 @ ( powerset @ SV171 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4222]) ).
thf(4404,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
!= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4223]) ).
thf(4405,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4223]) ).
thf(4406,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4224]) ).
thf(4407,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4225]) ).
thf(4408,plain,
! [SV179: $i,SV948: $i,SV810: $i,SV479: $i,SV1002: $i] :
( ( ( ~ ( in @ SV1002 @ ( binintersect @ SV479 @ SV810 ) ) )
= $true )
| ( ( in @ SV1002 @ ( binunion @ SV810 @ SV948 ) )
= $true )
| ( ( in @ SV1002 @ SV179 )
= $false )
| ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4226]) ).
thf(4409,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1020: $i] :
( ( ( in @ SV1020 @ SV687 )
= $false )
| ( ( SV892 @ SV1020 )
= $true )
| ( ( in @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ SV183 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4227]) ).
thf(4410,plain,
! [SV482: $i,SV183: $i,SV892: $i > $o,SV687: $i,SV1045: $i] :
( ( ( ~ ( in @ SV1045 @ SV687 )
| ( SV892 @ SV1045 ) )
= $true )
| ( ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4228]) ).
thf(4411,plain,
! [SV183: $i,SV482: $i,SV687: $i,SV892: $i > $o] :
( ( ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
= $true )
| ( ( ! [SY1717: $i] :
( ~ ( in @ SY1717 @ SV687 )
| ( SV892 @ SY1717 ) ) )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4229]) ).
thf(4412,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV687 )
| ( SV892 @ SV1046 ) )
= $true )
| ( ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) )
= $false )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4230]) ).
thf(4413,plain,
! [SV189: $i,SV813: $i,SV950: $i,SV487: $i > $o] :
( ( ( SV487 @ SV950 )
= $false )
| ( ( SV813 = SV950 )
= $true )
| ( ( SV487 @ SV813 )
= $false )
| ( ( in @ SV950 @ SV189 )
= $false )
| ( ( in @ SV813 @ SV189 )
= $false )
| ( ( ex1 @ SV189
@ ^ [SY1158: $i] : ( SV487 @ SY1158 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4231]) ).
thf(4414,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
| ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4232]) ).
thf(4415,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) )
| ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4233]) ).
thf(4416,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
| ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4234]) ).
thf(4417,plain,
! [SV202: $i,SV499: $i,SV980: $i,SV695: $i > $i] :
( ( ( ~ ( in @ ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) @ SV202 )
| ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) ) )
= ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4235]) ).
thf(4418,plain,
! [SV202: $i,SV499: $i,SV953: $i,SV695: $i > $i] :
( ( ( ~ ( in @ ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) @ SV202 ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4236]) ).
thf(4419,plain,
! [SV695: $i > $i,SV953: $i,SV202: $i,SV499: $i] :
( ( ( ( ap @ SV499 @ SV202 @ SV953 @ ( SV695 @ ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) ) )
= ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4236]) ).
thf(4420,plain,
! [SV209: $i,SV817: $i,SV504: $i] :
( ( ( in @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) @ SV209 )
= $true )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4237]) ).
thf(4421,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV504 ) )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4422,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV817 )
= $false )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4238]) ).
thf(4423,plain,
! [SV211: $i,SV954: $i,SV818: $i,SV506: $i,SV1004: $i] :
( ( ( ~ ( in @ SV1004 @ ( binintersect @ SV506 @ SV818 ) ) )
= $true )
| ( ( in @ SV1004 @ ( binunion @ SV506 @ SV954 ) )
= $true )
| ( ( in @ SV1004 @ SV211 )
= $false )
| ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4239]) ).
thf(4424,plain,
! [SV212: $i,SV1047: $i] :
( ( ~ ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1817: $i] :
( ~ ( in @ SY1817 @ SV1047 )
| ( in @ SY1817 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4240]) ).
thf(4425,plain,
! [SV212: $i,SV1048: $i] :
( ( ! [SY1818: $i] :
( ~ ~ ( ~ ( in @ SV1048 @ SV212 )
| ~ ( in @ SY1818 @ SV212 ) )
| ~ ! [SY1819: $i] :
( ~ ( in @ SY1819 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1819 )
| ( in @ SY1818 @ SY1819 ) )
| ~ ( ~ ( in @ SY1818 @ SY1819 )
| ( in @ SV1048 @ SY1819 ) ) ) )
| ( SV1048 = SY1818 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4241]) ).
thf(4426,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ( ~ ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) ) )
= $false )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4242]) ).
thf(4427,plain,
! [SV955: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
| ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 ) )
= $false )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4243]) ).
thf(4428,plain,
! [SV981: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1049: $i] :
( ( ( ~ ( in @ SV1049 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1820: $i] :
~ ( ~ ( SV702 @ SV1049 @ SY1820 )
| ~ ! [SY1821: $i] :
( ~ ( in @ SY1821 @ SV509 )
| ~ ( SV702 @ SV1049 @ SY1821 )
| ( in @ ( kpair @ SY1820 @ SY1821 ) @ SV981 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV981 )
= $false )
| ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4244]) ).
thf(4429,plain,
! [SV982: $i,SV215: $i,SV509: $i,SV702: $i > $i > $o] :
( ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( ! [SY1512: $i] :
( ~ ( in @ SY1512 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SY1512 )
| ! [SY1513: $i] :
( ~ ( in @ SY1513 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1514: $i] :
~ ( ~ ( SV702 @ SY1513 @ SY1514 )
| ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ SV509 )
| ~ ( SV702 @ SY1513 @ SY1515 )
| ( in @ ( kpair @ SY1514 @ SY1515 ) @ SY1512 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4430,plain,
! [SV226: $i,SV1050: $i] :
( ( ( ~ ( in @ SV1050 @ omega )
| ( in @ SV1050 @ SV226 ) )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4431,plain,
! [SV226: $i,SV1051: $i] :
( ( ( ~ ( in @ SV1051 @ omega )
| ( in @ SV1051 @ SV226 ) )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4248]) ).
thf(4432,plain,
! [SV232: $i,SV521: $i > $o,SV902: $i] :
( ( ( in @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) @ SV232 )
= $true )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4249]) ).
thf(4433,plain,
! [SV232: $i,SV902: $i,SV521: $i > $o] :
( ( ( ~ ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) ) )
= $true )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4250]) ).
thf(4434,plain,
! [SV822: $i,SV1006: $i,SV523: $i,SV956: $i,SV234: $i,SV1052: $i] :
( ( ( ~ ( in @ SV1052 @ SV234 )
| ~ ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
| ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) )
= $true )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4251]) ).
thf(4435,plain,
! [SV534: $i > $o,SV245: $i,SV1007: $i] :
( ( ( ~ ( in @ SV1007 @ SV245 ) )
= $true )
| ( ( ~ ( SV534 @ SV1007 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4252]) ).
thf(4436,plain,
! [SV534: $i > $o,SV245: $i,SV1033: $i] :
( ( ( ~ ( ~ ( in @ SV1033 @ SV245 )
| ~ ( SV534 @ SV1033 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4253]) ).
thf(4437,plain,
! [SV534: $i > $o,SV245: $i,SV1053: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1053 @ SV245 )
| ~ ( SV534 @ SV1053 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4254]) ).
thf(4438,plain,
! [SV534: $i > $o,SV245: $i] :
( ( ( ! [SY1242: $i] :
~ ~ ( ~ ( in @ SY1242 @ SV245 )
| ~ ( SV534 @ SY1242 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4255]) ).
thf(4439,plain,
! [SV534: $i > $o,SV245: $i,SV1054: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1054 @ SV245 )
| ~ ( SV534 @ SV1054 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4256]) ).
thf(4440,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) ) )
= $true )
| ( ( ! [SY1800: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SY1800 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SY1800 )
| SY1800 ) )
= $true )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4258]) ).
thf(4441,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1022 )
| ~ ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4259]) ).
thf(4442,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4260]) ).
thf(4443,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4260]) ).
thf(4444,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4261]) ).
thf(4445,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4446,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4263]) ).
thf(4447,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4264]) ).
thf(4448,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4265]) ).
thf(4449,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4265]) ).
thf(4450,plain,
! [SV269: $i,SV558: $i > $o,SV909: $i] :
( ( ( ~ ( in @ ( sK105_SY1285 @ SV909 @ SV558 @ SV269 ) @ SV269 )
| ( SV558 @ ( sK105_SY1285 @ SV909 @ SV558 @ SV269 ) ) )
= $false )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( SV558 @ SV909 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4266]) ).
thf(4451,plain,
! [SV274: $i,SV832: $i,SV562: $i,SV1009: $i,SV964: $i] :
( ( ( ~ ( in @ ( kpair @ SV964 @ SV1009 ) @ SV562 ) )
= $true )
| ( ( in @ ( kpair @ SV964 @ SV1009 ) @ ( binunion @ SV562 @ SV832 ) )
= $true )
| ( ( in @ SV1009 @ SV274 )
= $false )
| ( ( in @ SV964 @ SV274 )
= $false )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4452,plain,
! [SV283: $i,SV569: $i,SV833: $i > $o,SV911: $i > $o] :
( ( ( ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 )
= ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4269]) ).
thf(4453,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
| ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4270]) ).
thf(4454,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ! [SY752: $i] :
~ ~ ( ~ ( SV284 @ SY752 )
| ~ ! [SY753: $i] :
( ~ ( SV284 @ SY753 )
| ( SY752 = SY753 ) ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4271]) ).
thf(4455,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ~ ( ~ ( SV284 @ ( sK106_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV284 @ SY1822 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SY1822 ) ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4272]) ).
thf(4456,plain,
! [SV287: $i,SV759: $o,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( SV759 = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4274]) ).
thf(4457,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( $true = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4458,plain,
! [SV287: $i,SV572: $i,SV729: $i] :
( ( ( in @ SV729 @ SV572 )
= $true )
| ( $false = $true )
| ( ( in @ SV729 @ SV287 )
= $true )
| ( ( in @ SV729 @ ( binunion @ SV287 @ SV572 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4280]) ).
thf(4459,plain,
! [SV288: $i,SV573: $i,SV836: $i,SV1010: $i,SV966: $i] :
( ( ( ~ ( in @ ( kpair @ SV966 @ SV1010 ) @ SV836 ) )
= $true )
| ( ( in @ ( kpair @ SV966 @ SV1010 ) @ ( binunion @ SV573 @ SV836 ) )
= $true )
| ( ( in @ SV1010 @ SV288 )
= $false )
| ( ( in @ SV966 @ SV288 )
= $false )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4283]) ).
thf(4460,plain,
! [SV297: $i,SV839: $i,SV581: $i,SV1011: $i,SV967: $i] :
( ( ( ~ ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 ) ) )
= $true )
| ( ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) )
= $true )
| ( ( in @ SV1011 @ SV297 )
= $false )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4285]) ).
thf(4461,plain,
! [SV582: $i,SV915: $i,SV734: $i,SV298: $i] :
( ( ( ~ ( in @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) @ SV582 ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4287]) ).
thf(4462,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV734 )
| ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV915 ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4287]) ).
thf(4463,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ! [SY796: $i] :
~ ( SV300 @ SY796 ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4288]) ).
thf(4464,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ ( sK107_SY796 @ SV841 @ SV300 ) ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV841
= ( sK88_SY1674 @ SV841 @ SV300 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4289]) ).
thf(4465,plain,
! [SV309: $i,SV916: $o,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( SV916 = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4290]) ).
thf(4466,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( $true = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4293]) ).
thf(4467,plain,
! [SV309: $i,SV591: $i,SV736: $i] :
( ( ( in @ SV736 @ SV591 )
= $true )
| ( $false = $true )
| ( ( SV736 = SV309 )
= $true )
| ( ( in @ SV736 @ ( setadjoin @ SV309 @ SV591 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4296]) ).
thf(4468,plain,
! [SV315: $i,SV848: $i,SV972: $o,SV597: $i,SV985: $i] :
( ( ( ~ ( ~ ( in @ SV985 @ SV597 )
| SV972 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4300]) ).
thf(4469,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( ~ ( ~ ( in @ SV986 @ SV597 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4301]) ).
thf(4470,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( ~ ( ~ ( in @ SV987 @ SV597 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4302]) ).
thf(4471,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV974: $i] :
( ( ( ~ ( in @ SV974 @ SV850 ) )
= $false )
| ( ( ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( subset @ SV600 @ SV850 )
= $false )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4304]) ).
thf(4472,plain,
! [SV920: $i,SV3: $i,SV1023: $i] :
( ( ( in @ SV1023 @ ( binintersect @ SV3 @ SV920 ) )
= $false )
| ( ( subset @ SV1023 @ ( binintersect @ SV3 @ SV920 ) )
= $true )
| ( ( in @ ( sK61_SY1730 @ SV3 @ SV920 ) @ SV920 )
= $true )
| ( ( in @ ( sK5_SY5 @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4306]) ).
thf(4473,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1034: $i] :
( ( ( ~ ( in @ SV1034 @ SV11 ) )
= $true )
| ( ( ! [SY1810: $i] :
( ~ ( in @ SY1810 @ SV335 )
| ~ ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV614 ) ) )
= $true )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4474,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1024: $i] :
( ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ! [SY1807: $i] :
( ~ ( in @ SY1807 @ SV335 )
| ~ ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SY1807 ) @ SV614 ) ) )
= $true )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4310]) ).
thf(4475,plain,
! [SV342: $i,SV19: $i,SV859: $i > $o,SV618: $i,SV1035: $i] :
( ( ( ~ ( in @ SV1035 @ SV618 ) )
= $true )
| ( ( SV859 @ SV1035 )
= $true )
| ( ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4476,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1055: $i] :
( ( ( ~ ( in @ SV1055 @ SV618 )
| ( SV859 @ SV1055 ) )
= $true )
| ( ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4313]) ).
thf(4477,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1036: $i] :
( ( ( ~ ( in @ SV1036 @ SV618 ) )
= $true )
| ( ( SV859 @ SV1036 )
= $true )
| ( ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) )
= $false )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4478,plain,
! [SV26: $i,SV1016: $i,SV347: $i > $o] :
( ( ( SV347 @ SV1016 )
= $false )
| ( ( in @ SV1016 @ SV26 )
= $false )
| ( ( in @ ( sK37_SY899 @ SV347 @ SV26 ) @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4479,plain,
! [SV26: $i,SV1017: $i,SV347: $i > $o] :
( ( ( SV347 @ SV1017 )
= $false )
| ( ( in @ SV1017 @ SV26 )
= $false )
| ( ( SV347 @ ( sK37_SY899 @ SV347 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4480,plain,
! [SV27: $i,SV988: $i,SV348: $i > $o] :
( ( ( SV348 @ SV988 )
= $false )
| ( ( in @ SV988 @ SV27 )
= $false )
| ( ( in @ ( sK11_SY901 @ SV348 @ SV27 ) @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4318]) ).
thf(4481,plain,
! [SV27: $i,SV989: $i,SV348: $i > $o] :
( ( ( SV348 @ SV989 )
= $false )
| ( ( in @ SV989 @ SV27 )
= $false )
| ( ( SV348 @ ( sK11_SY901 @ SV348 @ SV27 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4319]) ).
thf(4482,plain,
! [SV768: $i,SV357: $i,SV40: $i,SV994: $i,SV928: $i] :
( ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( ~ ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4483,plain,
! [SV58: $i,SV1018: $i,SV373: $i > $o] :
( ( ( SV373 @ SV1018 )
= $false )
| ( ( in @ SV1018 @ SV58 )
= $false )
| ( ( in @ ( sK38_SY940 @ SV373 @ SV58 ) @ SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4325]) ).
thf(4484,plain,
! [SV58: $i,SV1019: $i,SV373: $i > $o] :
( ( ( SV373 @ SV1019 )
= $false )
| ( ( in @ SV1019 @ SV58 )
= $false )
| ( ( SV373 @ ( sK38_SY940 @ SV373 @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4326]) ).
thf(4485,plain,
! [SV61: $i,SV862: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK63_SY945 @ SV862 @ SV376 @ SV61 ) )
= $false )
| ( ( SV376 @ SV862 )
= $true )
| ( ( in @ SV862 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4328]) ).
thf(4486,plain,
! [SV66: $i,SV380: $i,SV778: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV778 ) )
= $false )
| ( ( ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV380 )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4329]) ).
thf(4487,plain,
! [SV73: $i,SV780: $i,SV1056: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SV1056 @ SV73 ) ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4330]) ).
thf(4488,plain,
! [SV77: $i,SV782: $i,SV387: $i,SV936: $i] :
( ( ( in @ SV936 @ SV387 )
= $false )
| ( ( in @ SV936 @ SV782 )
= $false )
| ( ( subset @ SV387 @ ( setminus @ SV77 @ SV782 ) )
= $false )
| ( ( in @ SV936 @ SV77 )
= $false )
| ( ( in @ SV782 @ ( powerset @ SV77 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV77 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4489,plain,
! [SV93: $i,SV786: $i,SV402: $i,SV995: $i,SV938: $i] :
( ( ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) )
= $false )
| ( ( ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
| ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 ) )
= $true )
| ( ( in @ SV995 @ SV93 )
= $false )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4490,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4335]) ).
thf(4491,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4336]) ).
thf(4492,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4493,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| SV874 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4494,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4339]) ).
thf(4495,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( SV874 = $true )
| ( SV874 = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4340]) ).
thf(4496,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4497,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4343]) ).
thf(4498,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4345]) ).
thf(4499,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4345]) ).
thf(4500,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4346]) ).
thf(4501,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4347]) ).
thf(4502,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4349]) ).
thf(4503,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV97 )
= $true )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4350]) ).
thf(4504,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV97 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4352]) ).
thf(4505,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4352]) ).
thf(4506,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4507,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4354]) ).
thf(4508,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV996: $i,SV939: $i] :
( ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( ! [SY1791: $o] :
( ~ ! [SY1792: $i] :
( ~ ( in @ SY1792 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1792 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1792 @ SV996 ) @ SV787 )
| SY1791 )
| SY1791 ) )
= $true )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4356]) ).
thf(4509,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV1057 )
| ~ ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4357]) ).
thf(4510,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ SV1058 )
| ~ ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4511,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4359]) ).
thf(4512,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4513,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4361]) ).
thf(4514,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4515,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4362]) ).
thf(4516,plain,
! [SV419: $i,SV653: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) @ SV419 )
| ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4517,plain,
! [SV117: $i,SV941: $i,SV790: $i,SV424: $i,SV997: $i] :
( ( ( in @ SV997 @ ( binintersect @ SV424 @ SV790 ) )
= $false )
| ( ( in @ SV997 @ ( binintersect @ ( binunion @ SV424 @ SV941 ) @ ( binunion @ SV790 @ SV941 ) ) )
= $true )
| ( ( in @ SV997 @ SV117 )
= $false )
| ( ( in @ SV941 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV790 @ ( powerset @ SV117 ) )
= $false )
| ( ( in @ SV424 @ ( powerset @ SV117 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4365]) ).
thf(4518,plain,
! [SV425: $i > $o,SV118: $i,SV998: $i] :
( ( ( in @ SV998 @ SV118 )
= $false )
| ( ( ~ ( SV425 @ SV998 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4519,plain,
! [SV425: $i > $o,SV118: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV118 )
| ~ ( SV425 @ SV1025 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4367]) ).
thf(4520,plain,
! [SV425: $i > $o,SV118: $i,SV1037: $i] :
( ( ( ~ ( ~ ( in @ SV1037 @ SV118 )
| ~ ( SV425 @ SV1037 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4521,plain,
! [SV425: $i > $o,SV118: $i,SV1059: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1059 @ SV118 )
| ~ ( SV425 @ SV1059 ) ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4369]) ).
thf(4522,plain,
! [SV425: $i > $o,SV118: $i,SV1038: $i] :
( ( ( ~ ( ~ ( in @ SV1038 @ SV118 )
| ~ ( SV425 @ SV1038 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4370]) ).
thf(4523,plain,
! [SV119: $i,SV876: $i,SV426: $i > $i] :
( ( ( ~ ( in @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) @ SV119 )
| ( SV876
!= ( SV426 @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4371]) ).
thf(4524,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i,SV1026: $i] :
( ( ( ~ ( in @ SV1026 @ SV119 )
| ( SV876
!= ( SV426 @ SV1026 ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4525,plain,
! [SV134: $i,SV999: $i,SV794: $i,SV943: $i,SV441: $i] :
( ( ( subset @ SV441 @ SV943 )
= $false )
| ( ( ~ ( subset @ SV794 @ SV999 )
| ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) ) )
= $true )
| ( ( in @ SV999 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4373]) ).
thf(4526,plain,
! [SV795: $i,SV1060: $i,SV1039: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1039 )
| ~ ( SV136 @ SV1060 )
| ( SV1039 = SV1060 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4374]) ).
thf(4527,plain,
! [SV795: $i,SV1040: $i,SV1027: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1027 ) )
= $true )
| ( ( ~ ( SV136 @ SV1040 )
| ( SV1027 = SV1040 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4375]) ).
thf(4528,plain,
! [SV796: $i,SV1061: $i,SV1041: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1041 )
| ~ ( SV138 @ SV1061 )
| ( SV1041 = SV1061 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4376]) ).
thf(4529,plain,
! [SV796: $i,SV1042: $i,SV1028: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1028 ) )
= $true )
| ( ( ~ ( SV138 @ SV1042 )
| ( SV1028 = SV1042 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4377]) ).
thf(4530,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ( ! [SY1772: $i] :
~ ~ ( ~ ( in @ SY1772 @ SV140 )
| ( SV977
!= ( SV445 @ SY1772 ) ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4531,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i] :
( ( ( ! [SY1773: $i] :
~ ~ ( ~ ( in @ SY1773 @ SV140 )
| ( SV977
!= ( SV445 @ SY1773 ) ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4379]) ).
thf(4532,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ~ ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
| ~ ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4380]) ).
thf(4533,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1029: $i] :
( ( ( in @ SV1029 @ SV451 )
= $false )
| ( ( SV799 @ SV1029 )
= $true )
| ( ( in @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) @ SV146 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4381]) ).
thf(4534,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1043: $i] :
( ( ( ~ ( in @ SV1043 @ SV451 ) )
= $true )
| ( ( SV799 @ SV1043 )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4382]) ).
thf(4535,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1030: $i] :
( ( ( in @ SV1030 @ SV451 )
= $false )
| ( ( SV799 @ SV1030 )
= $true )
| ( ( SV799 @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) )
= $false )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4536,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
| ~ ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4384]) ).
thf(4537,plain,
! [SV454: $i,SV800: $i,SV149: $i] :
( ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV149 )
| ~ ( in @ SY1619 @ SV800 )
| ( in @ SY1619 @ SV454 ) ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(4538,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
| ~ ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4386]) ).
thf(4539,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ~ ( ~ ( SV155 @ ( sK110_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1825: $i] :
( ~ ( SV155 @ SY1825 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SY1825 ) ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4387]) ).
thf(4540,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( ~ ( SV155 @ ( sK98_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1813: $i] :
( ~ ( SV155 @ SY1813 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SY1813 ) ) ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4388]) ).
thf(4541,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1031: $i] :
( ( ( in @ SV1031 @ SV460 )
= $false )
| ( ( SV803 @ SV1031 )
= $true )
| ( ( in @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) @ SV156 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4389]) ).
thf(4542,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1044: $i] :
( ( ( ~ ( in @ SV1044 @ SV460 ) )
= $true )
| ( ( SV803 @ SV1044 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4390]) ).
thf(4543,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1032: $i] :
( ( ( in @ SV1032 @ SV460 )
= $false )
| ( ( SV803 @ SV1032 )
= $true )
| ( ( SV803 @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) )
= $false )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4391]) ).
thf(4544,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( ~ ( SV166 @ ( sK99_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1814: $i] :
( ~ ( SV166 @ SY1814 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SY1814 ) ) ) )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4392]) ).
thf(4545,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ~ ( ~ ( SV166 @ ( sK111_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1826: $i] :
( ~ ( SV166 @ SY1826 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SY1826 ) ) ) )
= $false )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4393]) ).
thf(4546,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( ~ ( SV166 @ ( sK100_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1815: $i] :
( ~ ( SV166 @ SY1815 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SY1815 ) ) ) )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4394]) ).
thf(4547,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ~ ! [SY1827: $i] :
~ ( ~ ( ~ ( SV167 @ SY1827 )
| ( SY1827
= ( sK112_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SY1827
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SY1827 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4395]) ).
thf(4548,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ! [SY1816: $i] :
~ ( ~ ( ~ ( SV167 @ SY1816 )
| ( SY1816
= ( sK101_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SY1816
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SY1816 ) ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4396]) ).
thf(4549,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4397]) ).
thf(4550,plain,
! [SV470: $i,SV887: $i,SV678: $i,SV168: $i] :
( ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4398]) ).
thf(4551,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4399]) ).
thf(4552,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4399]) ).
thf(4553,plain,
! [SV170: $i,SV991: $i,SV472: $i > $i,SV679: $i] :
( ( ( SV679
= ( SV472 @ SV991 ) )
= $false )
| ( ( in @ SV991 @ SV170 )
= $false )
| ( ( in @ SV679
@ ( image1 @ SV170
@ ^ [SY1129: $i] : ( SV472 @ SY1129 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4554,plain,
! [SV174: $i > $o,SV808: $i] :
( ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ~ ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4404]) ).
thf(4555,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4405]) ).
thf(4556,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4406]) ).
thf(4557,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ~ ( ~ ( SV174 @ ( sK113_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1828: $i] :
( ~ ( SV174 @ SY1828 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SY1828 ) ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4407]) ).
thf(4558,plain,
! [SV179: $i,SV948: $i,SV810: $i,SV479: $i,SV1002: $i] :
( ( ( in @ SV1002 @ ( binintersect @ SV479 @ SV810 ) )
= $false )
| ( ( in @ SV1002 @ ( binunion @ SV810 @ SV948 ) )
= $true )
| ( ( in @ SV1002 @ SV179 )
= $false )
| ( ( in @ SV948 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV810 @ ( powerset @ SV179 ) )
= $false )
| ( ( in @ SV479 @ ( powerset @ SV179 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4408]) ).
thf(4559,plain,
! [SV482: $i,SV183: $i,SV892: $i > $o,SV687: $i,SV1045: $i] :
( ( ( ~ ( in @ SV1045 @ SV687 ) )
= $true )
| ( ( SV892 @ SV1045 )
= $true )
| ( ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4410]) ).
thf(4560,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1062: $i] :
( ( ( ~ ( in @ SV1062 @ SV687 )
| ( SV892 @ SV1062 ) )
= $true )
| ( ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4411]) ).
thf(4561,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1046: $i] :
( ( ( ~ ( in @ SV1046 @ SV687 ) )
= $true )
| ( ( SV892 @ SV1046 )
= $true )
| ( ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) )
= $false )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4412]) ).
thf(4562,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) ) )
= $true )
| ( ( ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4414]) ).
thf(4563,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4415]) ).
thf(4564,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4416]) ).
thf(4565,plain,
! [SV191: $i > $i > $o,SV489: $i,SV951: $i] :
( ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4416]) ).
thf(4566,plain,
! [SV202: $i,SV499: $i,SV980: $i,SV695: $i > $i] :
( ( ( ~ ( in @ ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) @ SV202 ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4417]) ).
thf(4567,plain,
! [SV695: $i > $i,SV980: $i,SV202: $i,SV499: $i] :
( ( ( ( ap @ SV499 @ SV202 @ SV980 @ ( SV695 @ ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) ) )
= ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) )
= $false )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4417]) ).
thf(4568,plain,
! [SV202: $i,SV499: $i,SV953: $i,SV695: $i > $i] :
( ( ( in @ ( sK96_SY1752 @ SV695 @ SV953 @ SV499 @ SV202 ) @ SV202 )
= $true )
| ( ( surjective @ SV499 @ SV202 @ SV953 )
= $true )
| ( ( in @ SV953 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( SV695 @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) ) @ SV499 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4418]) ).
thf(4569,plain,
! [SV209: $i,SV504: $i,SV817: $i] :
( ( ( in @ ( kpair @ ( sK69_SY1638 @ SV817 @ SV504 @ SV209 ) @ ( sK91_SY1788 @ SV504 @ SV817 @ SV209 ) ) @ SV504 )
= $true )
| ( ( subset @ SV504 @ SV817 )
= $true )
| ( ( breln1 @ SV209 @ SV817 )
= $false )
| ( ( breln1 @ SV209 @ SV504 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4421]) ).
thf(4570,plain,
! [SV211: $i,SV954: $i,SV818: $i,SV506: $i,SV1004: $i] :
( ( ( in @ SV1004 @ ( binintersect @ SV506 @ SV818 ) )
= $false )
| ( ( in @ SV1004 @ ( binunion @ SV506 @ SV954 ) )
= $true )
| ( ( in @ SV1004 @ SV211 )
= $false )
| ( ( in @ SV954 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV818 @ ( powerset @ SV211 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV211 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4571,plain,
! [SV212: $i,SV1047: $i] :
( ( ( ~ ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1817: $i] :
( ~ ( in @ SY1817 @ SV1047 )
| ( in @ SY1817 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4424]) ).
thf(4572,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ~ ~ ( ~ ( in @ SV1048 @ SV212 )
| ~ ( in @ SV1063 @ SV212 ) )
| ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[4425]) ).
thf(4573,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4426]) ).
thf(4574,plain,
! [SV955: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 ) )
= $false )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4427]) ).
thf(4575,plain,
! [SV955: $i,SV212: $i] :
( ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4427]) ).
thf(4576,plain,
! [SV981: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1049: $i] :
( ( ( ~ ( in @ SV1049 @ SV215 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1820: $i] :
~ ( ~ ( SV702 @ SV1049 @ SY1820 )
| ~ ! [SY1821: $i] :
( ~ ( in @ SY1821 @ SV509 )
| ~ ( SV702 @ SV1049 @ SY1821 )
| ( in @ ( kpair @ SY1820 @ SY1821 ) @ SV981 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV981 )
= $false )
| ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4428]) ).
thf(4577,plain,
! [SV982: $i,SV702: $i > $i > $o,SV215: $i,SV509: $i,SV1064: $i] :
( ( ( ~ ( in @ SV1064 @ ( breln1Set @ SV509 ) )
| ~ ( reflwellordering @ SV509 @ SV1064 )
| ! [SY1830: $i] :
( ~ ( in @ SY1830 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1831: $i] :
~ ( ~ ( SV702 @ SY1830 @ SY1831 )
| ~ ! [SY1832: $i] :
( ~ ( in @ SY1832 @ SV509 )
| ~ ( SV702 @ SY1830 @ SY1832 )
| ( in @ ( kpair @ SY1831 @ SY1832 ) @ SV1064 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4429]) ).
thf(4578,plain,
! [SV226: $i,SV1050: $i] :
( ( ( ~ ( in @ SV1050 @ omega ) )
= $true )
| ( ( in @ SV1050 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4430]) ).
thf(4579,plain,
! [SV226: $i,SV1051: $i] :
( ( ( ~ ( in @ SV1051 @ omega ) )
= $true )
| ( ( in @ SV1051 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4431]) ).
thf(4580,plain,
! [SV232: $i,SV902: $i,SV521: $i > $o] :
( ( ( SV521 @ ( sK71_SY1215 @ SV902 @ SV521 @ SV232 ) )
= $false )
| ( ( SV521 @ SV902 )
= $true )
| ( ( in @ SV902 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4433]) ).
thf(4581,plain,
! [SV822: $i,SV1006: $i,SV523: $i,SV956: $i,SV234: $i,SV1052: $i] :
( ( ( ~ ( in @ SV1052 @ SV234 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
| ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) )
= $true )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4434]) ).
thf(4582,plain,
! [SV534: $i > $o,SV245: $i,SV1007: $i] :
( ( ( in @ SV1007 @ SV245 )
= $false )
| ( ( ~ ( SV534 @ SV1007 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4435]) ).
thf(4583,plain,
! [SV534: $i > $o,SV245: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ SV245 )
| ~ ( SV534 @ SV1033 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4584,plain,
! [SV534: $i > $o,SV245: $i,SV1053: $i] :
( ( ( ~ ( ~ ( in @ SV1053 @ SV245 )
| ~ ( SV534 @ SV1053 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4437]) ).
thf(4585,plain,
! [SV534: $i > $o,SV245: $i,SV1065: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1065 @ SV245 )
| ~ ( SV534 @ SV1065 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4438]) ).
thf(4586,plain,
! [SV534: $i > $o,SV245: $i,SV1054: $i] :
( ( ( ~ ( ~ ( in @ SV1054 @ SV245 )
| ~ ( SV534 @ SV1054 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4439]) ).
thf(4587,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( ! [SY1800: $o] :
( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SY1800 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SY1800 )
| SY1800 ) )
= $true )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4440]) ).
thf(4588,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1022 ) )
= $true )
| ( ( ~ ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4441]) ).
thf(4589,plain,
! [SV260: $i > $o,SV550: $i > $o] :
( ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) )
| ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4442]) ).
thf(4590,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4443]) ).
thf(4591,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4444]) ).
thf(4592,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4445]) ).
thf(4593,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
| ! [SY1833: $i] :
( ~ ( in @ SY1833 @ SV264 )
| ~ ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1833 ) @ SV829 )
| ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1833 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4446]) ).
thf(4594,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4447]) ).
thf(4595,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) )
| ( SV553 = SV829 ) )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4448]) ).
thf(4596,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4449]) ).
thf(4597,plain,
! [SV269: $i,SV558: $i > $o,SV909: $i] :
( ( ( ~ ( in @ ( sK105_SY1285 @ SV909 @ SV558 @ SV269 ) @ SV269 ) )
= $false )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( SV558 @ SV909 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4598,plain,
! [SV269: $i,SV909: $i,SV558: $i > $o] :
( ( ( SV558 @ ( sK105_SY1285 @ SV909 @ SV558 @ SV269 ) )
= $false )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( SV558 @ SV909 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4450]) ).
thf(4599,plain,
! [SV274: $i,SV832: $i,SV562: $i,SV1009: $i,SV964: $i] :
( ( ( in @ ( kpair @ SV964 @ SV1009 ) @ SV562 )
= $false )
| ( ( in @ ( kpair @ SV964 @ SV1009 ) @ ( binunion @ SV562 @ SV832 ) )
= $true )
| ( ( in @ SV1009 @ SV274 )
= $false )
| ( ( in @ SV964 @ SV274 )
= $false )
| ( ( breln1 @ SV274 @ SV832 )
= $false )
| ( ( breln1 @ SV274 @ SV562 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4600,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( ~ ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4453]) ).
thf(4601,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ~ ( ~ ( SV284 @ ( sK115_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1834: $i] :
( ~ ( SV284 @ SY1834 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SY1834 ) ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4454]) ).
thf(4602,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( ~ ( SV284 @ ( sK106_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV284 @ SY1822 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SY1822 ) ) ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4455]) ).
thf(4603,plain,
! [SV288: $i,SV573: $i,SV836: $i,SV1010: $i,SV966: $i] :
( ( ( in @ ( kpair @ SV966 @ SV1010 ) @ SV836 )
= $false )
| ( ( in @ ( kpair @ SV966 @ SV1010 ) @ ( binunion @ SV573 @ SV836 ) )
= $true )
| ( ( in @ SV1010 @ SV288 )
= $false )
| ( ( in @ SV966 @ SV288 )
= $false )
| ( ( breln1 @ SV288 @ SV836 )
= $false )
| ( ( breln1 @ SV288 @ SV573 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4459]) ).
thf(4604,plain,
! [SV297: $i,SV839: $i,SV581: $i,SV1011: $i,SV967: $i] :
( ( ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
| ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 ) )
= $false )
| ( ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) )
= $true )
| ( ( in @ SV1011 @ SV297 )
= $false )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4460]) ).
thf(4605,plain,
! [SV582: $i,SV915: $i,SV734: $i,SV298: $i] :
( ( ( in @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) @ SV582 )
= $true )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4461]) ).
thf(4606,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV734 ) )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4462]) ).
thf(4607,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV915 )
= $false )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4462]) ).
thf(4608,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( ~ ( SV300 @ ( sK116_SY796 @ SV841 @ SV300 ) ) )
= $false )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4463]) ).
thf(4609,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( SV300 @ ( sK107_SY796 @ SV841 @ SV300 ) )
= $true )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV841
= ( sK88_SY1674 @ SV841 @ SV300 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4464]) ).
thf(4610,plain,
! [SV315: $i,SV848: $i,SV972: $o,SV597: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV597 )
| SV972 )
= $false )
| ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4468]) ).
thf(4611,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV597 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4469]) ).
thf(4612,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV597 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4470]) ).
thf(4613,plain,
! [SV318: $i,SV600: $i,SV850: $i,SV974: $i] :
( ( ( in @ SV974 @ SV850 )
= $true )
| ( ( ~ ( in @ SV974 @ SV600 ) )
= $true )
| ( ( subset @ SV600 @ SV850 )
= $false )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4471]) ).
thf(4614,plain,
! [SV614: $i,SV858: $i,SV335: $i,SV11: $i,SV1034: $i] :
( ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( ! [SY1810: $i] :
( ~ ( in @ SY1810 @ SV335 )
| ~ ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SY1810 ) @ SV614 ) ) )
= $true )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4473]) ).
thf(4615,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1024: $i,SV335: $i,SV1066: $i] :
( ( ( ~ ( in @ SV1066 @ SV335 )
| ~ ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV614 ) )
= $true )
| ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4474]) ).
thf(4616,plain,
! [SV342: $i,SV19: $i,SV859: $i > $o,SV618: $i,SV1035: $i] :
( ( ( in @ SV1035 @ SV618 )
= $false )
| ( ( SV859 @ SV1035 )
= $true )
| ( ( in @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) @ SV342 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4475]) ).
thf(4617,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1055: $i] :
( ( ( ~ ( in @ SV1055 @ SV618 ) )
= $true )
| ( ( SV859 @ SV1055 )
= $true )
| ( ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4476]) ).
thf(4618,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1036: $i] :
( ( ( in @ SV1036 @ SV618 )
= $false )
| ( ( SV859 @ SV1036 )
= $true )
| ( ( SV859 @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) )
= $false )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4619,plain,
! [SV768: $i,SV994: $i,SV357: $i,SV928: $i,SV40: $i] :
( ( ( ! [SY1790: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY1790 @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ SY1790 ) @ SV357 ) )
| ~ ( in @ ( kpair @ SY1790 @ SV994 ) @ SV768 ) ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4482]) ).
thf(4620,plain,
! [SV66: $i,SV380: $i,SV778: $i,SV934: $i] :
( ( ( in @ SV934 @ SV778 )
= $true )
| ( ( ~ ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) ) )
= $true )
| ( ( in @ SV934 @ SV380 )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4486]) ).
thf(4621,plain,
! [SV73: $i,SV780: $i,SV1056: $i] :
( ( ( ~ ( ~ ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SV1056 @ SV73 ) ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4487]) ).
thf(4622,plain,
! [SV93: $i,SV786: $i,SV402: $i,SV995: $i,SV938: $i] :
( ( ( in @ ( kpair @ SV938 @ SV995 ) @ SV402 )
= $true )
| ( ( in @ ( kpair @ SV938 @ SV995 ) @ SV786 )
= $true )
| ( ( in @ ( kpair @ SV938 @ SV995 ) @ ( binunion @ SV402 @ SV786 ) )
= $false )
| ( ( in @ SV995 @ SV93 )
= $false )
| ( ( in @ SV938 @ SV93 )
= $false )
| ( ( breln1 @ SV93 @ SV786 )
= $false )
| ( ( breln1 @ SV93 @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4489]) ).
thf(4623,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4492]) ).
thf(4624,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4493]) ).
thf(4625,plain,
! [SV97: $i,SV406: $i,SV647: $i,SV874: $o] :
( ( SV874 = $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4493]) ).
thf(4626,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4498]) ).
thf(4627,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4628,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4499]) ).
thf(4629,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV97 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4504]) ).
thf(4630,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV406 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4631,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4632,plain,
! [SV1067: $o,SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SY1835: $i] :
( ~ ( in @ SY1835 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1835 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1835 @ SV996 ) @ SV787 )
| SV1067 )
| SV1067 )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4508]) ).
thf(4633,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4508]) ).
thf(4634,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4508]) ).
thf(4635,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV1057 )
| ~ ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4509]) ).
thf(4636,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ SV1058 )
| ~ ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4510]) ).
thf(4637,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
| ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4511]) ).
thf(4638,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4639,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4512]) ).
thf(4640,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4513]) ).
thf(4641,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4513]) ).
thf(4642,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4514]) ).
thf(4643,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4515]) ).
thf(4644,plain,
! [SV419: $i,SV653: $i,SV111: $i] :
( ( ( ~ ( in @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) @ SV419 ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4516]) ).
thf(4645,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( SV653
!= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) ) )
= $false )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4516]) ).
thf(4646,plain,
! [SV118: $i,SV998: $i,SV425: $i > $o] :
( ( ( SV425 @ SV998 )
= $false )
| ( ( in @ SV998 @ SV118 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK14_SY1032 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4518]) ).
thf(4647,plain,
! [SV425: $i > $o,SV118: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV118 ) )
= $true )
| ( ( ~ ( SV425 @ SV1025 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4519]) ).
thf(4648,plain,
! [SV425: $i > $o,SV118: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ SV118 )
| ~ ( SV425 @ SV1037 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4520]) ).
thf(4649,plain,
! [SV425: $i > $o,SV118: $i,SV1059: $i] :
( ( ( ~ ( ~ ( in @ SV1059 @ SV118 )
| ~ ( SV425 @ SV1059 ) ) )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4521]) ).
thf(4650,plain,
! [SV425: $i > $o,SV118: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ SV118 )
| ~ ( SV425 @ SV1038 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4522]) ).
thf(4651,plain,
! [SV119: $i,SV876: $i,SV426: $i > $i] :
( ( ( ~ ( in @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) @ SV119 ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4523]) ).
thf(4652,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ( SV876
!= ( SV426 @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) ) )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4523]) ).
thf(4653,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i,SV1026: $i] :
( ( ( ~ ( in @ SV1026 @ SV119 ) )
= $true )
| ( ( SV876
!= ( SV426 @ SV1026 ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4524]) ).
thf(4654,plain,
! [SV134: $i,SV943: $i,SV441: $i,SV999: $i,SV794: $i] :
( ( ( ~ ( subset @ SV794 @ SV999 ) )
= $true )
| ( ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) )
= $true )
| ( ( subset @ SV441 @ SV943 )
= $false )
| ( ( in @ SV999 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4525]) ).
thf(4655,plain,
! [SV795: $i,SV1060: $i,SV1039: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1039 ) )
= $true )
| ( ( ~ ( SV136 @ SV1060 )
| ( SV1039 = SV1060 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4526]) ).
thf(4656,plain,
! [SV795: $i,SV1040: $i,SV1027: $i,SV136: $i > $o] :
( ( ( SV136 @ SV1027 )
= $false )
| ( ( ~ ( SV136 @ SV1040 )
| ( SV1027 = SV1040 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4527]) ).
thf(4657,plain,
! [SV796: $i,SV1061: $i,SV1041: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1041 ) )
= $true )
| ( ( ~ ( SV138 @ SV1061 )
| ( SV1041 = SV1061 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4528]) ).
thf(4658,plain,
! [SV796: $i,SV1042: $i,SV1028: $i,SV138: $i > $o] :
( ( ( SV138 @ SV1028 )
= $false )
| ( ( ~ ( SV138 @ SV1042 )
| ( SV1028 = SV1042 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4529]) ).
thf(4659,plain,
! [SV140: $i,SV977: $i,SV445: $i > $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) @ SV140 )
| ( SV977
!= ( SV445 @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) ) ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4530]) ).
thf(4660,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i,SV1068: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1068 @ SV140 )
| ( SV977
!= ( SV445 @ SV1068 ) ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4531]) ).
thf(4661,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ~ ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4532]) ).
thf(4662,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4532]) ).
thf(4663,plain,
! [SV146: $i,SV799: $i > $o,SV451: $i,SV1043: $i] :
( ( ( in @ SV1043 @ SV451 )
= $false )
| ( ( SV799 @ SV1043 )
= $true )
| ( ( in @ ( kpair @ ( sK49_SY1615 @ SV799 @ SV451 @ SV146 ) @ ( sK64_SY1747 @ SV451 @ SV799 @ SV146 ) ) @ SV451 )
= $true )
| ( ( breln1 @ SV146 @ SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4534]) ).
thf(4664,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4536]) ).
thf(4665,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4536]) ).
thf(4666,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
| ~ ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4537]) ).
thf(4667,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4668,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4538]) ).
thf(4669,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( ~ ( SV155 @ ( sK110_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1825: $i] :
( ~ ( SV155 @ SY1825 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SY1825 ) ) ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4539]) ).
thf(4670,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK98_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1813: $i] :
( ~ ( SV155 @ SY1813 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SY1813 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4671,plain,
! [SV156: $i,SV803: $i > $o,SV460: $i,SV1044: $i] :
( ( ( in @ SV1044 @ SV460 )
= $false )
| ( ( SV803 @ SV1044 )
= $true )
| ( ( in @ ( kpair @ ( sK50_SY1622 @ SV803 @ SV460 @ SV156 ) @ ( sK66_SY1748 @ SV460 @ SV803 @ SV156 ) ) @ SV460 )
= $true )
| ( ( breln1 @ SV156 @ SV460 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4542]) ).
thf(4672,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK99_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1814: $i] :
( ~ ( SV166 @ SY1814 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SY1814 ) ) )
= $false )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4544]) ).
thf(4673,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( ~ ( SV166 @ ( sK111_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1826: $i] :
( ~ ( SV166 @ SY1826 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SY1826 ) ) ) )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4545]) ).
thf(4674,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK100_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1815: $i] :
( ~ ( SV166 @ SY1815 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SY1815 ) ) )
= $false )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4546]) ).
thf(4675,plain,
! [SV806: $i,SV167: $i > $o] :
( ( ( ! [SY1827: $i] :
~ ( ~ ( ~ ( SV167 @ SY1827 )
| ( SY1827
= ( sK112_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SY1827
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SY1827 ) ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4547]) ).
thf(4676,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV167 @ SV1069 )
| ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SV1069
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1069 ) ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4548]) ).
thf(4677,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
| ! [SY1836: $i] :
( ~ ( in @ SY1836 @ SV470 )
| ~ ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1836 ) @ SV887 )
| ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1836 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4549]) ).
thf(4678,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4550]) ).
thf(4679,plain,
! [SV168: $i,SV470: $i,SV678: $i,SV887: $i] :
( ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) )
| ( SV678 = SV887 ) )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4551]) ).
thf(4680,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4552]) ).
thf(4681,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY462: $i] :
~ ~ ( ~ ( SV174 @ SY462 )
| ~ ! [SY463: $i] :
( ~ ( SV174 @ SY463 )
| ( SY462 = SY463 ) ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4554]) ).
thf(4682,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ~ ( ~ ( SV174 @ ( sK120_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1837: $i] :
( ~ ( SV174 @ SY1837 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SY1837 ) ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4555]) ).
thf(4683,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ~ ( ~ ( SV174 @ ( sK121_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1838: $i] :
( ~ ( SV174 @ SY1838 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SY1838 ) ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4556]) ).
thf(4684,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK113_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1828: $i] :
( ~ ( SV174 @ SY1828 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SY1828 ) ) ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4557]) ).
thf(4685,plain,
! [SV482: $i,SV183: $i,SV892: $i > $o,SV687: $i,SV1045: $i] :
( ( ( in @ SV1045 @ SV687 )
= $false )
| ( ( SV892 @ SV1045 )
= $true )
| ( ( in @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) @ SV482 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4559]) ).
thf(4686,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1062: $i] :
( ( ( ~ ( in @ SV1062 @ SV687 ) )
= $true )
| ( ( SV892 @ SV1062 )
= $true )
| ( ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4560]) ).
thf(4687,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1046: $i] :
( ( ( in @ SV1046 @ SV687 )
= $false )
| ( ( SV892 @ SV1046 )
= $true )
| ( ( SV892 @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) )
= $false )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4561]) ).
thf(4688,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( ~ ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4689,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4563]) ).
thf(4690,plain,
! [SV951: $i,SV489: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( ~ ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4564]) ).
thf(4691,plain,
! [SV951: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4565]) ).
thf(4692,plain,
! [SV202: $i,SV499: $i,SV980: $i,SV695: $i > $i] :
( ( ( in @ ( sK103_SY1783 @ SV695 @ SV980 @ SV499 @ SV202 ) @ SV202 )
= $true )
| ( ( surjective @ SV499 @ SV202 @ SV980 )
= $true )
| ( ( in @ SV980 @ ( funcSet @ SV499 @ SV202 ) )
= $false )
| ( ( in @ ( sK32_SY1481 @ SV499 @ SV695 @ SV202 ) @ SV202 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4566]) ).
thf(4693,plain,
! [SV212: $i,SV1047: $i] :
( ( ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( ! [SY1817: $i] :
( ~ ( in @ SY1817 @ SV1047 )
| ( in @ SY1817 @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4571]) ).
thf(4694,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1048 @ SV212 )
| ~ ( in @ SV1063 @ SV212 ) ) )
= $true )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4572]) ).
thf(4695,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4573]) ).
thf(4696,plain,
! [SV955: $i,SV212: $i] :
( ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4574]) ).
thf(4697,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4575]) ).
thf(4698,plain,
! [SV981: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1049: $i] :
( ( ( in @ SV1049 @ SV215 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1820: $i] :
~ ( ~ ( SV702 @ SV1049 @ SY1820 )
| ~ ! [SY1821: $i] :
( ~ ( in @ SY1821 @ SV509 )
| ~ ( SV702 @ SV1049 @ SY1821 )
| ( in @ ( kpair @ SY1820 @ SY1821 ) @ SV981 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV981 )
= $false )
| ( ( in @ SV981 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4576]) ).
thf(4699,plain,
! [SV982: $i,SV702: $i > $i > $o,SV215: $i,SV509: $i,SV1064: $i] :
( ( ( ~ ( in @ SV1064 @ ( breln1Set @ SV509 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV509 @ SV1064 )
| ! [SY1830: $i] :
( ~ ( in @ SY1830 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1831: $i] :
~ ( ~ ( SV702 @ SY1830 @ SY1831 )
| ~ ! [SY1832: $i] :
( ~ ( in @ SY1832 @ SV509 )
| ~ ( SV702 @ SY1830 @ SY1832 )
| ( in @ ( kpair @ SY1831 @ SY1832 ) @ SV1064 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4577]) ).
thf(4700,plain,
! [SV226: $i,SV1050: $i] :
( ( ( in @ SV1050 @ omega )
= $false )
| ( ( in @ SV1050 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(4701,plain,
! [SV226: $i,SV1051: $i] :
( ( ( in @ SV1051 @ omega )
= $false )
| ( ( in @ SV1051 @ SV226 )
= $true )
| ( ( in @ emptyset @ SV226 )
= $false )
| ( ( in @ ( sK51_SY601 @ SV226 ) @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(4702,plain,
! [SV822: $i,SV1006: $i,SV523: $i,SV956: $i,SV234: $i,SV1052: $i] :
( ( ( in @ SV1052 @ SV234 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
| ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) )
= $true )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4581]) ).
thf(4703,plain,
! [SV245: $i,SV1007: $i,SV534: $i > $o] :
( ( ( SV534 @ SV1007 )
= $false )
| ( ( in @ SV1007 @ SV245 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK20_SY1240 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4582]) ).
thf(4704,plain,
! [SV534: $i > $o,SV245: $i,SV1033: $i] :
( ( ( ~ ( in @ SV1033 @ SV245 ) )
= $true )
| ( ( ~ ( SV534 @ SV1033 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4583]) ).
thf(4705,plain,
! [SV534: $i > $o,SV245: $i,SV1053: $i] :
( ( ( ~ ( in @ SV1053 @ SV245 )
| ~ ( SV534 @ SV1053 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4584]) ).
thf(4706,plain,
! [SV534: $i > $o,SV245: $i,SV1065: $i] :
( ( ( ~ ( ~ ( in @ SV1065 @ SV245 )
| ~ ( SV534 @ SV1065 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4585]) ).
thf(4707,plain,
! [SV534: $i > $o,SV245: $i,SV1054: $i] :
( ( ( ~ ( in @ SV1054 @ SV245 )
| ~ ( SV534 @ SV1054 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4586]) ).
thf(4708,plain,
! [SV255: $i,SV826: $i,SV1070: $o,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SV1070 )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4587]) ).
thf(4709,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $true )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4587]) ).
thf(4710,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $false )
| ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4587]) ).
thf(4711,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4588]) ).
thf(4712,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4589]) ).
thf(4713,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4590]) ).
thf(4714,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4591]) ).
thf(4715,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4592]) ).
thf(4716,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4593]) ).
thf(4717,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ! [SY1833: $i] :
( ~ ( in @ SY1833 @ SV264 )
| ~ ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1833 ) @ SV829 )
| ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1833 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4593]) ).
thf(4718,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4594]) ).
thf(4719,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ~ ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4595]) ).
thf(4720,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4596]) ).
thf(4721,plain,
! [SV269: $i,SV558: $i > $o,SV909: $i] :
( ( ( in @ ( sK105_SY1285 @ SV909 @ SV558 @ SV269 ) @ SV269 )
= $true )
| ( ( in @ SV909 @ SV269 )
= $false )
| ( ( SV558 @ SV909 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4597]) ).
thf(4722,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
| ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
= $false )
| ( ( ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4600]) ).
thf(4723,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( ~ ( SV284 @ ( sK115_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1834: $i] :
( ~ ( SV284 @ SY1834 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SY1834 ) ) ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4601]) ).
thf(4724,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK106_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1822: $i] :
( ~ ( SV284 @ SY1822 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SY1822 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4602]) ).
thf(4725,plain,
! [SV297: $i,SV839: $i,SV581: $i,SV1011: $i,SV967: $i] :
( ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV581 )
= $false )
| ( ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) )
= $true )
| ( ( in @ SV1011 @ SV297 )
= $false )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4604]) ).
thf(4726,plain,
! [SV297: $i,SV581: $i,SV839: $i,SV1011: $i,SV967: $i] :
( ( ( in @ ( kpair @ SV967 @ SV1011 ) @ SV839 )
= $false )
| ( ( in @ ( kpair @ SV967 @ SV1011 ) @ ( binunion @ SV581 @ SV839 ) )
= $true )
| ( ( in @ SV1011 @ SV297 )
= $false )
| ( ( in @ SV967 @ SV297 )
= $false )
| ( ( breln1 @ SV297 @ SV839 )
= $false )
| ( ( breln1 @ SV297 @ SV581 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4604]) ).
thf(4727,plain,
! [SV298: $i,SV582: $i,SV734: $i,SV915: $i] :
( ( ( in @ ( kpair @ ( sK87_SY1728 @ SV915 @ SV734 @ SV582 @ SV298 ) @ ( sK97_SY1801 @ SV298 @ SV734 @ SV915 @ SV582 ) ) @ SV734 )
= $true )
| ( ( subset @ SV734 @ SV915 )
= $true )
| ( ( breln @ SV298 @ SV582 @ SV915 )
= $false )
| ( ( breln @ SV298 @ SV582 @ SV734 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4606]) ).
thf(4728,plain,
! [SV841: $i,SV300: $i > $o] :
( ( ( SV300 @ ( sK116_SY796 @ SV841 @ SV300 ) )
= $true )
| ( ( SV300 @ SV841 )
= $false )
| ( ( SV300 @ ( sK88_SY1674 @ SV841 @ SV300 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4608]) ).
thf(4729,plain,
! [SV315: $i,SV972: $o,SV848: $i,SV597: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV597 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4610]) ).
thf(4730,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV985: $i,SV972: $o] :
( ( SV972 = $false )
| ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4610]) ).
thf(4731,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV597 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4611]) ).
thf(4732,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4611]) ).
thf(4733,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV597 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4612]) ).
thf(4734,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4612]) ).
thf(4735,plain,
! [SV318: $i,SV850: $i,SV600: $i,SV974: $i] :
( ( ( in @ SV974 @ SV600 )
= $false )
| ( ( in @ SV974 @ SV850 )
= $true )
| ( ( subset @ SV600 @ SV850 )
= $false )
| ( ( in @ SV974 @ SV318 )
= $false )
| ( ( in @ SV850 @ ( powerset @ SV318 ) )
= $false )
| ( ( in @ SV600 @ ( powerset @ SV318 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4613]) ).
thf(4736,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1034: $i,SV335: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV335 )
| ~ ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV614 ) )
= $true )
| ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4614]) ).
thf(4737,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1024: $i,SV335: $i,SV1066: $i] :
( ( ( ~ ( in @ SV1066 @ SV335 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV614 ) )
= $true )
| ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4615]) ).
thf(4738,plain,
! [SV19: $i,SV342: $i,SV859: $i > $o,SV618: $i,SV1055: $i] :
( ( ( in @ SV1055 @ SV618 )
= $false )
| ( ( SV859 @ SV1055 )
= $true )
| ( ( in @ ( kpair @ ( sK54_SY1690 @ SV859 @ SV618 @ SV342 @ SV19 ) @ ( sK76_SY1770 @ SV19 @ SV618 @ SV859 @ SV342 ) ) @ SV618 )
= $true )
| ( ( breln @ SV19 @ SV342 @ SV618 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4617]) ).
thf(4739,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) )
| ~ ( in @ ( kpair @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV994 ) @ SV768 ) ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4619]) ).
thf(4740,plain,
! [SV66: $i,SV778: $i,SV380: $i,SV934: $i] :
( ( ( in @ SV934 @ ( binunion @ SV380 @ SV778 ) )
= $false )
| ( ( in @ SV934 @ SV778 )
= $true )
| ( ( in @ SV934 @ SV380 )
= $true )
| ( ( in @ SV934 @ SV66 )
= $false )
| ( ( in @ SV778 @ ( powerset @ SV66 ) )
= $false )
| ( ( in @ SV380 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4741,plain,
! [SV73: $i,SV780: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) )
| ~ ( in @ SV1056 @ SV73 ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4621]) ).
thf(4742,plain,
! [SV406: $i,SV874: $o,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4623]) ).
thf(4743,plain,
! [SV97: $i,SV874: $o,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( SV874 = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4624]) ).
thf(4744,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4626]) ).
thf(4745,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $true = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4627]) ).
thf(4746,plain,
! [SV406: $i,SV97: $i,SV647: $i] :
( ( ( in @ SV647 @ SV97 )
= $false )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4747,plain,
! [SV97: $i,SV406: $i,SV647: $i] :
( ( ( in @ SV647 @ SV406 )
= $true )
| ( $false = $true )
| ( ( in @ SV647 @ SV406 )
= $false )
| ( ( in @ SV647 @ ( symdiff @ SV97 @ SV406 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4630]) ).
thf(4748,plain,
! [SV1067: $o,SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SY1835: $i] :
( ~ ( in @ SY1835 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1835 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1835 @ SV996 ) @ SV787 )
| SV1067 ) )
= $true )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4632]) ).
thf(4749,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4633]) ).
thf(4750,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4634]) ).
thf(4751,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1057 )
| ~ ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4635]) ).
thf(4752,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1058 )
| ~ ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4636]) ).
thf(4753,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4637]) ).
thf(4754,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4637]) ).
thf(4755,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4638]) ).
thf(4756,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4639]) ).
thf(4757,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4640]) ).
thf(4758,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4641]) ).
thf(4759,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4642]) ).
thf(4760,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4643]) ).
thf(4761,plain,
! [SV419: $i,SV653: $i,SV111: $i] :
( ( ( in @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) @ SV419 )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4644]) ).
thf(4762,plain,
! [SV111: $i,SV419: $i,SV653: $i] :
( ( ( SV653
= ( kpair @ ( sK39_SY1424 @ SV653 @ SV419 @ SV111 ) @ ( sK93_SY1732 @ SV111 @ SV653 @ SV419 ) ) )
= $true )
| ( ( in @ SV653 @ ( cartprod @ SV111 @ SV419 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4645]) ).
thf(4763,plain,
! [SV425: $i > $o,SV118: $i,SV1025: $i] :
( ( ( in @ SV1025 @ SV118 )
= $false )
| ( ( ~ ( SV425 @ SV1025 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4647]) ).
thf(4764,plain,
! [SV425: $i > $o,SV118: $i,SV1037: $i] :
( ( ( ~ ( in @ SV1037 @ SV118 ) )
= $true )
| ( ( ~ ( SV425 @ SV1037 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4648]) ).
thf(4765,plain,
! [SV425: $i > $o,SV118: $i,SV1059: $i] :
( ( ( ~ ( in @ SV1059 @ SV118 )
| ~ ( SV425 @ SV1059 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4649]) ).
thf(4766,plain,
! [SV425: $i > $o,SV118: $i,SV1038: $i] :
( ( ( ~ ( in @ SV1038 @ SV118 ) )
= $true )
| ( ( ~ ( SV425 @ SV1038 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4650]) ).
thf(4767,plain,
! [SV119: $i,SV876: $i,SV426: $i > $i] :
( ( ( in @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) @ SV119 )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4651]) ).
thf(4768,plain,
! [SV119: $i,SV426: $i > $i,SV876: $i] :
( ( ( SV876
= ( SV426 @ ( sK94_SY1701 @ SV426 @ SV876 @ SV119 ) ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4652]) ).
thf(4769,plain,
! [SV426: $i > $i,SV876: $i,SV119: $i,SV1026: $i] :
( ( ( in @ SV1026 @ SV119 )
= $false )
| ( ( SV876
!= ( SV426 @ SV1026 ) )
= $true )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4653]) ).
thf(4770,plain,
! [SV134: $i,SV943: $i,SV441: $i,SV999: $i,SV794: $i] :
( ( ( subset @ SV794 @ SV999 )
= $false )
| ( ( subset @ ( binintersect @ SV441 @ SV794 ) @ ( binintersect @ SV943 @ SV999 ) )
= $true )
| ( ( subset @ SV441 @ SV943 )
= $false )
| ( ( in @ SV999 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV943 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV794 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV441 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4654]) ).
thf(4771,plain,
! [SV795: $i,SV1060: $i,SV1039: $i,SV136: $i > $o] :
( ( ( SV136 @ SV1039 )
= $false )
| ( ( ~ ( SV136 @ SV1060 )
| ( SV1039 = SV1060 ) )
= $true )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4655]) ).
thf(4772,plain,
! [SV795: $i,SV1027: $i,SV1040: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1040 ) )
= $true )
| ( ( SV1027 = SV1040 )
= $true )
| ( ( SV136 @ SV1027 )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4656]) ).
thf(4773,plain,
! [SV796: $i,SV1061: $i,SV1041: $i,SV138: $i > $o] :
( ( ( SV138 @ SV1041 )
= $false )
| ( ( ~ ( SV138 @ SV1061 )
| ( SV1041 = SV1061 ) )
= $true )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4774,plain,
! [SV796: $i,SV1028: $i,SV1042: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1042 ) )
= $true )
| ( ( SV1028 = SV1042 )
= $true )
| ( ( SV138 @ SV1028 )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4658]) ).
thf(4775,plain,
! [SV140: $i,SV977: $i,SV445: $i > $i] :
( ( ( ~ ( ~ ( in @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) @ SV140 )
| ( SV977
!= ( SV445 @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) ) ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4659]) ).
thf(4776,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i,SV1068: $i] :
( ( ( ~ ( ~ ( in @ SV1068 @ SV140 )
| ( SV977
!= ( SV445 @ SV1068 ) ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4660]) ).
thf(4777,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4661]) ).
thf(4778,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ! [SY1802: $i] :
~ ~ ( ~ ( in @ SY1802 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1802 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4662]) ).
thf(4779,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4664]) ).
thf(4780,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4781,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4782,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4666]) ).
thf(4783,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
| ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4666]) ).
thf(4784,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4667]) ).
thf(4785,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(4786,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(4787,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK110_SY401 @ SV802 @ SV155 ) )
| ~ ! [SY1825: $i] :
( ~ ( SV155 @ SY1825 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SY1825 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4669]) ).
thf(4788,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK98_SY401 @ SV802 @ SV155 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4670]) ).
thf(4789,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ! [SY1813: $i] :
( ~ ( SV155 @ SY1813 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SY1813 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4670]) ).
thf(4790,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK99_SY432 @ SV805 @ SV166 ) ) )
= $false )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4672]) ).
thf(4791,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ! [SY1814: $i] :
( ~ ( SV166 @ SY1814 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SY1814 ) ) )
= $false )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4672]) ).
thf(4792,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK111_SY432 @ SV805 @ SV166 ) )
| ~ ! [SY1826: $i] :
( ~ ( SV166 @ SY1826 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SY1826 ) ) )
= $false )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4673]) ).
thf(4793,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK100_SY432 @ SV805 @ SV166 ) ) )
= $false )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4674]) ).
thf(4794,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ! [SY1815: $i] :
( ~ ( SV166 @ SY1815 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SY1815 ) ) )
= $false )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4674]) ).
thf(4795,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV167 @ SV1072 )
| ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SV1072
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1072 ) ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4675]) ).
thf(4796,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV1069 )
| ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SV1069
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1069 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4676]) ).
thf(4797,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4798,plain,
! [SV168: $i,SV887: $i,SV678: $i,SV470: $i] :
( ( ( ! [SY1836: $i] :
( ~ ( in @ SY1836 @ SV470 )
| ~ ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1836 ) @ SV887 )
| ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1836 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4677]) ).
thf(4799,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4678]) ).
thf(4800,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ~ ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4679]) ).
thf(4801,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4680]) ).
thf(4802,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ~ ( ~ ( SV174 @ ( sK123_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1839: $i] :
( ~ ( SV174 @ SY1839 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SY1839 ) ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4681]) ).
thf(4803,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK120_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1837: $i] :
( ~ ( SV174 @ SY1837 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SY1837 ) ) ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4682]) ).
thf(4804,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK121_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1838: $i] :
( ~ ( SV174 @ SY1838 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SY1838 ) ) ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4683]) ).
thf(4805,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK113_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1828: $i] :
( ~ ( SV174 @ SY1828 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SY1828 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4684]) ).
thf(4806,plain,
! [SV183: $i,SV482: $i,SV892: $i > $o,SV687: $i,SV1062: $i] :
( ( ( in @ SV1062 @ SV687 )
= $false )
| ( ( SV892 @ SV1062 )
= $true )
| ( ( in @ ( kpair @ ( sK57_SY1715 @ SV892 @ SV687 @ SV482 @ SV183 ) @ ( sK84_SY1779 @ SV183 @ SV687 @ SV892 @ SV482 ) ) @ SV687 )
= $true )
| ( ( breln @ SV183 @ SV482 @ SV687 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4686]) ).
thf(4807,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1794: $i] :
~ ~ ( ~ ( in @ SY1794 @ SV489 )
| ~ ( SV191 @ SY1794 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4688]) ).
thf(4808,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1795: $i] :
~ ~ ( ~ ( in @ SY1795 @ SV489 )
| ~ ( SV191 @ SY1795 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4689]) ).
thf(4809,plain,
! [SV951: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1167: $i] :
~ ! [SY1168: $i] :
~ ( ~ ( ~ ( in @ SY1168 @ SY1167 )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1168 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1168 ) )
| ( in @ SY1168 @ SY1167 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4690]) ).
thf(4810,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i] :
( ( ( ~ ! [SY1840: $i] :
~ ( ~ ( ~ ( in @ SY1840 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1840 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1840 ) )
| ( in @ SY1840 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4691]) ).
thf(4811,plain,
! [SV212: $i,SV1047: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV1047 )
| ( in @ SV1073 @ SV212 ) )
= $true )
| ( ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4693]) ).
thf(4812,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ( ~ ( ~ ( in @ SV1048 @ SV212 )
| ~ ( in @ SV1063 @ SV212 ) ) )
= $false )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4694]) ).
thf(4813,plain,
! [SV1021: $i,SV212: $i,SV1005: $i] :
( ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( ~ ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4695]) ).
thf(4814,plain,
! [SV212: $i,SV955: $i] :
( ( ( ~ ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4815,plain,
! [SV212: $i,SV955: $i] :
( ( ( ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4697]) ).
thf(4816,plain,
! [SV982: $i,SV702: $i > $i > $o,SV215: $i,SV509: $i,SV1064: $i] :
( ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV509 @ SV1064 )
| ! [SY1830: $i] :
( ~ ( in @ SY1830 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1831: $i] :
~ ( ~ ( SV702 @ SY1830 @ SY1831 )
| ~ ! [SY1832: $i] :
( ~ ( in @ SY1832 @ SV509 )
| ~ ( SV702 @ SY1830 @ SY1832 )
| ( in @ ( kpair @ SY1831 @ SY1832 ) @ SV1064 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4817,plain,
! [SV234: $i,SV822: $i,SV1006: $i,SV523: $i,SV1052: $i,SV956: $i] :
( ( ( ~ ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) )
= $true )
| ( ( in @ SV1052 @ SV234 )
= $false )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4702]) ).
thf(4818,plain,
! [SV534: $i > $o,SV245: $i,SV1033: $i] :
( ( ( in @ SV1033 @ SV245 )
= $false )
| ( ( ~ ( SV534 @ SV1033 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4704]) ).
thf(4819,plain,
! [SV534: $i > $o,SV245: $i,SV1053: $i] :
( ( ( ~ ( in @ SV1053 @ SV245 ) )
= $true )
| ( ( ~ ( SV534 @ SV1053 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4705]) ).
thf(4820,plain,
! [SV534: $i > $o,SV245: $i,SV1065: $i] :
( ( ( ~ ( in @ SV1065 @ SV245 )
| ~ ( SV534 @ SV1065 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4706]) ).
thf(4821,plain,
! [SV534: $i > $o,SV245: $i,SV1054: $i] :
( ( ( ~ ( in @ SV1054 @ SV245 ) )
= $true )
| ( ( ~ ( SV534 @ SV1054 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4707]) ).
thf(4822,plain,
! [SV255: $i,SV826: $i,SV1070: $o,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SV1070 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4708]) ).
thf(4823,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4709]) ).
thf(4824,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4710]) ).
thf(4825,plain,
! [SV550: $i > $o,SV1022: $i,SV260: $i > $o] :
( ( ( ! [SY1806: $i] :
( ~ ( SV260 @ SY1806 )
| ( SV1022 = SY1806 ) ) )
= $false )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4826,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4712]) ).
thf(4827,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4713]) ).
thf(4828,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4714]) ).
thf(4829,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( ~ ~ ( ~ ( SV260 @ SV1074 )
| ~ ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4715]) ).
thf(4830,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4716]) ).
thf(4831,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) @ SV264 )
| ~ ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4717]) ).
thf(4832,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
| ! [SY1844: $i] :
( ~ ( in @ SY1844 @ SV264 )
| ~ ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1844 ) @ SV829 )
| ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1844 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4718]) ).
thf(4833,plain,
! [SV553: $i,SV829: $i,SV264: $i] :
( ( ( ! [SY1656: $i] :
( ~ ( in @ SY1656 @ SV264 )
| ! [SY1657: $i] :
( ~ ( in @ SY1657 @ SV264 )
| ~ ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV829 )
| ( in @ ( kpair @ SY1656 @ SY1657 ) @ SV553 ) ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4719]) ).
thf(4834,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
| ! [SY1845: $i] :
( ~ ( in @ SY1845 @ SV264 )
| ~ ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1845 ) @ SV829 )
| ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1845 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4720]) ).
thf(4835,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( ~ ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) )
= $false )
| ( ( ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4722]) ).
thf(4836,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4722]) ).
thf(4837,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK115_SY752 @ SV834 @ SV284 ) )
| ~ ! [SY1834: $i] :
( ~ ( SV284 @ SY1834 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SY1834 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4723]) ).
thf(4838,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK106_SY752 @ SV834 @ SV284 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4724]) ).
thf(4839,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ! [SY1822: $i] :
( ~ ( SV284 @ SY1822 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SY1822 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4724]) ).
thf(4840,plain,
! [SV315: $i,SV972: $o,SV848: $i,SV597: $i,SV985: $i] :
( ( ( in @ SV985 @ SV597 )
= $true )
| ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 )
| SV972 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4729]) ).
thf(4841,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 ) )
= $true )
| ( SV972 = $true )
| ( SV972 = $false )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4730]) ).
thf(4842,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( ( in @ SV986 @ SV597 )
= $true )
| ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true )
| $true )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4731]) ).
thf(4843,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4732]) ).
thf(4844,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( ( in @ SV987 @ SV597 )
= $true )
| ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false )
| $false )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4733]) ).
thf(4845,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4734]) ).
thf(4846,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1034: $i,SV335: $i,SV1071: $i] :
( ( ( ~ ( in @ SV1071 @ SV335 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV614 ) )
= $true )
| ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4736]) ).
thf(4847,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1024: $i,SV335: $i,SV1066: $i] :
( ( ( in @ SV1066 @ SV335 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV858 )
| ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV614 ) )
= $true )
| ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4737]) ).
thf(4848,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) )
| ~ ( in @ ( kpair @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV994 ) @ SV768 ) ) )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4739]) ).
thf(4849,plain,
! [SV73: $i,SV780: $i,SV1056: $i] :
( ( ( ~ ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) ) )
= $true )
| ( ( ~ ( in @ SV1056 @ SV73 ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4741]) ).
thf(4850,plain,
! [SV1067: $o,SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ! [SY1835: $i] :
( ~ ( in @ SY1835 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SY1835 ) @ SV408 )
| ~ ( in @ ( kpair @ SY1835 @ SV996 ) @ SV787 )
| SV1067 ) )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4748]) ).
thf(4851,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4749]) ).
thf(4852,plain,
! [SV787: $i,SV996: $i,SV408: $i,SV939: $i,SV99: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ SX0 ) @ SV408 )
| ~ ( in @ ( kpair @ SX0 @ SV996 ) @ SV787 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4750]) ).
thf(4853,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1057 ) )
= $true )
| ( ( ~ ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4751]) ).
thf(4854,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1058 ) )
= $true )
| ( ( ~ ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4752]) ).
thf(4855,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) )
| ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4753]) ).
thf(4856,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) )
| ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4754]) ).
thf(4857,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4755]) ).
thf(4858,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4756]) ).
thf(4859,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4757]) ).
thf(4860,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4758]) ).
thf(4861,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4759]) ).
thf(4862,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(4863,plain,
! [SV118: $i,SV1025: $i,SV425: $i > $o] :
( ( ( SV425 @ SV1025 )
= $false )
| ( ( in @ SV1025 @ SV118 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( in @ ( sK40_SY1605 @ SV425 @ SV118 ) @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4763]) ).
thf(4864,plain,
! [SV425: $i > $o,SV118: $i,SV1037: $i] :
( ( ( in @ SV1037 @ SV118 )
= $false )
| ( ( ~ ( SV425 @ SV1037 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4764]) ).
thf(4865,plain,
! [SV425: $i > $o,SV118: $i,SV1059: $i] :
( ( ( ~ ( in @ SV1059 @ SV118 ) )
= $true )
| ( ( ~ ( SV425 @ SV1059 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4765]) ).
thf(4866,plain,
! [SV425: $i > $o,SV118: $i,SV1038: $i] :
( ( ( in @ SV1038 @ SV118 )
= $false )
| ( ( ~ ( SV425 @ SV1038 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4867,plain,
! [SV119: $i,SV1026: $i,SV426: $i > $i,SV876: $i] :
( ( ( SV876
= ( SV426 @ SV1026 ) )
= $false )
| ( ( in @ SV1026 @ SV119 )
= $false )
| ( ( in @ SV876 @ ( sK7_SY1036 @ SV426 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4769]) ).
thf(4868,plain,
! [SV795: $i,SV1039: $i,SV1060: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV1060 ) )
= $true )
| ( ( SV1039 = SV1060 )
= $true )
| ( ( SV136 @ SV1039 )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4771]) ).
thf(4869,plain,
! [SV795: $i,SV1027: $i,SV1040: $i,SV136: $i > $o] :
( ( ( SV136 @ SV1040 )
= $false )
| ( ( SV1027 = SV1040 )
= $true )
| ( ( SV136 @ SV1027 )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV795
= ( sK78_SY1610 @ SV795 @ SV136 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4870,plain,
! [SV796: $i,SV1041: $i,SV1061: $i,SV138: $i > $o] :
( ( ( ~ ( SV138 @ SV1061 ) )
= $true )
| ( ( SV1041 = SV1061 )
= $true )
| ( ( SV138 @ SV1041 )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4773]) ).
thf(4871,plain,
! [SV796: $i,SV1028: $i,SV1042: $i,SV138: $i > $o] :
( ( ( SV138 @ SV1042 )
= $false )
| ( ( SV1028 = SV1042 )
= $true )
| ( ( SV138 @ SV1028 )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV796
= ( sK79_SY1611 @ SV796 @ SV138 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4774]) ).
thf(4872,plain,
! [SV140: $i,SV977: $i,SV445: $i > $i] :
( ( ( ~ ( in @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) @ SV140 )
| ( SV977
!= ( SV445 @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4775]) ).
thf(4873,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i,SV1068: $i] :
( ( ( ~ ( in @ SV1068 @ SV140 )
| ( SV977
!= ( SV445 @ SV1068 ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4776]) ).
thf(4874,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4777]) ).
thf(4875,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i,SV1075: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1075 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SV1075 ) ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4778]) ).
thf(4876,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK108_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV149 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4780]) ).
thf(4877,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV149 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4782]) ).
thf(4878,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( ~ ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 ) )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4783]) ).
thf(4879,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV454 )
= $false )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4783]) ).
thf(4880,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK109_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV800 )
= $false )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4785]) ).
thf(4881,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ ( sK110_SY401 @ SV802 @ SV155 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4787]) ).
thf(4882,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ~ ! [SY1825: $i] :
( ~ ( SV155 @ SY1825 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SY1825 ) ) )
= $false )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4787]) ).
thf(4883,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( SV155 @ ( sK98_SY401 @ SV802 @ SV155 ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4788]) ).
thf(4884,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ! [SY1813: $i] :
( ~ ( SV155 @ SY1813 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SY1813 ) ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4789]) ).
thf(4885,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ ( sK99_SY432 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4790]) ).
thf(4886,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY1814: $i] :
( ~ ( SV166 @ SY1814 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SY1814 ) ) )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4791]) ).
thf(4887,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ ( sK111_SY432 @ SV805 @ SV166 ) ) )
= $false )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4792]) ).
thf(4888,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ~ ! [SY1826: $i] :
( ~ ( SV166 @ SY1826 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SY1826 ) ) )
= $false )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4792]) ).
thf(4889,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ ( sK100_SY432 @ SV805 @ SV166 ) )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4793]) ).
thf(4890,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY1815: $i] :
( ~ ( SV166 @ SY1815 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SY1815 ) ) )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4794]) ).
thf(4891,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV1072 )
| ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) ) )
| ~ ( ( SV1072
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1072 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4795]) ).
thf(4892,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV1069 )
| ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4893,plain,
! [SV167: $i > $o,SV806: $i,SV1069: $i] :
( ( ( ~ ( ( SV1069
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1069 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4796]) ).
thf(4894,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4797]) ).
thf(4895,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
| ~ ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4798]) ).
thf(4896,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
| ! [SY1846: $i] :
( ~ ( in @ SY1846 @ SV470 )
| ~ ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1846 ) @ SV887 )
| ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1846 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4799]) ).
thf(4897,plain,
! [SV678: $i,SV887: $i,SV470: $i,SV168: $i] :
( ( ( ! [SY1713: $i] :
( ~ ( in @ SY1713 @ SV168 )
| ! [SY1714: $i] :
( ~ ( in @ SY1714 @ SV470 )
| ~ ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV887 )
| ( in @ ( kpair @ SY1713 @ SY1714 ) @ SV678 ) ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(4898,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
| ! [SY1847: $i] :
( ~ ( in @ SY1847 @ SV470 )
| ~ ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1847 ) @ SV887 )
| ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1847 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4801]) ).
thf(4899,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( ~ ( SV174 @ ( sK123_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1839: $i] :
( ~ ( SV174 @ SY1839 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SY1839 ) ) ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4802]) ).
thf(4900,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK120_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1837: $i] :
( ~ ( SV174 @ SY1837 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SY1837 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4803]) ).
thf(4901,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK121_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1838: $i] :
( ~ ( SV174 @ SY1838 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SY1838 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4804]) ).
thf(4902,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK113_SY462 @ SV808 @ SV174 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4805]) ).
thf(4903,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ! [SY1828: $i] :
( ~ ( SV174 @ SY1828 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SY1828 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4805]) ).
thf(4904,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4807]) ).
thf(4905,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i,SV1076: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1076 @ SV489 )
| ~ ( SV191 @ SV1076 @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4808]) ).
thf(4906,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i] :
( ( ( ~ ! [SY1848: $i] :
~ ( ~ ( ~ ( in @ SY1848 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1848 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1848 ) )
| ( in @ SY1848 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4809]) ).
thf(4907,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i] :
( ( ( ! [SY1840: $i] :
~ ( ~ ( ~ ( in @ SY1840 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1840 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1840 ) )
| ( in @ SY1840 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4810]) ).
thf(4908,plain,
! [SV212: $i,SV1047: $i,SV1073: $i] :
( ( ( ~ ( in @ SV1073 @ SV1047 ) )
= $true )
| ( ( in @ SV1073 @ SV212 )
= $true )
| ( ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(4909,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ SV212 )
| ~ ( in @ SV1063 @ SV212 ) )
= $true )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4812]) ).
thf(4910,plain,
! [SV1005: $i,SV212: $i,SV1021: $i] :
( ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) )
| ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4813]) ).
thf(4911,plain,
! [SV212: $i,SV955: $i] :
( ( ( ! [SY1755: $i] :
~ ( in @ SY1755 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4814]) ).
thf(4912,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( in @ SV1077 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4815]) ).
thf(4913,plain,
! [SV982: $i,SV702: $i > $i > $o,SV215: $i,SV1064: $i,SV509: $i] :
( ( ( ~ ( reflwellordering @ SV509 @ SV1064 ) )
= $true )
| ( ( ! [SY1830: $i] :
( ~ ( in @ SY1830 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1831: $i] :
~ ( ~ ( SV702 @ SY1830 @ SY1831 )
| ~ ! [SY1832: $i] :
( ~ ( in @ SY1832 @ SV509 )
| ~ ( SV702 @ SY1830 @ SY1832 )
| ( in @ ( kpair @ SY1831 @ SY1832 ) @ SV1064 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(4914,plain,
! [SV234: $i,SV822: $i,SV1006: $i,SV523: $i,SV1052: $i,SV956: $i] :
( ( ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
| ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) ) )
= $true )
| ( ( in @ SV1052 @ SV234 )
= $false )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4817]) ).
thf(4915,plain,
! [SV245: $i,SV1033: $i,SV534: $i > $o] :
( ( ( SV534 @ SV1033 )
= $false )
| ( ( in @ SV1033 @ SV245 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( in @ ( sK44_SY1645 @ SV534 @ SV245 ) @ SV245 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4916,plain,
! [SV534: $i > $o,SV245: $i,SV1053: $i] :
( ( ( in @ SV1053 @ SV245 )
= $false )
| ( ( ~ ( SV534 @ SV1053 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(4917,plain,
! [SV534: $i > $o,SV245: $i,SV1065: $i] :
( ( ( ~ ( in @ SV1065 @ SV245 ) )
= $true )
| ( ( ~ ( SV534 @ SV1065 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4820]) ).
thf(4918,plain,
! [SV534: $i > $o,SV245: $i,SV1054: $i] :
( ( ( in @ SV1054 @ SV245 )
= $false )
| ( ( ~ ( SV534 @ SV1054 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(4919,plain,
! [SV255: $i,SV826: $i,SV1070: $o,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| SV1070 )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(4920,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(4921,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4922,plain,
! [SV1022: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
| ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4825]) ).
thf(4923,plain,
! [SV550: $i > $o,SV260: $i > $o] :
( ( ( ! [SY694: $i] :
~ ~ ( ~ ( SV260 @ SY694 )
| ~ ! [SY695: $i] :
( ~ ( SV260 @ SY695 )
| ( SY694 = SY695 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4826]) ).
thf(4924,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( ~ ~ ( ~ ( SV260 @ SV1078 )
| ~ ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4827]) ).
thf(4925,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( ~ ~ ( ~ ( SV260 @ SV1079 )
| ~ ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4828]) ).
thf(4926,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ SV1074 )
| ~ ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4829]) ).
thf(4927,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4831]) ).
thf(4928,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4831]) ).
thf(4929,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4832]) ).
thf(4930,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ! [SY1844: $i] :
( ~ ( in @ SY1844 @ SV264 )
| ~ ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1844 ) @ SV829 )
| ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1844 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4832]) ).
thf(4931,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
| ! [SY1853: $i] :
( ~ ( in @ SY1853 @ SV264 )
| ~ ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1853 ) @ SV829 )
| ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1853 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4833]) ).
thf(4932,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4834]) ).
thf(4933,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ! [SY1845: $i] :
( ~ ( in @ SY1845 @ SV264 )
| ~ ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1845 ) @ SV829 )
| ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1845 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4834]) ).
thf(4934,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $true )
| ( ( ~ ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4835]) ).
thf(4935,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) )
= $false )
| ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4836]) ).
thf(4936,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ ( sK115_SY752 @ SV834 @ SV284 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4937,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ~ ! [SY1834: $i] :
( ~ ( SV284 @ SY1834 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SY1834 ) ) )
= $false )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4938,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( SV284 @ ( sK106_SY752 @ SV834 @ SV284 ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4838]) ).
thf(4939,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ! [SY1822: $i] :
( ~ ( SV284 @ SY1822 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SY1822 ) ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4839]) ).
thf(4940,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( ~ ( in @ SV985 @ SV848 )
| SV972 ) )
= $true )
| ( SV972 = $true )
| ( ( in @ SV985 @ SV597 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4840]) ).
thf(4941,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV848 )
| SV972 )
= $false )
| ( SV972 = $true )
| ( SV972 = $false )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4841]) ).
thf(4942,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( ~ ( in @ SV986 @ SV848 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV986 @ SV597 )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(4943,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV848 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4944,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( ~ ( in @ SV987 @ SV848 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV987 @ SV597 )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4844]) ).
thf(4945,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV848 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(4946,plain,
! [SV11: $i,SV614: $i,SV858: $i,SV1034: $i,SV335: $i,SV1071: $i] :
( ( ( in @ SV1071 @ SV335 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV858 )
| ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV614 ) )
= $true )
| ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4846]) ).
thf(4947,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i,SV1066: $i,SV1024: $i] :
( ( ( ~ ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV858 ) )
= $true )
| ( ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV614 )
= $true )
| ( ( in @ SV1066 @ SV335 )
= $false )
| ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4847]) ).
thf(4948,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) )
| ~ ( in @ ( kpair @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV994 ) @ SV768 ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(4949,plain,
! [SV73: $i,SV780: $i,SV1056: $i] :
( ( ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) )
= $false )
| ( ( ~ ( in @ SV1056 @ SV73 ) )
= $true )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(4950,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( ~ ( in @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| SV1067 )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4850]) ).
thf(4951,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4851]) ).
thf(4952,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
| ~ ( in @ ( kpair @ SV939 @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4852]) ).
thf(4953,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4954,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4854]) ).
thf(4955,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4855]) ).
thf(4956,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4856]) ).
thf(4957,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4857]) ).
thf(4958,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4858]) ).
thf(4959,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4859]) ).
thf(4960,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4860]) ).
thf(4961,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4861]) ).
thf(4962,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4862]) ).
thf(4963,plain,
! [SV118: $i,SV1037: $i,SV425: $i > $o] :
( ( ( SV425 @ SV1037 )
= $false )
| ( ( in @ SV1037 @ SV118 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK14_SY1032 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4864]) ).
thf(4964,plain,
! [SV425: $i > $o,SV118: $i,SV1059: $i] :
( ( ( in @ SV1059 @ SV118 )
= $false )
| ( ( ~ ( SV425 @ SV1059 ) )
= $true )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(4965,plain,
! [SV118: $i,SV1038: $i,SV425: $i > $o] :
( ( ( SV425 @ SV1038 )
= $false )
| ( ( in @ SV1038 @ SV118 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( ( sK14_SY1032 @ SV425 @ SV118 )
= ( sK40_SY1605 @ SV425 @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4866]) ).
thf(4966,plain,
! [SV795: $i,SV1039: $i,SV1060: $i,SV136: $i > $o] :
( ( ( SV136 @ SV1060 )
= $false )
| ( ( SV1039 = SV1060 )
= $true )
| ( ( SV136 @ SV1039 )
= $false )
| ( ( SV136 @ SV795 )
= $false )
| ( ( SV136 @ ( sK78_SY1610 @ SV795 @ SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4868]) ).
thf(4967,plain,
! [SV796: $i,SV1041: $i,SV1061: $i,SV138: $i > $o] :
( ( ( SV138 @ SV1061 )
= $false )
| ( ( SV1041 = SV1061 )
= $true )
| ( ( SV138 @ SV1041 )
= $false )
| ( ( SV138 @ SV796 )
= $false )
| ( ( SV138 @ ( sK79_SY1611 @ SV796 @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4870]) ).
thf(4968,plain,
! [SV140: $i,SV977: $i,SV445: $i > $i] :
( ( ( ~ ( in @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) @ SV140 ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4872]) ).
thf(4969,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ( SV977
!= ( SV445 @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) ) )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4872]) ).
thf(4970,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i,SV1068: $i] :
( ( ( ~ ( in @ SV1068 @ SV140 ) )
= $true )
| ( ( SV977
!= ( SV445 @ SV1068 ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4873]) ).
thf(4971,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4874]) ).
thf(4972,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4874]) ).
thf(4973,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i,SV1075: $i] :
( ( ( ~ ( ~ ( in @ SV1075 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SV1075 ) ) ) )
= $false )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4875]) ).
thf(4974,plain,
! [SV149: $i,SV800: $i,SV454: $i] :
( ( ( in @ ( sK118_SY1619 @ SV454 @ SV800 @ SV149 ) @ SV800 )
= $true )
| ( ( SV454 = SV800 )
= $true )
| ( ( in @ ( sK65_SY1618 @ SV800 @ SV454 @ SV149 ) @ SV454 )
= $true )
| ( ( in @ SV800 @ ( powerset @ SV149 ) )
= $false )
| ( ( in @ SV454 @ ( powerset @ SV149 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4878]) ).
thf(4975,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( SV155 @ ( sK110_SY401 @ SV802 @ SV155 ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4881]) ).
thf(4976,plain,
! [SV802: $i,SV155: $i > $o] :
( ( ( ! [SY1825: $i] :
( ~ ( SV155 @ SY1825 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SY1825 ) ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4882]) ).
thf(4977,plain,
! [SV802: $i,SV1080: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV1080 )
| ( ( sK98_SY401 @ SV802 @ SV155 )
= SV1080 ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4884]) ).
thf(4978,plain,
! [SV805: $i,SV1081: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1081 )
| ( ( sK99_SY432 @ SV805 @ SV166 )
= SV1081 ) )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4886]) ).
thf(4979,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( SV166 @ ( sK111_SY432 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4887]) ).
thf(4980,plain,
! [SV805: $i,SV166: $i > $o] :
( ( ( ! [SY1826: $i] :
( ~ ( SV166 @ SY1826 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SY1826 ) ) )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4888]) ).
thf(4981,plain,
! [SV805: $i,SV1082: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1082 )
| ( ( sK100_SY432 @ SV805 @ SV166 )
= SV1082 ) )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4890]) ).
thf(4982,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( ~ ( ~ ( SV167 @ SV1072 )
| ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4983,plain,
! [SV167: $i > $o,SV806: $i,SV1072: $i] :
( ( ( ~ ( ( SV1072
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1072 ) ) )
= $false )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4984,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV1069 )
| ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4892]) ).
thf(4985,plain,
! [SV167: $i > $o,SV806: $i,SV1069: $i] :
( ( ( ( SV1069
!= ( sK101_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1069 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4893]) ).
thf(4986,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4895]) ).
thf(4987,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4895]) ).
thf(4988,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4896]) ).
thf(4989,plain,
! [SV168: $i,SV887: $i,SV678: $i,SV470: $i] :
( ( ( ! [SY1846: $i] :
( ~ ( in @ SY1846 @ SV470 )
| ~ ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1846 ) @ SV887 )
| ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1846 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4896]) ).
thf(4990,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
| ! [SY1854: $i] :
( ~ ( in @ SY1854 @ SV470 )
| ~ ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1854 ) @ SV887 )
| ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1854 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4897]) ).
thf(4991,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(4992,plain,
! [SV168: $i,SV887: $i,SV678: $i,SV470: $i] :
( ( ( ! [SY1847: $i] :
( ~ ( in @ SY1847 @ SV470 )
| ~ ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1847 ) @ SV887 )
| ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1847 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4898]) ).
thf(4993,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK123_SY462 @ SV808 @ SV174 ) )
| ~ ! [SY1839: $i] :
( ~ ( SV174 @ SY1839 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SY1839 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4899]) ).
thf(4994,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK120_SY462 @ SV808 @ SV174 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4900]) ).
thf(4995,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ! [SY1837: $i] :
( ~ ( SV174 @ SY1837 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SY1837 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4900]) ).
thf(4996,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK121_SY462 @ SV808 @ SV174 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4901]) ).
thf(4997,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ! [SY1838: $i] :
( ~ ( SV174 @ SY1838 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SY1838 ) ) )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4901]) ).
thf(4998,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK113_SY462 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4902]) ).
thf(4999,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY1828: $i] :
( ~ ( SV174 @ SY1828 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SY1828 ) ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4903]) ).
thf(5000,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( ~ ( in @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV1003 ) ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4904]) ).
thf(5001,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i,SV1076: $i] :
( ( ( ~ ( ~ ( in @ SV1076 @ SV489 )
| ~ ( SV191 @ SV1076 @ SV1003 ) ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4905]) ).
thf(5002,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i] :
( ( ( ! [SY1848: $i] :
~ ( ~ ( ~ ( in @ SY1848 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1169: $i] :
~ ~ ( ~ ( in @ SY1169 @ SV489 )
| ~ ( SV191 @ SY1169 @ SY1848 ) ) )
| ~ ( ~ ~ ! [SY1170: $i] :
~ ~ ( ~ ( in @ SY1170 @ SV489 )
| ~ ( SV191 @ SY1170 @ SY1848 ) )
| ( in @ SY1848 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4906]) ).
thf(5003,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
| ~ ( ~ ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) )
| ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4907]) ).
thf(5004,plain,
! [SV212: $i,SV1047: $i,SV1073: $i] :
( ( ( in @ SV1073 @ SV1047 )
= $false )
| ( ( in @ SV1073 @ SV212 )
= $true )
| ( ( in @ SV1047 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4908]) ).
thf(5005,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ SV212 ) )
= $true )
| ( ( ~ ( in @ SV1063 @ SV212 ) )
= $true )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4909]) ).
thf(5006,plain,
! [SV212: $i,SV1021: $i,SV1005: $i] :
( ( ( ! [SY1804: $i] :
( ~ ( in @ SY1804 @ SV1005 )
| ( in @ SY1804 @ SV1021 ) ) )
= $true )
| ( ( ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4910]) ).
thf(5007,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( in @ SV1084 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4911]) ).
thf(5008,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( in @ SV1077 @ SV955 )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4912]) ).
thf(5009,plain,
! [SV982: $i,SV702: $i > $i > $o,SV215: $i,SV1064: $i,SV509: $i] :
( ( ( reflwellordering @ SV509 @ SV1064 )
= $false )
| ( ( ! [SY1830: $i] :
( ~ ( in @ SY1830 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1831: $i] :
~ ( ~ ( SV702 @ SY1830 @ SY1831 )
| ~ ! [SY1832: $i] :
( ~ ( in @ SY1832 @ SV509 )
| ~ ( SV702 @ SY1830 @ SY1832 )
| ( in @ ( kpair @ SY1831 @ SY1832 ) @ SV1064 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4913]) ).
thf(5010,plain,
! [SV523: $i,SV234: $i,SV956: $i,SV822: $i,SV1006: $i,SV1052: $i] :
( ( ( ~ ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 ) )
= $true )
| ( ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) )
= $true )
| ( ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
= $false )
| ( ( in @ SV1052 @ SV234 )
= $false )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4914]) ).
thf(5011,plain,
! [SV245: $i,SV1053: $i,SV534: $i > $o] :
( ( ( SV534 @ SV1053 )
= $false )
| ( ( in @ SV1053 @ SV245 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK20_SY1240 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4916]) ).
thf(5012,plain,
! [SV534: $i > $o,SV245: $i,SV1065: $i] :
( ( ( in @ SV1065 @ SV245 )
= $false )
| ( ( ~ ( SV534 @ SV1065 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4917]) ).
thf(5013,plain,
! [SV245: $i,SV1054: $i,SV534: $i > $o] :
( ( ( SV534 @ SV1054 )
= $false )
| ( ( in @ SV1054 @ SV245 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( ( sK20_SY1240 @ SV534 @ SV245 )
= ( sK44_SY1645 @ SV534 @ SV245 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4918]) ).
thf(5014,plain,
! [SV255: $i,SV1070: $o,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4919]) ).
thf(5015,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i,SV1070: $o] :
( ( SV1070 = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4919]) ).
thf(5016,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4920]) ).
thf(5017,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4920]) ).
thf(5018,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4921]) ).
thf(5019,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4921]) ).
thf(5020,plain,
! [SV1022: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4922]) ).
thf(5021,plain,
! [SV260: $i > $o,SV550: $i > $o,SV1022: $i] :
( ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4922]) ).
thf(5022,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( ~ ~ ( ~ ( SV260 @ SV1085 )
| ~ ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4923]) ).
thf(5023,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ SV1078 )
| ~ ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4924]) ).
thf(5024,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ SV1079 )
| ~ ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4925]) ).
thf(5025,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1074 )
| ~ ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4926]) ).
thf(5026,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4927]) ).
thf(5027,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4928]) ).
thf(5028,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV553 )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4928]) ).
thf(5029,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4929]) ).
thf(5030,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) @ SV264 )
| ~ ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4930]) ).
thf(5031,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4931]) ).
thf(5032,plain,
! [SV829: $i,SV553: $i,SV264: $i] :
( ( ( ! [SY1853: $i] :
( ~ ( in @ SY1853 @ SV264 )
| ~ ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1853 ) @ SV829 )
| ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SY1853 ) @ SV553 ) ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4931]) ).
thf(5033,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4932]) ).
thf(5034,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) @ SV264 )
| ~ ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4933]) ).
thf(5035,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
| ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) ) )
= $false )
| ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4934]) ).
thf(5036,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
= $false )
| ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4935]) ).
thf(5037,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $false )
| ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4935]) ).
thf(5038,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( SV284 @ ( sK115_SY752 @ SV834 @ SV284 ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4936]) ).
thf(5039,plain,
! [SV834: $i,SV284: $i > $o] :
( ( ( ! [SY1834: $i] :
( ~ ( SV284 @ SY1834 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SY1834 ) ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4937]) ).
thf(5040,plain,
! [SV834: $i,SV1086: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV1086 )
| ( ( sK106_SY752 @ SV834 @ SV284 )
= SV1086 ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4939]) ).
thf(5041,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV848 )
| SV972 )
= $false )
| ( SV972 = $true )
| ( ( in @ SV985 @ SV597 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4940]) ).
thf(5042,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV848 ) )
= $false )
| ( SV972 = $true )
| ( SV972 = $false )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4941]) ).
thf(5043,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV985: $i,SV972: $o] :
( ( SV972 = $false )
| ( SV972 = $true )
| ( SV972 = $false )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4941]) ).
thf(5044,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV848 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV986 @ SV597 )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4942]) ).
thf(5045,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV848 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4943]) ).
thf(5046,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4943]) ).
thf(5047,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV848 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV987 @ SV597 )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4944]) ).
thf(5048,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV848 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5049,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4945]) ).
thf(5050,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i,SV1071: $i,SV1034: $i] :
( ( ( ~ ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV858 ) )
= $true )
| ( ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV614 )
= $true )
| ( ( in @ SV1071 @ SV335 )
= $false )
| ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4946]) ).
thf(5051,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i,SV1066: $i,SV1024: $i] :
( ( ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV858 )
= $false )
| ( ( in @ ( kpair @ SV1024 @ SV1066 ) @ SV614 )
= $true )
| ( ( in @ SV1066 @ SV335 )
= $false )
| ( ( in @ SV1024 @ SV11 )
= $false )
| ( ( ( ap @ SV11 @ SV335 @ SV614 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) )
= ( ap @ SV11 @ SV335 @ SV858 @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) ) )
= $false )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4947]) ).
thf(5052,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5053,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV994 ) @ SV768 ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(5054,plain,
! [SV780: $i,SV73: $i,SV1056: $i] :
( ( ( in @ SV1056 @ SV73 )
= $false )
| ( ( in @ SV1056 @ ( sK45_SY168 @ SV780 @ SV73 ) )
= $false )
| ( ( in @ SV780 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4949]) ).
thf(5055,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( ~ ( in @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 ) )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4950]) ).
thf(5056,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| SV1067 )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4950]) ).
thf(5057,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4951]) ).
thf(5058,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4951]) ).
thf(5059,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4952]) ).
thf(5060,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
| ~ ( in @ ( kpair @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4952]) ).
thf(5061,plain,
! [SV415: $i > $o,SV1057: $i,SV107: $i > $o] :
( ( ( ! [SY1823: $i] :
( ~ ( SV107 @ SY1823 )
| ( SV1057 = SY1823 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4953]) ).
thf(5062,plain,
! [SV107: $i > $o,SV1058: $i,SV415: $i > $o] :
( ( ( ! [SY1824: $i] :
( ~ ( SV415 @ SY1824 )
| ( SV1058 = SY1824 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(5063,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4955]) ).
thf(5064,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(5065,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4957]) ).
thf(5066,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4958]) ).
thf(5067,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4959]) ).
thf(5068,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4960]) ).
thf(5069,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV1087 )
| ~ ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4961]) ).
thf(5070,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ SV1088 )
| ~ ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4962]) ).
thf(5071,plain,
! [SV118: $i,SV1059: $i,SV425: $i > $o] :
( ( ( SV425 @ SV1059 )
= $false )
| ( ( in @ SV1059 @ SV118 )
= $false )
| ( ( ex1 @ SV118
@ ^ [SY1035: $i] : ( SV425 @ SY1035 ) )
= $true )
| ( ( SV425 @ ( sK40_SY1605 @ SV425 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4964]) ).
thf(5072,plain,
! [SV140: $i,SV977: $i,SV445: $i > $i] :
( ( ( in @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) @ SV140 )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4968]) ).
thf(5073,plain,
! [SV140: $i,SV445: $i > $i,SV977: $i] :
( ( ( SV977
= ( SV445 @ ( sK117_SY1772 @ SV445 @ SV977 @ SV140 ) ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4969]) ).
thf(5074,plain,
! [SV445: $i > $i,SV977: $i,SV140: $i,SV1068: $i] :
( ( ( in @ SV1068 @ SV140 )
= $false )
| ( ( SV977
!= ( SV445 @ SV1068 ) )
= $true )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4970]) ).
thf(5075,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $true )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4971]) ).
thf(5076,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i,SV1075: $i] :
( ( ( ~ ( in @ SV1075 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SV1075 ) ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4973]) ).
thf(5077,plain,
! [SV802: $i,SV1089: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV1089 )
| ( ( sK110_SY401 @ SV802 @ SV155 )
= SV1089 ) )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4976]) ).
thf(5078,plain,
! [SV802: $i,SV1080: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV1080 ) )
= $true )
| ( ( ( sK98_SY401 @ SV802 @ SV155 )
= SV1080 )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4977]) ).
thf(5079,plain,
! [SV805: $i,SV1081: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1081 ) )
= $true )
| ( ( ( sK99_SY432 @ SV805 @ SV166 )
= SV1081 )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4978]) ).
thf(5080,plain,
! [SV805: $i,SV1090: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1090 )
| ( ( sK111_SY432 @ SV805 @ SV166 )
= SV1090 ) )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4980]) ).
thf(5081,plain,
! [SV805: $i,SV1082: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1082 ) )
= $true )
| ( ( ( sK100_SY432 @ SV805 @ SV166 )
= SV1082 )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4981]) ).
thf(5082,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV1072 )
| ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4982]) ).
thf(5083,plain,
! [SV167: $i > $o,SV806: $i,SV1072: $i] :
( ( ( ( SV1072
!= ( sK112_SY436 @ SV806 @ SV167 ) )
| ( SV167 @ SV1072 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4983]) ).
thf(5084,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV1069 ) )
= $true )
| ( ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4984]) ).
thf(5085,plain,
! [SV167: $i > $o,SV806: $i,SV1069: $i] :
( ( ( SV1069
!= ( sK101_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV1069 )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4985]) ).
thf(5086,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( in @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4986]) ).
thf(5087,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4987]) ).
thf(5088,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4987]) ).
thf(5089,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4988]) ).
thf(5090,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
| ~ ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4989]) ).
thf(5091,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4990]) ).
thf(5092,plain,
! [SV168: $i,SV887: $i,SV678: $i,SV470: $i] :
( ( ( ! [SY1854: $i] :
( ~ ( in @ SY1854 @ SV470 )
| ~ ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1854 ) @ SV887 )
| ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SY1854 ) @ SV678 ) ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4990]) ).
thf(5093,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4991]) ).
thf(5094,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
| ~ ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4992]) ).
thf(5095,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ ( sK123_SY462 @ SV808 @ SV174 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4993]) ).
thf(5096,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ~ ! [SY1839: $i] :
( ~ ( SV174 @ SY1839 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SY1839 ) ) )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4993]) ).
thf(5097,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK120_SY462 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4994]) ).
thf(5098,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY1837: $i] :
( ~ ( SV174 @ SY1837 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SY1837 ) ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4995]) ).
thf(5099,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK121_SY462 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4996]) ).
thf(5100,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY1838: $i] :
( ~ ( SV174 @ SY1838 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SY1838 ) ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4997]) ).
thf(5101,plain,
! [SV808: $i,SV1091: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1091 )
| ( ( sK113_SY462 @ SV808 @ SV174 )
= SV1091 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4999]) ).
thf(5102,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV1003 ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5000]) ).
thf(5103,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i,SV1076: $i] :
( ( ( ~ ( in @ SV1076 @ SV489 )
| ~ ( SV191 @ SV1076 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5001]) ).
thf(5104,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
| ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) )
| ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5002]) ).
thf(5105,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( ~ ( ~ ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
| ~ ( ~ ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) )
| ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5003]) ).
thf(5106,plain,
! [SV1063: $i,SV212: $i,SV1048: $i] :
( ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( ~ ( in @ SV1063 @ SV212 ) )
= $true )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5005]) ).
thf(5107,plain,
! [SV212: $i,SV1021: $i,SV1005: $i,SV1093: $i] :
( ( ( ~ ( in @ SV1093 @ SV1005 )
| ( in @ SV1093 @ SV1021 ) )
= $true )
| ( ( ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5006]) ).
thf(5108,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( in @ SV1084 @ SV955 )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( ~ ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5109,plain,
! [SV1077: $i,SV955: $i,SV212: $i] :
( ( ( ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5110,plain,
! [SV982: $i,SV1064: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1094: $i] :
( ( ( ~ ( in @ SV1094 @ SV215 )
| ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1862: $i] :
~ ( ~ ( SV702 @ SV1094 @ SY1862 )
| ~ ! [SY1863: $i] :
( ~ ( in @ SY1863 @ SV509 )
| ~ ( SV702 @ SV1094 @ SY1863 )
| ( in @ ( kpair @ SY1862 @ SY1863 ) @ SV1064 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV1064 )
= $false )
| ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5009]) ).
thf(5111,plain,
! [SV523: $i,SV234: $i,SV956: $i,SV822: $i,SV1006: $i,SV1052: $i] :
( ( ( in @ ( kpair @ SV1052 @ SV1006 ) @ SV822 )
= $false )
| ( ( in @ ( kpair @ SV956 @ SV1006 ) @ ( breln1compset @ SV234 @ SV523 @ SV822 ) )
= $true )
| ( ( in @ ( kpair @ SV956 @ SV1052 ) @ SV523 )
= $false )
| ( ( in @ SV1052 @ SV234 )
= $false )
| ( ( in @ SV1006 @ SV234 )
= $false )
| ( ( in @ SV956 @ SV234 )
= $false )
| ( ( breln1 @ SV234 @ SV822 )
= $false )
| ( ( breln1 @ SV234 @ SV523 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5010]) ).
thf(5112,plain,
! [SV245: $i,SV1065: $i,SV534: $i > $o] :
( ( ( SV534 @ SV1065 )
= $false )
| ( ( in @ SV1065 @ SV245 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV245
@ ^ [SY1243: $i] : ( SV534 @ SY1243 ) ) )
= $true )
| ( ( SV534 @ ( sK44_SY1645 @ SV534 @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5012]) ).
thf(5113,plain,
! [SV255: $i,SV1070: $o,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
| SV1070 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5014]) ).
thf(5114,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 ) )
= $true )
| ( SV1070 = $true )
| ( SV1070 = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5015]) ).
thf(5115,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5016]) ).
thf(5116,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5017]) ).
thf(5117,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5018]) ).
thf(5118,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5019]) ).
thf(5119,plain,
! [SV1022: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5020]) ).
thf(5120,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5021]) ).
thf(5121,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( ~ ( ~ ( SV260 @ SV1085 )
| ~ ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5122,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1078 )
| ~ ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5023]) ).
thf(5123,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1079 )
| ~ ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5024]) ).
thf(5124,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1074 ) )
= $true )
| ( ( ~ ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5125,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK114_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK125_SY1833 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5027]) ).
thf(5126,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5030]) ).
thf(5127,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5030]) ).
thf(5128,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5031]) ).
thf(5129,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) @ SV264 )
| ~ ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5032]) ).
thf(5130,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5034]) ).
thf(5131,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5034]) ).
thf(5132,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( ~ ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) ) )
= $false )
| ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5035]) ).
thf(5133,plain,
! [SV283: $i,SV569: $i,SV911: $i > $o,SV833: $i > $o] :
( ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $false )
| ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5035]) ).
thf(5134,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $true )
| ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $false )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5036]) ).
thf(5135,plain,
! [SV834: $i,SV1095: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV1095 )
| ( ( sK115_SY752 @ SV834 @ SV284 )
= SV1095 ) )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5039]) ).
thf(5136,plain,
! [SV834: $i,SV1086: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV1086 ) )
= $true )
| ( ( ( sK106_SY752 @ SV834 @ SV284 )
= SV1086 )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5040]) ).
thf(5137,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ SV848 ) )
= $false )
| ( SV972 = $true )
| ( ( in @ SV985 @ SV597 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5041]) ).
thf(5138,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV985: $i,SV972: $o] :
( ( SV972 = $false )
| ( SV972 = $true )
| ( ( in @ SV985 @ SV597 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5041]) ).
thf(5139,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( in @ SV985 @ SV848 )
= $true )
| ( SV972 = $true )
| ( SV972 = $false )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5042]) ).
thf(5140,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( ~ ( in @ SV986 @ SV848 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV986 @ SV597 )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5044]) ).
thf(5141,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV986: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV986 @ SV597 )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5044]) ).
thf(5142,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( in @ SV986 @ SV848 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5045]) ).
thf(5143,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV848 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV987 @ SV597 )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5047]) ).
thf(5144,plain,
! [SV315: $i,SV848: $i,SV597: $i,SV987: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV987 @ SV597 )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5047]) ).
thf(5145,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( in @ SV987 @ SV848 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5048]) ).
thf(5146,plain,
! [SV11: $i,SV335: $i,SV614: $i,SV858: $i,SV1071: $i,SV1034: $i] :
( ( ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV858 )
= $false )
| ( ( in @ ( kpair @ SV1034 @ SV1071 ) @ SV614 )
= $true )
| ( ( in @ SV1071 @ SV335 )
= $false )
| ( ( in @ SV1034 @ SV11 )
= $false )
| ( ( in @ ( sK75_SY1687 @ SV858 @ SV614 @ SV335 @ SV11 ) @ SV11 )
= $true )
| ( ( func @ SV11 @ SV335 @ SV858 )
= $false )
| ( ( func @ SV11 @ SV335 @ SV614 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5050]) ).
thf(5147,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) ) )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5052]) ).
thf(5148,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( in @ ( kpair @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV994 ) @ SV768 )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5053]) ).
thf(5149,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( in @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
= $true )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5055]) ).
thf(5150,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 ) )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5056]) ).
thf(5151,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| SV1067 )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5056]) ).
thf(5152,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( in @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5057]) ).
thf(5153,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5058]) ).
thf(5154,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5058]) ).
thf(5155,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( in @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV99 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5059]) ).
thf(5156,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( ~ ( in @ ( kpair @ SV939 @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5060]) ).
thf(5157,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5060]) ).
thf(5158,plain,
! [SV1057: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
| ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5061]) ).
thf(5159,plain,
! [SV1058: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
| ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5062]) ).
thf(5160,plain,
! [SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY253: $i] :
~ ~ ( ~ ( SV107 @ SY253 )
| ~ ! [SY254: $i] :
( ~ ( SV107 @ SY254 )
| ( SY253 = SY254 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5063]) ).
thf(5161,plain,
! [SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1014: $i] :
~ ~ ( ~ ( SV415 @ SY1014 )
| ~ ! [SY1015: $i] :
( ~ ( SV415 @ SY1015 )
| ( SY1014 = SY1015 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5064]) ).
thf(5162,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV1096 )
| ~ ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5065]) ).
thf(5163,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ SV1097 )
| ~ ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5066]) ).
thf(5164,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV1098 )
| ~ ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5067]) ).
thf(5165,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ SV1099 )
| ~ ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5068]) ).
thf(5166,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV1087 )
| ~ ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5069]) ).
thf(5167,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ SV1088 )
| ~ ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5070]) ).
thf(5168,plain,
! [SV140: $i,SV1068: $i,SV445: $i > $i,SV977: $i] :
( ( ( SV977
= ( SV445 @ SV1068 ) )
= $false )
| ( ( in @ SV1068 @ SV140 )
= $false )
| ( ( in @ SV977 @ ( sK8_SY1067 @ SV445 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5074]) ).
thf(5169,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5075]) ).
thf(5170,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i,SV1075: $i] :
( ( ( ~ ( in @ SV1075 @ SV140 ) )
= $true )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SV1075 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5076]) ).
thf(5171,plain,
! [SV802: $i,SV1089: $i,SV155: $i > $o] :
( ( ( ~ ( SV155 @ SV1089 ) )
= $true )
| ( ( ( sK110_SY401 @ SV802 @ SV155 )
= SV1089 )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5077]) ).
thf(5172,plain,
! [SV802: $i,SV1080: $i,SV155: $i > $o] :
( ( ( SV155 @ SV1080 )
= $false )
| ( ( ( sK98_SY401 @ SV802 @ SV155 )
= SV1080 )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV802
= ( sK81_SY1621 @ SV802 @ SV155 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5078]) ).
thf(5173,plain,
! [SV805: $i,SV1081: $i,SV166: $i > $o] :
( ( ( SV166 @ SV1081 )
= $false )
| ( ( ( sK99_SY432 @ SV805 @ SV166 )
= SV1081 )
= $true )
| ( ( SV166 @ ( sK56_SY430 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5079]) ).
thf(5174,plain,
! [SV805: $i,SV1090: $i,SV166: $i > $o] :
( ( ( ~ ( SV166 @ SV1090 ) )
= $true )
| ( ( ( sK111_SY432 @ SV805 @ SV166 )
= SV1090 )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5080]) ).
thf(5175,plain,
! [SV805: $i,SV1082: $i,SV166: $i > $o] :
( ( ( SV166 @ SV1082 )
= $false )
| ( ( ( sK100_SY432 @ SV805 @ SV166 )
= SV1082 )
= $true )
| ( ( ( sK56_SY430 @ SV805 @ SV166 )
= ( sK67_SY1777 @ SV805 @ SV166 ) )
= $false )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5176,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( ~ ( SV167 @ SV1072 ) )
= $true )
| ( ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5082]) ).
thf(5177,plain,
! [SV167: $i > $o,SV806: $i,SV1072: $i] :
( ( ( SV1072
!= ( sK112_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV1072 )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5083]) ).
thf(5178,plain,
! [SV806: $i,SV1069: $i,SV167: $i > $o] :
( ( ( SV167 @ SV1069 )
= $false )
| ( ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5084]) ).
thf(5179,plain,
! [SV167: $i > $o,SV806: $i,SV1069: $i] :
( ( ( SV1069
= ( sK101_SY436 @ SV806 @ SV167 ) )
= $false )
| ( ( SV167 @ SV1069 )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV806
= ( sK82_SY1625 @ SV806 @ SV167 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5180,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK119_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK128_SY1836 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5087]) ).
thf(5181,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5090]) ).
thf(5182,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5090]) ).
thf(5183,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ SV168 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5091]) ).
thf(5184,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
| ~ ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5092]) ).
thf(5185,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5186,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5094]) ).
thf(5187,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( SV174 @ ( sK123_SY462 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5095]) ).
thf(5188,plain,
! [SV808: $i,SV174: $i > $o] :
( ( ( ! [SY1839: $i] :
( ~ ( SV174 @ SY1839 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SY1839 ) ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5096]) ).
thf(5189,plain,
! [SV808: $i,SV1100: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1100 )
| ( ( sK120_SY462 @ SV808 @ SV174 )
= SV1100 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5098]) ).
thf(5190,plain,
! [SV808: $i,SV1101: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1101 )
| ( ( sK121_SY462 @ SV808 @ SV174 )
= SV1101 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5100]) ).
thf(5191,plain,
! [SV808: $i,SV1091: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1091 ) )
= $true )
| ( ( ( sK113_SY462 @ SV808 @ SV174 )
= SV1091 )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5192,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( ~ ( in @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV489 ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5193,plain,
! [SV489: $i,SV1003: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV1003 ) )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5194,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i,SV1076: $i] :
( ( ( ~ ( in @ SV1076 @ SV489 ) )
= $true )
| ( ( ~ ( SV191 @ SV1076 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5103]) ).
thf(5195,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( ~ ( ~ ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
| ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) )
| ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5104]) ).
thf(5196,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( ~ ( ~ ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5105]) ).
thf(5197,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ( ~ ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) )
| ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5105]) ).
thf(5198,plain,
! [SV1048: $i,SV212: $i,SV1063: $i] :
( ( ( in @ SV1063 @ SV212 )
= $false )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) )
| ( SV1048 = SV1063 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5106]) ).
thf(5199,plain,
! [SV212: $i,SV1021: $i,SV1005: $i,SV1093: $i] :
( ( ( ~ ( in @ SV1093 @ SV1005 ) )
= $true )
| ( ( in @ SV1093 @ SV1021 )
= $true )
| ( ( ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5200,plain,
! [SV1084: $i,SV955: $i,SV212: $i] :
( ( ( ! [SY1756: $i] :
~ ~ ! [SY1757: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1756 @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1757 @ SV955 ) )
| ~ ~ ~ ! [SY1758: $i] :
~ ~ ( ~ ( in @ SY1758 @ SY1756 )
| ~ ( in @ SY1758 @ SV955 ) ) )
| ~ ! [SY1504: $i] :
( ~ ( in @ SY1504 @ ( sK4_SY557 @ SV212 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY1504 )
| ( in @ SX6 @ SY1756 ) )
| ( in @ SY1757 @ SY1504 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5108]) ).
thf(5201,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ! [SY1868: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1868 @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1870: $i] :
( ~ ( in @ SY1870 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1870 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ SY1868 @ SY1870 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5109]) ).
thf(5202,plain,
! [SV982: $i,SV1064: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1094: $i] :
( ( ( ~ ( in @ SV1094 @ SV215 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1862: $i] :
~ ( ~ ( SV702 @ SV1094 @ SY1862 )
| ~ ! [SY1863: $i] :
( ~ ( in @ SY1863 @ SV509 )
| ~ ( SV702 @ SV1094 @ SY1863 )
| ( in @ ( kpair @ SY1862 @ SY1863 ) @ SV1064 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV1064 )
= $false )
| ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5203,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 ) )
= $true )
| ( SV1070 = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5113]) ).
thf(5204,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
= $false )
| ( SV1070 = $true )
| ( SV1070 = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5114]) ).
thf(5205,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5115]) ).
thf(5206,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5116]) ).
thf(5207,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5117]) ).
thf(5208,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5118]) ).
thf(5209,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5119]) ).
thf(5210,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5211,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1085 )
| ~ ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5121]) ).
thf(5212,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1078 ) )
= $true )
| ( ( ~ ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5122]) ).
thf(5213,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1079 ) )
= $true )
| ( ( ~ ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5123]) ).
thf(5214,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5124]) ).
thf(5215,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5126]) ).
thf(5216,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5217,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV553 )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5218,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( ~ ( in @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) @ SV264 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5219,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
| ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV553 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5129]) ).
thf(5220,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5130]) ).
thf(5221,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5131]) ).
thf(5222,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV553 )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5131]) ).
thf(5223,plain,
! [SV569: $i,SV833: $i > $o,SV283: $i,SV911: $i > $o] :
( ( ( SV911 @ ( sK85_SY1787 @ SV283 @ SV833 @ SV911 @ SV569 ) )
= $true )
| ( ( SV833 @ ( sK60_SY1724 @ SV911 @ SV833 @ SV569 @ SV283 ) )
= $true )
| ( ( ( dsetconstr @ SV283
@ ^ [SY1664: $i] : ( SV833 @ SY1664 ) )
= ( dsetconstr @ SV569
@ ^ [SY1727: $i] : ( SV911 @ SY1727 ) ) )
= $true )
| ( ( SV283 = SV569 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5132]) ).
thf(5224,plain,
! [SV834: $i,SV1095: $i,SV284: $i > $o] :
( ( ( ~ ( SV284 @ SV1095 ) )
= $true )
| ( ( ( sK115_SY752 @ SV834 @ SV284 )
= SV1095 )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5135]) ).
thf(5225,plain,
! [SV834: $i,SV1086: $i,SV284: $i > $o] :
( ( ( SV284 @ SV1086 )
= $false )
| ( ( ( sK106_SY752 @ SV834 @ SV284 )
= SV1086 )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV834
= ( sK86_SY1666 @ SV834 @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5136]) ).
thf(5226,plain,
! [SV315: $i,SV597: $i,SV972: $o,SV848: $i,SV985: $i] :
( ( ( in @ SV985 @ SV848 )
= $true )
| ( SV972 = $true )
| ( ( in @ SV985 @ SV597 )
= $true )
| ( ( in @ SV985 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV985 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5137]) ).
thf(5227,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV986: $i] :
( ( ( in @ SV986 @ SV848 )
= $true )
| ( $true = $true )
| ( ( in @ SV986 @ SV597 )
= $true )
| ( ( in @ SV986 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV986 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5140]) ).
thf(5228,plain,
! [SV315: $i,SV597: $i,SV848: $i,SV987: $i] :
( ( ( in @ SV987 @ SV848 )
= $true )
| ( $false = $true )
| ( ( in @ SV987 @ SV597 )
= $true )
| ( ( in @ SV987 @ ( binunion @ SV597 @ SV848 ) )
= $false )
| ( ( in @ SV987 @ SV315 )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV315 ) )
= $false )
| ( ( in @ SV597 @ ( powerset @ SV315 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5143]) ).
thf(5229,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
| ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5230,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o,SV939: $i] :
( ( ( in @ ( kpair @ SV939 @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
= $true )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5150]) ).
thf(5231,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 ) )
= $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5151]) ).
thf(5232,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV996: $i,SV939: $i,SV1067: $o] :
( ( SV1067 = $false )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5151]) ).
thf(5233,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( in @ ( kpair @ SV939 @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5153]) ).
thf(5234,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5154]) ).
thf(5235,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV996: $i,SV939: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5154]) ).
thf(5236,plain,
! [SV99: $i,SV408: $i,SV996: $i,SV787: $i,SV939: $i] :
( ( ( in @ ( kpair @ SV939 @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) ) @ SV408 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5156]) ).
thf(5237,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5157]) ).
thf(5238,plain,
! [SV787: $i,SV408: $i,SV99: $i,SV996: $i,SV939: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5157]) ).
thf(5239,plain,
! [SV1057: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5158]) ).
thf(5240,plain,
! [SV107: $i > $o,SV415: $i > $o,SV1057: $i] :
( ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5158]) ).
thf(5241,plain,
! [SV1058: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5159]) ).
thf(5242,plain,
! [SV415: $i > $o,SV107: $i > $o,SV1058: $i] :
( ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5159]) ).
thf(5243,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ SV1102 )
| ~ ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5160]) ).
thf(5244,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ SV1103 )
| ~ ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5161]) ).
thf(5245,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV1096 )
| ~ ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5162]) ).
thf(5246,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ SV1097 )
| ~ ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5163]) ).
thf(5247,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV1098 )
| ~ ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5164]) ).
thf(5248,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ SV1099 )
| ~ ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5165]) ).
thf(5249,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1087 )
| ~ ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5166]) ).
thf(5250,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1088 )
| ~ ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5167]) ).
thf(5251,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) ) ) ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5169]) ).
thf(5252,plain,
! [SV978: $i,SV445: $i > $i,SV140: $i,SV1075: $i] :
( ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SV1075 ) )
= $true )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5170]) ).
thf(5253,plain,
! [SV802: $i,SV1089: $i,SV155: $i > $o] :
( ( ( SV155 @ SV1089 )
= $false )
| ( ( ( sK110_SY401 @ SV802 @ SV155 )
= SV1089 )
= $true )
| ( ( SV155 @ SV802 )
= $false )
| ( ( SV155 @ ( sK81_SY1621 @ SV802 @ SV155 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5171]) ).
thf(5254,plain,
! [SV805: $i,SV1090: $i,SV166: $i > $o] :
( ( ( SV166 @ SV1090 )
= $false )
| ( ( ( sK111_SY432 @ SV805 @ SV166 )
= SV1090 )
= $true )
| ( ( SV166 @ ( sK67_SY1777 @ SV805 @ SV166 ) )
= $true )
| ( ( SV166 @ SV805 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5174]) ).
thf(5255,plain,
! [SV806: $i,SV1072: $i,SV167: $i > $o] :
( ( ( SV167 @ SV1072 )
= $false )
| ( ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5176]) ).
thf(5256,plain,
! [SV167: $i > $o,SV806: $i,SV1072: $i] :
( ( ( SV1072
= ( sK112_SY436 @ SV806 @ SV167 ) )
= $false )
| ( ( SV167 @ SV1072 )
= $true )
| ( ( SV167 @ SV806 )
= $false )
| ( ( SV167 @ ( sK82_SY1625 @ SV806 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5177]) ).
thf(5257,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( in @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5181]) ).
thf(5258,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5182]) ).
thf(5259,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5182]) ).
thf(5260,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( ~ ( in @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5184]) ).
thf(5261,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
| ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5184]) ).
thf(5262,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( in @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5185]) ).
thf(5263,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5186]) ).
thf(5264,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5186]) ).
thf(5265,plain,
! [SV808: $i,SV1104: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1104 )
| ( ( sK123_SY462 @ SV808 @ SV174 )
= SV1104 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5188]) ).
thf(5266,plain,
! [SV808: $i,SV1100: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1100 ) )
= $true )
| ( ( ( sK120_SY462 @ SV808 @ SV174 )
= SV1100 )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5189]) ).
thf(5267,plain,
! [SV808: $i,SV1101: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1101 ) )
= $true )
| ( ( ( sK121_SY462 @ SV808 @ SV174 )
= SV1101 )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5190]) ).
thf(5268,plain,
! [SV808: $i,SV1091: $i,SV174: $i > $o] :
( ( ( SV174 @ SV1091 )
= $false )
| ( ( ( sK113_SY462 @ SV808 @ SV174 )
= SV1091 )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5191]) ).
thf(5269,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1003: $i] :
( ( ( in @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV489 )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5192]) ).
thf(5270,plain,
! [SV489: $i,SV1003: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ ( sK131_SY1794 @ SV1003 @ SV191 @ SV489 ) @ SV1003 )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $false )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5193]) ).
thf(5271,plain,
! [SV1003: $i,SV191: $i > $i > $o,SV489: $i,SV1076: $i] :
( ( ( in @ SV1076 @ SV489 )
= $false )
| ( ( ~ ( SV191 @ SV1076 @ SV1003 ) )
= $true )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5194]) ).
thf(5272,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( ~ ( ~ ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5195]) ).
thf(5273,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) )
| ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5195]) ).
thf(5274,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( ~ ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5196]) ).
thf(5275,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) )
| ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5197]) ).
thf(5276,plain,
! [SV1063: $i,SV1048: $i,SV212: $i] :
( ( ( ~ ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5198]) ).
thf(5277,plain,
! [SV212: $i,SV1021: $i,SV1005: $i,SV1093: $i] :
( ( ( in @ SV1093 @ SV1005 )
= $false )
| ( ( in @ SV1093 @ SV1021 )
= $true )
| ( ( ! [SY1805: $i] :
( ~ ( in @ SY1805 @ SV1021 )
| ( in @ SY1805 @ SV1005 ) ) )
= $true )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5199]) ).
thf(5278,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ! [SY1874: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1874 @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1876: $i] :
( ~ ( in @ SY1876 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1876 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ SY1874 @ SY1876 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5200]) ).
thf(5279,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ! [SY1868: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1868 @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1870: $i] :
( ~ ( in @ SY1870 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1870 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ SY1868 @ SY1870 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5201]) ).
thf(5280,plain,
! [SV982: $i,SV1064: $i,SV702: $i > $i > $o,SV509: $i,SV215: $i,SV1094: $i] :
( ( ( in @ SV1094 @ SV215 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV509
@ ^ [SY1862: $i] :
~ ( ~ ( SV702 @ SV1094 @ SY1862 )
| ~ ! [SY1863: $i] :
( ~ ( in @ SY1863 @ SV509 )
| ~ ( SV702 @ SV1094 @ SY1863 )
| ( in @ ( kpair @ SY1862 @ SY1863 ) @ SV1064 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV509 @ SV1064 )
= $false )
| ( ( in @ SV1064 @ ( breln1Set @ SV509 ) )
= $false )
| ( ( in @ SV982 @ SV509 )
= $false )
| ( ( SV702 @ ( sK33_SY1510 @ SV702 @ SV509 @ SV215 ) @ SV982 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5202]) ).
thf(5281,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| SV1070 )
= $false )
| ( SV1070 = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5203]) ).
thf(5282,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( SV1070 = $true )
| ( SV1070 = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5204]) ).
thf(5283,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i,SV1070: $o] :
( ( SV1070 = $false )
| ( SV1070 = $true )
| ( SV1070 = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5204]) ).
thf(5284,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5205]) ).
thf(5285,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5206]) ).
thf(5286,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5206]) ).
thf(5287,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5207]) ).
thf(5288,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5208]) ).
thf(5289,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5208]) ).
thf(5290,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5209]) ).
thf(5291,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5210]) ).
thf(5292,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ SV1085 ) )
= $true )
| ( ( ~ ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5211]) ).
thf(5293,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5212]) ).
thf(5294,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5213]) ).
thf(5295,plain,
! [SV550: $i > $o,SV1074: $i,SV260: $i > $o] :
( ( ( ! [SY1843: $i] :
( ~ ( SV260 @ SY1843 )
| ( SV1074 = SY1843 ) ) )
= $false )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5214]) ).
thf(5296,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK126_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK139_SY1844 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) @ SV264 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5216]) ).
thf(5297,plain,
! [SV264: $i,SV553: $i,SV829: $i] :
( ( ( in @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) @ SV264 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5218]) ).
thf(5298,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV829 ) )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5219]) ).
thf(5299,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV553 )
= $false )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5219]) ).
thf(5300,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK127_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK140_SY1845 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5221]) ).
thf(5301,plain,
! [SV834: $i,SV1095: $i,SV284: $i > $o] :
( ( ( SV284 @ SV1095 )
= $false )
| ( ( ( sK115_SY752 @ SV834 @ SV284 )
= SV1095 )
= $true )
| ( ( SV284 @ SV834 )
= $false )
| ( ( SV284 @ ( sK86_SY1666 @ SV834 @ SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5224]) ).
thf(5302,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( ~ ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5229]) ).
thf(5303,plain,
! [SV40: $i,SV357: $i,SV994: $i,SV768: $i,SV928: $i] :
( ( ( ~ ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 ) )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5229]) ).
thf(5304,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i,SV1067: $o] :
( ( ( in @ ( kpair @ ( sK135_SY1835 @ SV1067 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
= $true )
| ( SV1067 = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5231]) ).
thf(5305,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( in @ ( kpair @ ( sK136_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5234]) ).
thf(5306,plain,
! [SV99: $i,SV939: $i,SV408: $i,SV996: $i,SV787: $i] :
( ( ( in @ ( kpair @ ( sK137_SX0 @ SV787 @ SV996 @ SV408 @ SV939 @ SV99 ) @ SV996 ) @ SV787 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV939 @ SV996 ) @ ( breln1compset @ SV99 @ SV408 @ SV787 ) )
= $false )
| ( ( in @ SV996 @ SV99 )
= $false )
| ( ( in @ SV939 @ SV99 )
= $false )
| ( ( breln1 @ SV99 @ SV787 )
= $false )
| ( ( breln1 @ SV99 @ SV408 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5237]) ).
thf(5307,plain,
! [SV1057: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5239]) ).
thf(5308,plain,
! [SV1057: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5240]) ).
thf(5309,plain,
! [SV1058: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5241]) ).
thf(5310,plain,
! [SV1058: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5242]) ).
thf(5311,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ SV1102 )
| ~ ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5243]) ).
thf(5312,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ SV1103 )
| ~ ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) ) )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5244]) ).
thf(5313,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1096 )
| ~ ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5245]) ).
thf(5314,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1097 )
| ~ ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5246]) ).
thf(5315,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1098 )
| ~ ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5247]) ).
thf(5316,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1099 )
| ~ ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5248]) ).
thf(5317,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1087 ) )
= $true )
| ( ( ~ ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5249]) ).
thf(5318,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1088 ) )
= $true )
| ( ( ~ ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5319,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i] :
( ( ( ~ ( ~ ( in @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) ) ) ) )
= $true )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5251]) ).
thf(5320,plain,
! [SV1075: $i,SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ~ ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) ) )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5252]) ).
thf(5321,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK129_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK141_SY1846 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) @ SV470 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5258]) ).
thf(5322,plain,
! [SV470: $i,SV678: $i,SV887: $i,SV168: $i] :
( ( ( in @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) @ SV470 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5260]) ).
thf(5323,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 ) )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5261]) ).
thf(5324,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV678 )
= $false )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5261]) ).
thf(5325,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK130_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK142_SY1847 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5263]) ).
thf(5326,plain,
! [SV808: $i,SV1104: $i,SV174: $i > $o] :
( ( ( ~ ( SV174 @ SV1104 ) )
= $true )
| ( ( ( sK123_SY462 @ SV808 @ SV174 )
= SV1104 )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5265]) ).
thf(5327,plain,
! [SV808: $i,SV1100: $i,SV174: $i > $o] :
( ( ( SV174 @ SV1100 )
= $false )
| ( ( ( sK120_SY462 @ SV808 @ SV174 )
= SV1100 )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5266]) ).
thf(5328,plain,
! [SV808: $i,SV1101: $i,SV174: $i > $o] :
( ( ( SV174 @ SV1101 )
= $false )
| ( ( ( sK121_SY462 @ SV808 @ SV174 )
= SV1101 )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $false )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5267]) ).
thf(5329,plain,
! [SV489: $i,SV1003: $i,SV1076: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ SV1076 @ SV1003 )
= $false )
| ( ( in @ SV1076 @ SV489 )
= $false )
| ( ( in @ SV1003 @ ( sK58_SY1167 @ SV191 @ SV489 ) )
= $true )
| ( ( in @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5271]) ).
thf(5330,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( ~ ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
| ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5272]) ).
thf(5331,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) )
| ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5273]) ).
thf(5332,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( ~ ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) ) )
= $true )
| ( ( ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(5333,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5275]) ).
thf(5334,plain,
! [SV1063: $i,SV1048: $i,SV212: $i] :
( ( ( ! [SY1829: $i] :
( ~ ( in @ SY1829 @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ SY1829 )
| ( in @ SV1063 @ SY1829 ) )
| ~ ( ~ ( in @ SV1063 @ SY1829 )
| ( in @ SV1048 @ SY1829 ) ) ) ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5276]) ).
thf(5335,plain,
! [SV212: $i,SV1093: $i,SV1005: $i,SV1021: $i,SV1105: $i] :
( ( ( ~ ( in @ SV1105 @ SV1021 )
| ( in @ SV1105 @ SV1005 ) )
= $true )
| ( ( in @ SV1093 @ SV1021 )
= $true )
| ( ( in @ SV1093 @ SV1005 )
= $false )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5277]) ).
thf(5336,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ! [SY1874: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1874 @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1876: $i] :
( ~ ( in @ SY1876 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1876 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ SY1874 @ SY1876 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5278]) ).
thf(5337,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ! [SY1868: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1868 @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1870: $i] :
( ~ ( in @ SY1870 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1870 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ SY1868 @ SY1870 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5338,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( SV1070 = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5281]) ).
thf(5339,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i,SV1070: $o] :
( ( SV1070 = $false )
| ( SV1070 = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5281]) ).
thf(5340,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( SV1070 = $true )
| ( SV1070 = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5282]) ).
thf(5341,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5284]) ).
thf(5342,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5284]) ).
thf(5343,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5285]) ).
thf(5344,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( ~ ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5345,plain,
! [SV255: $i,SV826: $i,SV545: $i,SV1008: $i,SV960: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5287]) ).
thf(5346,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5288]) ).
thf(5347,plain,
! [SV1022: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5290]) ).
thf(5348,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1106 )
| ~ ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5291]) ).
thf(5349,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) )
= $true )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5292]) ).
thf(5350,plain,
! [SV550: $i > $o,SV1078: $i,SV260: $i > $o] :
( ( ( ! [SY1851: $i] :
( ~ ( SV260 @ SY1851 )
| ( SV1078 = SY1851 ) ) )
= $false )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5293]) ).
thf(5351,plain,
! [SV550: $i > $o,SV1079: $i,SV260: $i > $o] :
( ( ( ! [SY1852: $i] :
( ~ ( SV260 @ SY1852 )
| ( SV1079 = SY1852 ) ) )
= $false )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5294]) ).
thf(5352,plain,
! [SV1074: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
| ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5295]) ).
thf(5353,plain,
! [SV264: $i,SV829: $i,SV553: $i] :
( ( ( in @ ( kpair @ ( sK134_SY1656 @ SV553 @ SV829 @ SV264 ) @ ( sK143_SY1853 @ SV829 @ SV553 @ SV264 ) ) @ SV829 )
= $true )
| ( ( SV553 = SV829 )
= $true )
| ( ( in @ ( kpair @ ( sK72_SY1654 @ SV829 @ SV553 @ SV264 ) @ ( sK92_SY1789 @ SV553 @ SV829 @ SV264 ) ) @ SV553 )
= $true )
| ( ( breln1 @ SV264 @ SV829 )
= $false )
| ( ( breln1 @ SV264 @ SV553 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5298]) ).
thf(5354,plain,
! [SV40: $i,SV928: $i,SV357: $i,SV994: $i,SV768: $i] :
( ( ( in @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) @ SV40 )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5302]) ).
thf(5355,plain,
! [SV40: $i,SV357: $i,SV994: $i,SV768: $i,SV928: $i] :
( ( ( in @ ( kpair @ SV928 @ ( sK122_SY1790 @ SV768 @ SV994 @ SV357 @ SV928 @ SV40 ) ) @ SV357 )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV994 ) @ ( breln1compset @ SV40 @ SV357 @ SV768 ) )
= $false )
| ( ( in @ SV994 @ SV40 )
= $false )
| ( ( in @ SV928 @ SV40 )
= $false )
| ( ( breln1 @ SV40 @ SV768 )
= $false )
| ( ( breln1 @ SV40 @ SV357 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5303]) ).
thf(5356,plain,
! [SV1057: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5307]) ).
thf(5357,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1879: $i] :
( ~ ( SV415 @ SY1879 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1879 ) ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5308]) ).
thf(5358,plain,
! [SV1058: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5309]) ).
thf(5359,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK152_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1880: $i] :
( ~ ( SV107 @ SY1880 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1880 ) ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5310]) ).
thf(5360,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1102 )
| ~ ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5311]) ).
thf(5361,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1103 )
| ~ ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5312]) ).
thf(5362,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1096 ) )
= $true )
| ( ( ~ ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5313]) ).
thf(5363,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1097 ) )
= $true )
| ( ( ~ ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5314]) ).
thf(5364,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1098 ) )
= $true )
| ( ( ~ ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5315]) ).
thf(5365,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1099 ) )
= $true )
| ( ( ~ ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5316]) ).
thf(5366,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5367,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5318]) ).
thf(5368,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i] :
( ( ( ~ ( in @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) ) ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5319]) ).
thf(5369,plain,
! [SV1075: $i,SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) )
| ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5320]) ).
thf(5370,plain,
! [SV168: $i,SV470: $i,SV887: $i,SV678: $i] :
( ( ( in @ ( kpair @ ( sK138_SY1713 @ SV678 @ SV887 @ SV470 @ SV168 ) @ ( sK146_SY1854 @ SV168 @ SV887 @ SV678 @ SV470 ) ) @ SV887 )
= $true )
| ( ( SV678 = SV887 )
= $true )
| ( ( in @ ( kpair @ ( sK83_SY1711 @ SV887 @ SV678 @ SV470 @ SV168 ) @ ( sK95_SY1793 @ SV168 @ SV678 @ SV887 @ SV470 ) ) @ SV678 )
= $true )
| ( ( breln @ SV168 @ SV470 @ SV887 )
= $false )
| ( ( breln @ SV168 @ SV470 @ SV678 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5323]) ).
thf(5371,plain,
! [SV808: $i,SV1104: $i,SV174: $i > $o] :
( ( ( SV174 @ SV1104 )
= $false )
| ( ( ( sK123_SY462 @ SV808 @ SV174 )
= SV1104 )
= $true )
| ( ( SV174 @ ( sK42_SY1627 @ SV808 @ SV174 ) )
= $true )
| ( ( ( sK42_SY1627 @ SV808 @ SV174 )
= SV808 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5326]) ).
thf(5372,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( ~ ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) ) )
= $true )
| ( ( ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5330]) ).
thf(5373,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5331]) ).
thf(5374,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1083: $i] :
( ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( ~ ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5332]) ).
thf(5375,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5333]) ).
thf(5376,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( ~ ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
| ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5334]) ).
thf(5377,plain,
! [SV212: $i,SV1093: $i,SV1005: $i,SV1021: $i,SV1105: $i] :
( ( ( ~ ( in @ SV1105 @ SV1021 ) )
= $true )
| ( ( in @ SV1105 @ SV1005 )
= $true )
| ( ( in @ SV1093 @ SV1021 )
= $true )
| ( ( in @ SV1093 @ SV1005 )
= $false )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5335]) ).
thf(5378,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ! [SY1874: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ SY1874 @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1876: $i] :
( ~ ( in @ SY1876 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1876 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ SY1874 @ SY1876 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5336]) ).
thf(5379,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1882: $i] :
( ~ ( in @ SY1882 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1882 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SY1882 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5337]) ).
thf(5380,plain,
! [SV255: $i,SV545: $i,SV1070: $o,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( SV1070 = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5338]) ).
thf(5381,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5341]) ).
thf(5382,plain,
! [SV255: $i,SV545: $i,SV826: $i,SV1008: $i,SV960: $i] :
( ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV826 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ SV545 )
= $true )
| ( ( in @ ( kpair @ SV960 @ SV1008 ) @ ( binunion @ SV545 @ SV826 ) )
= $false )
| ( ( in @ SV1008 @ SV255 )
= $false )
| ( ( in @ SV960 @ SV255 )
= $false )
| ( ( breln1 @ SV255 @ SV826 )
= $false )
| ( ( breln1 @ SV255 @ SV545 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5344]) ).
thf(5383,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1107 )
| ~ ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5347]) ).
thf(5384,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1106 )
| ~ ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5348]) ).
thf(5385,plain,
! [SV550: $i > $o,SV1085: $i,SV260: $i > $o] :
( ( ( ! [SY1857: $i] :
( ~ ( SV260 @ SY1857 )
| ( SV1085 = SY1857 ) ) )
= $false )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5349]) ).
thf(5386,plain,
! [SV1078: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
| ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5350]) ).
thf(5387,plain,
! [SV1079: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
| ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5351]) ).
thf(5388,plain,
! [SV1074: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5352]) ).
thf(5389,plain,
! [SV260: $i > $o,SV550: $i > $o,SV1074: $i] :
( ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5352]) ).
thf(5390,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1885: $i] :
( ~ ( SV415 @ SY1885 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1885 ) ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5356]) ).
thf(5391,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1879: $i] :
( ~ ( SV415 @ SY1879 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1879 ) ) ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5357]) ).
thf(5392,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK158_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1886: $i] :
( ~ ( SV107 @ SY1886 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1886 ) ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5358]) ).
thf(5393,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK152_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1880: $i] :
( ~ ( SV107 @ SY1880 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1880 ) ) ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5359]) ).
thf(5394,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1102 ) )
= $true )
| ( ( ~ ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5360]) ).
thf(5395,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1103 ) )
= $true )
| ( ( ~ ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5361]) ).
thf(5396,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5362]) ).
thf(5397,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5363]) ).
thf(5398,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5364]) ).
thf(5399,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5365]) ).
thf(5400,plain,
! [SV415: $i > $o,SV1087: $i,SV107: $i > $o] :
( ( ( ! [SY1858: $i] :
( ~ ( SV107 @ SY1858 )
| ( SV1087 = SY1858 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5366]) ).
thf(5401,plain,
! [SV107: $i > $o,SV1088: $i,SV415: $i > $o] :
( ( ( ! [SY1859: $i] :
( ~ ( SV415 @ SY1859 )
| ( SV1088 = SY1859 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5367]) ).
thf(5402,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i] :
( ( ( ~ ( in @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) @ SV140 ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5368]) ).
thf(5403,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) ) )
= $false )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5368]) ).
thf(5404,plain,
! [SV1075: $i,SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5369]) ).
thf(5405,plain,
! [SV1075: $i,SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5369]) ).
thf(5406,plain,
! [SV489: $i,SV191: $i > $i > $o,SV951: $i,SV1092: $i] :
( ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( ~ ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5372]) ).
thf(5407,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ~ ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5373]) ).
thf(5408,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1855: $i] :
~ ~ ( ~ ( in @ SY1855 @ SV489 )
| ~ ( SV191 @ SY1855 @ SV1083 ) ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5374]) ).
thf(5409,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1856: $i] :
~ ~ ( ~ ( in @ SY1856 @ SV489 )
| ~ ( SV191 @ SY1856 @ SV1083 ) ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5375]) ).
thf(5410,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) @ ( sK4_SY557 @ SV212 ) ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5376]) ).
thf(5411,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
| ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5376]) ).
thf(5412,plain,
! [SV212: $i,SV1093: $i,SV1005: $i,SV1021: $i,SV1105: $i] :
( ( ( in @ SV1105 @ SV1021 )
= $false )
| ( ( in @ SV1105 @ SV1005 )
= $true )
| ( ( in @ SV1093 @ SV1021 )
= $true )
| ( ( in @ SV1093 @ SV1005 )
= $false )
| ( ( in @ SV1005 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ SV1021 @ ( sK4_SY557 @ SV212 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5377]) ).
thf(5413,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1888: $i] :
( ~ ( in @ SY1888 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1888 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SY1888 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5378]) ).
thf(5414,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1882: $i] :
( ~ ( in @ SY1882 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1882 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SY1882 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5379]) ).
thf(5415,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1107 )
| ~ ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5383]) ).
thf(5416,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1106 )
| ~ ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5384]) ).
thf(5417,plain,
! [SV1085: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
| ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5385]) ).
thf(5418,plain,
! [SV1078: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5386]) ).
thf(5419,plain,
! [SV260: $i > $o,SV550: $i > $o,SV1078: $i] :
( ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5386]) ).
thf(5420,plain,
! [SV1079: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5387]) ).
thf(5421,plain,
! [SV260: $i > $o,SV550: $i > $o,SV1079: $i] :
( ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5387]) ).
thf(5422,plain,
! [SV1074: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5388]) ).
thf(5423,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5389]) ).
thf(5424,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1885: $i] :
( ~ ( SV415 @ SY1885 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1885 ) ) ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5390]) ).
thf(5425,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1879: $i] :
( ~ ( SV415 @ SY1879 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1879 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5391]) ).
thf(5426,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK158_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1886: $i] :
( ~ ( SV107 @ SY1886 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1886 ) ) ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5392]) ).
thf(5427,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK152_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1880: $i] :
( ~ ( SV107 @ SY1880 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1880 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5393]) ).
thf(5428,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5394]) ).
thf(5429,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) )
= $true )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5395]) ).
thf(5430,plain,
! [SV415: $i > $o,SV1096: $i,SV107: $i > $o] :
( ( ( ! [SY1864: $i] :
( ~ ( SV107 @ SY1864 )
| ( SV1096 = SY1864 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5396]) ).
thf(5431,plain,
! [SV107: $i > $o,SV1097: $i,SV415: $i > $o] :
( ( ( ! [SY1865: $i] :
( ~ ( SV415 @ SY1865 )
| ( SV1097 = SY1865 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5397]) ).
thf(5432,plain,
! [SV415: $i > $o,SV1098: $i,SV107: $i > $o] :
( ( ( ! [SY1866: $i] :
( ~ ( SV107 @ SY1866 )
| ( SV1098 = SY1866 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5398]) ).
thf(5433,plain,
! [SV107: $i > $o,SV1099: $i,SV415: $i > $o] :
( ( ( ! [SY1867: $i] :
( ~ ( SV415 @ SY1867 )
| ( SV1099 = SY1867 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5399]) ).
thf(5434,plain,
! [SV1087: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
| ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5400]) ).
thf(5435,plain,
! [SV1088: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
| ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5401]) ).
thf(5436,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i] :
( ( ( in @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) @ SV140 )
= $true )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5402]) ).
thf(5437,plain,
! [SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ ( sK148_SY1803 @ SV978 @ SV445 @ SV140 ) ) )
= $true )
| ( ( in @ ( sK90_SY1774 @ SV445 @ SV140 @ SV978 ) @ SV978 )
= $true )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5403]) ).
thf(5438,plain,
! [SV1075: $i,SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ~ ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $true )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5404]) ).
thf(5439,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1860: $i] :
~ ~ ( ~ ( in @ SY1860 @ SV489 )
| ~ ( SV191 @ SY1860 @ SV1092 ) ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5406]) ).
thf(5440,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i] :
( ( ( ! [SY1861: $i] :
~ ~ ( ~ ( in @ SY1861 @ SV489 )
| ~ ( SV191 @ SY1861 @ SV1092 ) ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5407]) ).
thf(5441,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1083: $i,SV951: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV1083 ) ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5408]) ).
thf(5442,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i,SV1108: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1108 @ SV489 )
| ~ ( SV191 @ SV1108 @ SV1083 ) ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5409]) ).
thf(5443,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( in @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5410]) ).
thf(5444,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( ~ ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
| ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5411]) ).
thf(5445,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1888: $i] :
( ~ ( in @ SY1888 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1888 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SY1888 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5413]) ).
thf(5446,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
| ~ ! [SY1882: $i] :
( ~ ( in @ SY1882 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1882 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SY1882 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5414]) ).
thf(5447,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1107 )
| ~ ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5415]) ).
thf(5448,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1106 ) )
= $true )
| ( ( ~ ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5416]) ).
thf(5449,plain,
! [SV1085: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) ) )
= $false )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5417]) ).
thf(5450,plain,
! [SV260: $i > $o,SV550: $i > $o,SV1085: $i] :
( ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5417]) ).
thf(5451,plain,
! [SV1078: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5418]) ).
thf(5452,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5419]) ).
thf(5453,plain,
! [SV1079: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5420]) ).
thf(5454,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5421]) ).
thf(5455,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5422]) ).
thf(5456,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5423]) ).
thf(5457,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 ) )
| ~ ! [SY1885: $i] :
( ~ ( SV415 @ SY1885 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1885 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5424]) ).
thf(5458,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5425]) ).
thf(5459,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1879: $i] :
( ~ ( SV415 @ SY1879 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1879 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5425]) ).
thf(5460,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK158_SY259 @ SV1058 @ SV415 @ SV107 ) )
| ~ ! [SY1886: $i] :
( ~ ( SV107 @ SY1886 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1886 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5426]) ).
thf(5461,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK152_SY259 @ SV1058 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5427]) ).
thf(5462,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1880: $i] :
( ~ ( SV107 @ SY1880 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1880 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5427]) ).
thf(5463,plain,
! [SV415: $i > $o,SV1102: $i,SV107: $i > $o] :
( ( ( ! [SY1872: $i] :
( ~ ( SV107 @ SY1872 )
| ( SV1102 = SY1872 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5428]) ).
thf(5464,plain,
! [SV107: $i > $o,SV1103: $i,SV415: $i > $o] :
( ( ( ! [SY1873: $i] :
( ~ ( SV415 @ SY1873 )
| ( SV1103 = SY1873 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5429]) ).
thf(5465,plain,
! [SV1096: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
| ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5430]) ).
thf(5466,plain,
! [SV1097: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
| ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5431]) ).
thf(5467,plain,
! [SV1098: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
| ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5432]) ).
thf(5468,plain,
! [SV1099: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
| ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5433]) ).
thf(5469,plain,
! [SV1087: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5434]) ).
thf(5470,plain,
! [SV107: $i > $o,SV415: $i > $o,SV1087: $i] :
( ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5434]) ).
thf(5471,plain,
! [SV1088: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5435]) ).
thf(5472,plain,
! [SV415: $i > $o,SV107: $i > $o,SV1088: $i] :
( ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5435]) ).
thf(5473,plain,
! [SV1075: $i,SV978: $i,SV445: $i > $i,SV140: $i] :
( ( ( ! [SY1803: $i] :
~ ~ ( ~ ( in @ SY1803 @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ SY1803 ) ) ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5438]) ).
thf(5474,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1092: $i,SV951: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV1092 ) ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5439]) ).
thf(5475,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i,SV1109: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1109 @ SV489 )
| ~ ( SV191 @ SV1109 @ SV1092 ) ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5440]) ).
thf(5476,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1083: $i,SV951: $i] :
( ( ( ~ ( ~ ( in @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV1083 ) ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5441]) ).
thf(5477,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i,SV1108: $i] :
( ( ( ~ ( ~ ( in @ SV1108 @ SV489 )
| ~ ( SV191 @ SV1108 @ SV1083 ) ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5442]) ).
thf(5478,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( ~ ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5444]) ).
thf(5479,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
| ~ ! [SY1888: $i] :
( ~ ( in @ SY1888 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1888 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SY1888 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5445]) ).
thf(5480,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5446]) ).
thf(5481,plain,
! [SV955: $i,SV1077: $i,SV212: $i] :
( ( ( ~ ! [SY1882: $i] :
( ~ ( in @ SY1882 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1882 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SY1882 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5446]) ).
thf(5482,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1107 ) )
= $true )
| ( ( ~ ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5447]) ).
thf(5483,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1106 )
= $false )
| ( ( ~ ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5448]) ).
thf(5484,plain,
! [SV1085: $i,SV550: $i > $o,SV260: $i > $o] :
( ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) )
| ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5449]) ).
thf(5485,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5450]) ).
thf(5486,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5451]) ).
thf(5487,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5452]) ).
thf(5488,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5453]) ).
thf(5489,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5454]) ).
thf(5490,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5455]) ).
thf(5491,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5456]) ).
thf(5492,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5457]) ).
thf(5493,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1885: $i] :
( ~ ( SV415 @ SY1885 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1885 ) ) )
= $false )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5457]) ).
thf(5494,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5458]) ).
thf(5495,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ! [SY1879: $i] :
( ~ ( SV415 @ SY1879 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1879 ) ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5459]) ).
thf(5496,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK158_SY259 @ SV1058 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5460]) ).
thf(5497,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1886: $i] :
( ~ ( SV107 @ SY1886 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1886 ) ) )
= $false )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5460]) ).
thf(5498,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK152_SY259 @ SV1058 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5461]) ).
thf(5499,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ! [SY1880: $i] :
( ~ ( SV107 @ SY1880 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1880 ) ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5462]) ).
thf(5500,plain,
! [SV1102: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
| ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5463]) ).
thf(5501,plain,
! [SV1103: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
| ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5464]) ).
thf(5502,plain,
! [SV1096: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5465]) ).
thf(5503,plain,
! [SV107: $i > $o,SV415: $i > $o,SV1096: $i] :
( ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5465]) ).
thf(5504,plain,
! [SV1097: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5466]) ).
thf(5505,plain,
! [SV415: $i > $o,SV107: $i > $o,SV1097: $i] :
( ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5466]) ).
thf(5506,plain,
! [SV1098: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5467]) ).
thf(5507,plain,
! [SV107: $i > $o,SV415: $i > $o,SV1098: $i] :
( ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5467]) ).
thf(5508,plain,
! [SV1099: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5468]) ).
thf(5509,plain,
! [SV415: $i > $o,SV107: $i > $o,SV1099: $i] :
( ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5468]) ).
thf(5510,plain,
! [SV1087: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5469]) ).
thf(5511,plain,
! [SV1087: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5470]) ).
thf(5512,plain,
! [SV1088: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5471]) ).
thf(5513,plain,
! [SV1088: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5472]) ).
thf(5514,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i,SV1075: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) ) ) ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5473]) ).
thf(5515,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1092: $i,SV951: $i] :
( ( ( ~ ( ~ ( in @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV1092 ) ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5474]) ).
thf(5516,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i,SV1109: $i] :
( ( ( ~ ( ~ ( in @ SV1109 @ SV489 )
| ~ ( SV191 @ SV1109 @ SV1092 ) ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5475]) ).
thf(5517,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1083: $i,SV951: $i] :
( ( ( ~ ( in @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV1083 ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5476]) ).
thf(5518,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i,SV1108: $i] :
( ( ( ~ ( in @ SV1108 @ SV489 )
| ~ ( SV191 @ SV1108 @ SV1083 ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5477]) ).
thf(5519,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5478]) ).
thf(5520,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5479]) ).
thf(5521,plain,
! [SV955: $i,SV1084: $i,SV212: $i] :
( ( ( ~ ! [SY1888: $i] :
( ~ ( in @ SY1888 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1888 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SY1888 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5479]) ).
thf(5522,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5480]) ).
thf(5523,plain,
! [SV955: $i,SV1077: $i,SV212: $i] :
( ( ( ! [SY1882: $i] :
( ~ ( in @ SY1882 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1871: $i] :
( ~ ( in @ SY1871 @ SY1882 )
| ( in @ SY1871 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SY1882 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5481]) ).
thf(5524,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1107 )
= $false )
| ( ( ~ ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5482]) ).
thf(5525,plain,
! [SV1022: $i,SV260: $i > $o,SV1106: $i,SV550: $i > $o] :
( ( ( ! [SY1878: $i] :
( ~ ( SV550 @ SY1878 )
| ( SV1106 = SY1878 ) ) )
= $false )
| ( ( SV550 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5483]) ).
thf(5526,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5484]) ).
thf(5527,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5485]) ).
thf(5528,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5486]) ).
thf(5529,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5487]) ).
thf(5530,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5488]) ).
thf(5531,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5489]) ).
thf(5532,plain,
! [SV1074: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5490]) ).
thf(5533,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1110 )
| ~ ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5491]) ).
thf(5534,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5492]) ).
thf(5535,plain,
! [SV107: $i > $o,SV1057: $i,SV415: $i > $o] :
( ( ( ! [SY1885: $i] :
( ~ ( SV415 @ SY1885 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SY1885 ) ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5493]) ).
thf(5536,plain,
! [SV107: $i > $o,SV1057: $i,SV1111: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1111 )
| ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1111 ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5495]) ).
thf(5537,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK158_SY259 @ SV1058 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5496]) ).
thf(5538,plain,
! [SV415: $i > $o,SV1058: $i,SV107: $i > $o] :
( ( ( ! [SY1886: $i] :
( ~ ( SV107 @ SY1886 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SY1886 ) ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5497]) ).
thf(5539,plain,
! [SV415: $i > $o,SV1058: $i,SV1112: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1112 )
| ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1112 ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5499]) ).
thf(5540,plain,
! [SV1102: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5500]) ).
thf(5541,plain,
! [SV107: $i > $o,SV415: $i > $o,SV1102: $i] :
( ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5500]) ).
thf(5542,plain,
! [SV1103: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5543,plain,
! [SV415: $i > $o,SV107: $i > $o,SV1103: $i] :
( ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5501]) ).
thf(5544,plain,
! [SV1096: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5502]) ).
thf(5545,plain,
! [SV1096: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5503]) ).
thf(5546,plain,
! [SV1097: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5504]) ).
thf(5547,plain,
! [SV1097: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5505]) ).
thf(5548,plain,
! [SV1098: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5506]) ).
thf(5549,plain,
! [SV1098: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5507]) ).
thf(5550,plain,
! [SV1099: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5508]) ).
thf(5551,plain,
! [SV1099: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5509]) ).
thf(5552,plain,
! [SV1087: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5510]) ).
thf(5553,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1891: $i] :
( ~ ( SV415 @ SY1891 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1891 ) ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5511]) ).
thf(5554,plain,
! [SV1088: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5512]) ).
thf(5555,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK173_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1892: $i] :
( ~ ( SV107 @ SY1892 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1892 ) ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5513]) ).
thf(5556,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i,SV1075: $i] :
( ( ( ~ ( ~ ( in @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) ) ) ) )
= $true )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5514]) ).
thf(5557,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1092: $i,SV951: $i] :
( ( ( ~ ( in @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV489 )
| ~ ( SV191 @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV1092 ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5515]) ).
thf(5558,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i,SV1109: $i] :
( ( ( ~ ( in @ SV1109 @ SV489 )
| ~ ( SV191 @ SV1109 @ SV1092 ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5516]) ).
thf(5559,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1083: $i,SV951: $i] :
( ( ( ~ ( in @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV489 ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5517]) ).
thf(5560,plain,
! [SV489: $i,SV1083: $i,SV951: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV1083 ) )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5517]) ).
thf(5561,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i,SV1108: $i] :
( ( ( ~ ( in @ SV1108 @ SV489 ) )
= $true )
| ( ( ~ ( SV191 @ SV1108 @ SV1083 ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5518]) ).
thf(5562,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( ~ ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5519]) ).
thf(5563,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5519]) ).
thf(5564,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5520]) ).
thf(5565,plain,
! [SV955: $i,SV1084: $i,SV212: $i] :
( ( ( ! [SY1888: $i] :
( ~ ( in @ SY1888 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1877: $i] :
( ~ ( in @ SY1877 @ SY1888 )
| ( in @ SY1877 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SY1888 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5521]) ).
thf(5566,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
| ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5522]) ).
thf(5567,plain,
! [SV955: $i,SV1077: $i,SV212: $i,SV1113: $i] :
( ( ( ~ ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SV1113 )
| ( in @ SY1893 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5523]) ).
thf(5568,plain,
! [SV1022: $i,SV260: $i > $o,SV1107: $i,SV550: $i > $o] :
( ( ( ! [SY1884: $i] :
( ~ ( SV550 @ SY1884 )
| ( SV1107 = SY1884 ) ) )
= $false )
| ( ( SV550 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5524]) ).
thf(5569,plain,
! [SV1106: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK174_SY1878 @ SV1022 @ SV260 @ SV1106 @ SV550 ) )
| ( SV1106
= ( sK174_SY1878 @ SV1022 @ SV260 @ SV1106 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5525]) ).
thf(5570,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ~ ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5526]) ).
thf(5571,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5527]) ).
thf(5572,plain,
! [SV1078: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5528]) ).
thf(5573,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1114 )
| ~ ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5529]) ).
thf(5574,plain,
! [SV1079: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5530]) ).
thf(5575,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1115 )
| ~ ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5531]) ).
thf(5576,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1116 )
| ~ ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5532]) ).
thf(5577,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1110 )
| ~ ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5533]) ).
thf(5578,plain,
! [SV107: $i > $o,SV1057: $i,SV1117: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1117 )
| ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1117 ) )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5535]) ).
thf(5579,plain,
! [SV107: $i > $o,SV1057: $i,SV1111: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1111 ) )
= $true )
| ( ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1111 )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5536]) ).
thf(5580,plain,
! [SV415: $i > $o,SV1058: $i,SV1118: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1118 )
| ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1118 ) )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5538]) ).
thf(5581,plain,
! [SV415: $i > $o,SV1058: $i,SV1112: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1112 ) )
= $true )
| ( ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1112 )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5539]) ).
thf(5582,plain,
! [SV1102: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5540]) ).
thf(5583,plain,
! [SV1102: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5541]) ).
thf(5584,plain,
! [SV1103: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5542]) ).
thf(5585,plain,
! [SV1103: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5543]) ).
thf(5586,plain,
! [SV1096: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5544]) ).
thf(5587,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV415 @ SY1897 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1897 ) ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5545]) ).
thf(5588,plain,
! [SV1097: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5546]) ).
thf(5589,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK176_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV107 @ SY1898 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1898 ) ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5547]) ).
thf(5590,plain,
! [SV1098: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5548]) ).
thf(5591,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1899: $i] :
( ~ ( SV415 @ SY1899 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1899 ) ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5549]) ).
thf(5592,plain,
! [SV1099: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5550]) ).
thf(5593,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK178_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1900: $i] :
( ~ ( SV107 @ SY1900 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1900 ) ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5551]) ).
thf(5594,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1901: $i] :
( ~ ( SV415 @ SY1901 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1901 ) ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5552]) ).
thf(5595,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1891: $i] :
( ~ ( SV415 @ SY1891 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1891 ) ) ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5553]) ).
thf(5596,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK180_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1902: $i] :
( ~ ( SV107 @ SY1902 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1902 ) ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5554]) ).
thf(5597,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK173_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1892: $i] :
( ~ ( SV107 @ SY1892 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1892 ) ) ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5555]) ).
thf(5598,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i,SV1075: $i] :
( ( ( ~ ( in @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) @ SV140 )
| ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) ) ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5556]) ).
thf(5599,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1092: $i,SV951: $i] :
( ( ( ~ ( in @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV489 ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5557]) ).
thf(5600,plain,
! [SV489: $i,SV1092: $i,SV951: $i,SV191: $i > $i > $o] :
( ( ( ~ ( SV191 @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV1092 ) )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5557]) ).
thf(5601,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i,SV1109: $i] :
( ( ( ~ ( in @ SV1109 @ SV489 ) )
= $true )
| ( ( ~ ( SV191 @ SV1109 @ SV1092 ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5558]) ).
thf(5602,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1083: $i,SV951: $i] :
( ( ( in @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV489 )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5559]) ).
thf(5603,plain,
! [SV489: $i,SV1083: $i,SV951: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ ( sK163_SY1855 @ SV951 @ SV1083 @ SV191 @ SV489 ) @ SV1083 )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5560]) ).
thf(5604,plain,
! [SV951: $i,SV1083: $i,SV191: $i > $i > $o,SV489: $i,SV1108: $i] :
( ( ( in @ SV1108 @ SV489 )
= $false )
| ( ( ~ ( SV191 @ SV1108 @ SV1083 ) )
= $true )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5561]) ).
thf(5605,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5562]) ).
thf(5606,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5563]) ).
thf(5607,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
| ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5564]) ).
thf(5608,plain,
! [SV955: $i,SV1084: $i,SV212: $i,SV1119: $i] :
( ( ( ~ ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
| ! [SY1903: $i] :
( ~ ( in @ SY1903 @ SV1119 )
| ( in @ SY1903 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5565]) ).
thf(5609,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5566]) ).
thf(5610,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5566]) ).
thf(5611,plain,
! [SV955: $i,SV1077: $i,SV212: $i,SV1113: $i] :
( ( ( ~ ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SV1113 )
| ( in @ SY1893 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5567]) ).
thf(5612,plain,
! [SV1107: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK181_SY1884 @ SV1022 @ SV260 @ SV1107 @ SV550 ) )
| ( SV1107
= ( sK181_SY1884 @ SV1022 @ SV260 @ SV1107 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5568]) ).
thf(5613,plain,
! [SV1106: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK174_SY1878 @ SV1022 @ SV260 @ SV1106 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5569]) ).
thf(5614,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1022: $i,SV1106: $i] :
( ( ( SV1106
= ( sK174_SY1878 @ SV1022 @ SV260 @ SV1106 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5569]) ).
thf(5615,plain,
! [SV1085: $i,SV260: $i > $o,SV550: $i > $o] :
( ( ( ! [SY1270: $i] :
~ ~ ( ~ ( SV550 @ SY1270 )
| ~ ! [SY1271: $i] :
( ~ ( SV550 @ SY1271 )
| ( SY1270 = SY1271 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5570]) ).
thf(5616,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1120 )
| ~ ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5571]) ).
thf(5617,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1121 )
| ~ ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5572]) ).
thf(5618,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1114 )
| ~ ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5573]) ).
thf(5619,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1122 )
| ~ ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5574]) ).
thf(5620,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1115 )
| ~ ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5575]) ).
thf(5621,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1116 )
| ~ ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5576]) ).
thf(5622,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1110 )
| ~ ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5577]) ).
thf(5623,plain,
! [SV107: $i > $o,SV1057: $i,SV1117: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1117 ) )
= $true )
| ( ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1117 )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5578]) ).
thf(5624,plain,
! [SV107: $i > $o,SV1057: $i,SV1111: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1111 )
= $false )
| ( ( ( sK151_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1111 )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV1057
= ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5579]) ).
thf(5625,plain,
! [SV415: $i > $o,SV1058: $i,SV1118: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1118 ) )
= $true )
| ( ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1118 )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5580]) ).
thf(5626,plain,
! [SV415: $i > $o,SV1058: $i,SV1112: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1112 )
= $false )
| ( ( ( sK152_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1112 )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV1058
= ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $false )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5581]) ).
thf(5627,plain,
! [SV1102: $i,SV107: $i > $o,SV415: $i > $o] :
( ( ( ! [SY1012: $i] :
~ ~ ( ~ ( SV415 @ SY1012 )
| ~ ! [SY1013: $i] :
( ~ ( SV415 @ SY1013 )
| ( SY1012 = SY1013 ) ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5582]) ).
thf(5628,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1907: $i] :
( ~ ( SV415 @ SY1907 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1907 ) ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5583]) ).
thf(5629,plain,
! [SV1103: $i,SV415: $i > $o,SV107: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV107 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV107 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5584]) ).
thf(5630,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK183_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1908: $i] :
( ~ ( SV107 @ SY1908 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1908 ) ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5585]) ).
thf(5631,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV415 @ SY1909 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1909 ) ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5586]) ).
thf(5632,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV415 @ SY1897 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1897 ) ) ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5587]) ).
thf(5633,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK185_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV107 @ SY1910 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1910 ) ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5588]) ).
thf(5634,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK176_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV107 @ SY1898 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1898 ) ) ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5589]) ).
thf(5635,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1911: $i] :
( ~ ( SV415 @ SY1911 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1911 ) ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5590]) ).
thf(5636,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1899: $i] :
( ~ ( SV415 @ SY1899 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1899 ) ) ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5591]) ).
thf(5637,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK187_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1912: $i] :
( ~ ( SV107 @ SY1912 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1912 ) ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5592]) ).
thf(5638,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK178_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1900: $i] :
( ~ ( SV107 @ SY1900 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1900 ) ) ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5593]) ).
thf(5639,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1901: $i] :
( ~ ( SV415 @ SY1901 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1901 ) ) ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5594]) ).
thf(5640,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1891: $i] :
( ~ ( SV415 @ SY1891 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1891 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5595]) ).
thf(5641,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK180_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1902: $i] :
( ~ ( SV107 @ SY1902 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1902 ) ) ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5596]) ).
thf(5642,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK173_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1892: $i] :
( ~ ( SV107 @ SY1892 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1892 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5597]) ).
thf(5643,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i,SV1075: $i] :
( ( ( ~ ( in @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) @ SV140 ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5598]) ).
thf(5644,plain,
! [SV1075: $i,SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
!= ( SV445 @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) ) )
= $false )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5598]) ).
thf(5645,plain,
! [SV489: $i,SV191: $i > $i > $o,SV1092: $i,SV951: $i] :
( ( ( in @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV489 )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5599]) ).
thf(5646,plain,
! [SV489: $i,SV1092: $i,SV951: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ ( sK168_SY1860 @ SV951 @ SV1092 @ SV191 @ SV489 ) @ SV1092 )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5600]) ).
thf(5647,plain,
! [SV951: $i,SV1092: $i,SV191: $i > $i > $o,SV489: $i,SV1109: $i] :
( ( ( in @ SV1109 @ SV489 )
= $false )
| ( ( ~ ( SV191 @ SV1109 @ SV1092 ) )
= $true )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5601]) ).
thf(5648,plain,
! [SV951: $i,SV489: $i,SV1083: $i,SV1108: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ SV1108 @ SV1083 )
= $false )
| ( ( in @ SV1108 @ SV489 )
= $false )
| ( ( in @ SV1083 @ ( sK124_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV951
= ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5604]) ).
thf(5649,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
| ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5605]) ).
thf(5650,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5606]) ).
thf(5651,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5606]) ).
thf(5652,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5607]) ).
thf(5653,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5607]) ).
thf(5654,plain,
! [SV955: $i,SV1084: $i,SV212: $i,SV1119: $i] :
( ( ( ~ ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) ) )
= $true )
| ( ( ! [SY1903: $i] :
( ~ ( in @ SY1903 @ SV1119 )
| ( in @ SY1903 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5608]) ).
thf(5655,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5609]) ).
thf(5656,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5610]) ).
thf(5657,plain,
! [SV955: $i,SV1077: $i,SV212: $i,SV1113: $i] :
( ( ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SV1113 )
| ( in @ SY1893 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
| ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5611]) ).
thf(5658,plain,
! [SV1107: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK181_SY1884 @ SV1022 @ SV260 @ SV1107 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5612]) ).
thf(5659,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1022: $i,SV1107: $i] :
( ( ( SV1107
= ( sK181_SY1884 @ SV1022 @ SV260 @ SV1107 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5612]) ).
thf(5660,plain,
! [SV1106: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK174_SY1878 @ SV1022 @ SV260 @ SV1106 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1106 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV1022
= ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $false )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5613]) ).
thf(5661,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( ~ ~ ( ~ ( SV550 @ SV1123 )
| ~ ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5615]) ).
thf(5662,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1120 )
| ~ ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5616]) ).
thf(5663,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1121 )
| ~ ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5617]) ).
thf(5664,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1114 )
| ~ ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5618]) ).
thf(5665,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1122 )
| ~ ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5619]) ).
thf(5666,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1115 )
| ~ ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5620]) ).
thf(5667,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1116 )
| ~ ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5621]) ).
thf(5668,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1110 ) )
= $true )
| ( ( ~ ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5622]) ).
thf(5669,plain,
! [SV107: $i > $o,SV1057: $i,SV1117: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1117 )
= $false )
| ( ( ( sK157_SY1012 @ SV1057 @ SV107 @ SV415 )
= SV1117 )
= $true )
| ( ( SV107 @ SV1057 )
= $false )
| ( ( SV107 @ ( sK144_SY1823 @ SV415 @ SV1057 @ SV107 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5623]) ).
thf(5670,plain,
! [SV415: $i > $o,SV1058: $i,SV1118: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1118 )
= $false )
| ( ( ( sK158_SY259 @ SV1058 @ SV415 @ SV107 )
= SV1118 )
= $true )
| ( ( SV415 @ SV1058 )
= $false )
| ( ( SV415 @ ( sK145_SY1824 @ SV107 @ SV1058 @ SV415 ) )
= $true )
| ( ( ( sK13_SY1008 @ SV415 @ SV107 )
= ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5625]) ).
thf(5671,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ~ ( ~ ( SV415 @ ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1914: $i] :
( ~ ( SV415 @ SY1914 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1914 ) ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5627]) ).
thf(5672,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1907: $i] :
( ~ ( SV415 @ SY1907 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1907 ) ) ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5628]) ).
thf(5673,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ~ ( ~ ( SV107 @ ( sK189_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV107 @ SY1915 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1915 ) ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5629]) ).
thf(5674,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK183_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1908: $i] :
( ~ ( SV107 @ SY1908 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1908 ) ) ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5630]) ).
thf(5675,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV415 @ SY1909 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1909 ) ) ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5631]) ).
thf(5676,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1897: $i] :
( ~ ( SV415 @ SY1897 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1897 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5632]) ).
thf(5677,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK185_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV107 @ SY1910 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1910 ) ) ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5633]) ).
thf(5678,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK176_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1898: $i] :
( ~ ( SV107 @ SY1898 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1898 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5634]) ).
thf(5679,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1911: $i] :
( ~ ( SV415 @ SY1911 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1911 ) ) ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5635]) ).
thf(5680,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1899: $i] :
( ~ ( SV415 @ SY1899 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1899 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5636]) ).
thf(5681,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK187_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1912: $i] :
( ~ ( SV107 @ SY1912 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1912 ) ) ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5637]) ).
thf(5682,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK178_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1900: $i] :
( ~ ( SV107 @ SY1900 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1900 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5638]) ).
thf(5683,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 ) )
| ~ ! [SY1901: $i] :
( ~ ( SV415 @ SY1901 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1901 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5639]) ).
thf(5684,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5640]) ).
thf(5685,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1891: $i] :
( ~ ( SV415 @ SY1891 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1891 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5640]) ).
thf(5686,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK180_SY259 @ SV1088 @ SV415 @ SV107 ) )
| ~ ! [SY1902: $i] :
( ~ ( SV107 @ SY1902 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1902 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5641]) ).
thf(5687,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK173_SY259 @ SV1088 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5642]) ).
thf(5688,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1892: $i] :
( ~ ( SV107 @ SY1892 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1892 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5642]) ).
thf(5689,plain,
! [SV140: $i,SV445: $i > $i,SV978: $i,SV1075: $i] :
( ( ( in @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) @ SV140 )
= $true )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5643]) ).
thf(5690,plain,
! [SV1075: $i,SV978: $i,SV140: $i,SV445: $i > $i] :
( ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ ( sK171_SY1803 @ SV1075 @ SV978 @ SV445 @ SV140 ) ) )
= $true )
| ( ( in @ SV1075 @ SV140 )
= $false )
| ( ( ( sK90_SY1774 @ SV445 @ SV140 @ SV978 )
= ( SV445 @ SV1075 ) )
= $false )
| ( ( ( sK8_SY1067 @ SV445 @ SV140 )
= SV978 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5644]) ).
thf(5691,plain,
! [SV951: $i,SV489: $i,SV1092: $i,SV1109: $i,SV191: $i > $i > $o] :
( ( ( SV191 @ SV1109 @ SV1092 )
= $false )
| ( ( in @ SV1109 @ SV489 )
= $false )
| ( ( in @ SV1092 @ ( sK132_SY1167 @ SV951 @ SV191 @ SV489 ) )
= $true )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ SV951 )
= $false )
| ( ( SV191 @ ( sK18_SY1164 @ SV191 @ SV489 ) @ ( sK102_SY1751 @ SV951 @ SV489 @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5647]) ).
thf(5692,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( ~ ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) ) )
= $false )
| ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5693,plain,
! [SV212: $i,SV1063: $i,SV1048: $i] :
( ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5649]) ).
thf(5694,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $false )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5650]) ).
thf(5695,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5652]) ).
thf(5696,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5653]) ).
thf(5697,plain,
! [SV955: $i,SV1084: $i,SV212: $i,SV1119: $i] :
( ( ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( ! [SY1903: $i] :
( ~ ( in @ SY1903 @ SV1119 )
| ( in @ SY1903 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
| ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5654]) ).
thf(5698,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5655]) ).
thf(5699,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5656]) ).
thf(5700,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1113: $i] :
( ( ( ! [SY1893: $i] :
( ~ ( in @ SY1893 @ SV1113 )
| ( in @ SY1893 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) ) )
= $true )
| ( ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 )
= $true )
| ( ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5657]) ).
thf(5701,plain,
! [SV1107: $i,SV260: $i > $o,SV1022: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK181_SY1884 @ SV1022 @ SV260 @ SV1107 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1107 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1022 )
= $false )
| ( ( SV260 @ ( sK133_SY1806 @ SV550 @ SV1022 @ SV260 ) )
= $true )
| ( ( ( sK21_SY1266 @ SV550 @ SV260 )
= ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5658]) ).
thf(5702,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( ~ ( ~ ( SV550 @ SV1123 )
| ~ ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5661]) ).
thf(5703,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1120 )
| ~ ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5662]) ).
thf(5704,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1121 )
| ~ ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5663]) ).
thf(5705,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1114 ) )
= $true )
| ( ( ~ ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5664]) ).
thf(5706,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1122 )
| ~ ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5665]) ).
thf(5707,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1115 ) )
= $true )
| ( ( ~ ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5666]) ).
thf(5708,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1116 ) )
= $true )
| ( ( ~ ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5667]) ).
thf(5709,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1110 )
= $false )
| ( ( ~ ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5668]) ).
thf(5710,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( ~ ( SV415 @ ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1914: $i] :
( ~ ( SV415 @ SY1914 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1914 ) ) ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5671]) ).
thf(5711,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1907: $i] :
( ~ ( SV415 @ SY1907 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1907 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5672]) ).
thf(5712,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( ~ ( SV107 @ ( sK189_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV107 @ SY1915 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1915 ) ) ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5673]) ).
thf(5713,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK183_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1908: $i] :
( ~ ( SV107 @ SY1908 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1908 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5674]) ).
thf(5714,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 ) )
| ~ ! [SY1909: $i] :
( ~ ( SV415 @ SY1909 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1909 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5675]) ).
thf(5715,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5676]) ).
thf(5716,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1897: $i] :
( ~ ( SV415 @ SY1897 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1897 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5676]) ).
thf(5717,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK185_SY259 @ SV1097 @ SV415 @ SV107 ) )
| ~ ! [SY1910: $i] :
( ~ ( SV107 @ SY1910 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1910 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5677]) ).
thf(5718,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK176_SY259 @ SV1097 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5678]) ).
thf(5719,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1898: $i] :
( ~ ( SV107 @ SY1898 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1898 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5678]) ).
thf(5720,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 ) )
| ~ ! [SY1911: $i] :
( ~ ( SV415 @ SY1911 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1911 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5679]) ).
thf(5721,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5680]) ).
thf(5722,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1899: $i] :
( ~ ( SV415 @ SY1899 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1899 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5680]) ).
thf(5723,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK187_SY259 @ SV1099 @ SV415 @ SV107 ) )
| ~ ! [SY1912: $i] :
( ~ ( SV107 @ SY1912 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1912 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5681]) ).
thf(5724,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK178_SY259 @ SV1099 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5725,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1900: $i] :
( ~ ( SV107 @ SY1900 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1900 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5682]) ).
thf(5726,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5683]) ).
thf(5727,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1901: $i] :
( ~ ( SV415 @ SY1901 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1901 ) ) )
= $false )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5683]) ).
thf(5728,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5684]) ).
thf(5729,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ! [SY1891: $i] :
( ~ ( SV415 @ SY1891 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1891 ) ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5685]) ).
thf(5730,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK180_SY259 @ SV1088 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5686]) ).
thf(5731,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1902: $i] :
( ~ ( SV107 @ SY1902 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1902 ) ) )
= $false )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5686]) ).
thf(5732,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK173_SY259 @ SV1088 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5687]) ).
thf(5733,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ! [SY1892: $i] :
( ~ ( SV107 @ SY1892 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1892 ) ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5688]) ).
thf(5734,plain,
! [SV212: $i,SV1048: $i,SV1063: $i] :
( ( ( in @ SV1063 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( in @ SV1048 @ ( sK153_SY1829 @ SV1063 @ SV1048 @ SV212 ) )
= $true )
| ( ( SV1048 = SV1063 )
= $true )
| ( ( in @ SV1048 @ SV212 )
= $false )
| ( ( in @ SV1063 @ SV212 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5692]) ).
thf(5735,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
| ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5695]) ).
thf(5736,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5696]) ).
thf(5737,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1119: $i] :
( ( ( ! [SY1903: $i] :
( ~ ( in @ SY1903 @ SV1119 )
| ( in @ SY1903 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) ) )
= $true )
| ( ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 )
= $true )
| ( ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5697]) ).
thf(5738,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ~ ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5698]) ).
thf(5739,plain,
! [SV1077: $i,SV955: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5698]) ).
thf(5740,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( ! [SY1869: $i] :
~ ~ ( ~ ( in @ SY1869 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SY1869 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5699]) ).
thf(5741,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1113: $i,SV1124: $i] :
( ( ( ~ ( in @ SV1124 @ SV1113 )
| ( in @ SV1124 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
= $true )
| ( ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 )
= $true )
| ( ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5700]) ).
thf(5742,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1123 )
| ~ ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5702]) ).
thf(5743,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1120 ) )
= $true )
| ( ( ~ ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5703]) ).
thf(5744,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1121 ) )
= $true )
| ( ( ~ ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5704]) ).
thf(5745,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1114 )
= $false )
| ( ( ~ ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5705]) ).
thf(5746,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1122 ) )
= $true )
| ( ( ~ ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5706]) ).
thf(5747,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1115 )
= $false )
| ( ( ~ ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5707]) ).
thf(5748,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1116 )
= $false )
| ( ( ~ ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5708]) ).
thf(5749,plain,
! [SV1074: $i,SV260: $i > $o,SV1110: $i,SV550: $i > $o] :
( ( ( ! [SY1890: $i] :
( ~ ( SV550 @ SY1890 )
| ( SV1110 = SY1890 ) ) )
= $false )
| ( ( SV550 @ SV1110 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5709]) ).
thf(5750,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 ) )
| ~ ! [SY1914: $i] :
( ~ ( SV415 @ SY1914 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1914 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5710]) ).
thf(5751,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5711]) ).
thf(5752,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1907: $i] :
( ~ ( SV415 @ SY1907 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1907 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5711]) ).
thf(5753,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK189_SY259 @ SV1103 @ SV415 @ SV107 ) )
| ~ ! [SY1915: $i] :
( ~ ( SV107 @ SY1915 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1915 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5712]) ).
thf(5754,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK183_SY259 @ SV1103 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5713]) ).
thf(5755,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1908: $i] :
( ~ ( SV107 @ SY1908 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1908 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5713]) ).
thf(5756,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5714]) ).
thf(5757,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1909: $i] :
( ~ ( SV415 @ SY1909 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1909 ) ) )
= $false )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5714]) ).
thf(5758,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5715]) ).
thf(5759,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ! [SY1897: $i] :
( ~ ( SV415 @ SY1897 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1897 ) ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5716]) ).
thf(5760,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK185_SY259 @ SV1097 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5717]) ).
thf(5761,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1910: $i] :
( ~ ( SV107 @ SY1910 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1910 ) ) )
= $false )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5717]) ).
thf(5762,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK176_SY259 @ SV1097 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5718]) ).
thf(5763,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ! [SY1898: $i] :
( ~ ( SV107 @ SY1898 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1898 ) ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5719]) ).
thf(5764,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5720]) ).
thf(5765,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1911: $i] :
( ~ ( SV415 @ SY1911 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1911 ) ) )
= $false )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5720]) ).
thf(5766,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5721]) ).
thf(5767,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ! [SY1899: $i] :
( ~ ( SV415 @ SY1899 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1899 ) ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5722]) ).
thf(5768,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK187_SY259 @ SV1099 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5723]) ).
thf(5769,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1912: $i] :
( ~ ( SV107 @ SY1912 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1912 ) ) )
= $false )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5723]) ).
thf(5770,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK178_SY259 @ SV1099 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5724]) ).
thf(5771,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ! [SY1900: $i] :
( ~ ( SV107 @ SY1900 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1900 ) ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5725]) ).
thf(5772,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5726]) ).
thf(5773,plain,
! [SV107: $i > $o,SV1087: $i,SV415: $i > $o] :
( ( ( ! [SY1901: $i] :
( ~ ( SV415 @ SY1901 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SY1901 ) ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5727]) ).
thf(5774,plain,
! [SV107: $i > $o,SV1087: $i,SV1125: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1125 )
| ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1125 ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5729]) ).
thf(5775,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK180_SY259 @ SV1088 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5730]) ).
thf(5776,plain,
! [SV415: $i > $o,SV1088: $i,SV107: $i > $o] :
( ( ( ! [SY1902: $i] :
( ~ ( SV107 @ SY1902 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SY1902 ) ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5731]) ).
thf(5777,plain,
! [SV415: $i > $o,SV1088: $i,SV1126: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1126 )
| ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1126 ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5733]) ).
thf(5778,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ~ ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5735]) ).
thf(5779,plain,
! [SV1084: $i,SV955: $i,SV212: $i] :
( ( ( ~ ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5735]) ).
thf(5780,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( ! [SY1875: $i] :
~ ~ ( ~ ( in @ SY1875 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SY1875 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5736]) ).
thf(5781,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1119: $i,SV1127: $i] :
( ( ( ~ ( in @ SV1127 @ SV1119 )
| ( in @ SV1127 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
= $true )
| ( ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 )
= $true )
| ( ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5737]) ).
thf(5782,plain,
! [SV212: $i,SV955: $i,SV1077: $i] :
( ( ( in @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5738]) ).
thf(5783,plain,
! [SV1077: $i,SV955: $i,SV212: $i] :
( ( ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV955 )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5739]) ).
thf(5784,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1128: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SV1128 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5740]) ).
thf(5785,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1113: $i,SV1124: $i] :
( ( ( ~ ( in @ SV1124 @ SV1113 ) )
= $true )
| ( ( in @ SV1124 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
= $true )
| ( ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 )
= $true )
| ( ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5741]) ).
thf(5786,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ SV1123 ) )
= $true )
| ( ( ~ ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5742]) ).
thf(5787,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1120 )
= $false )
| ( ( ~ ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5743]) ).
thf(5788,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1121 )
= $false )
| ( ( ~ ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5744]) ).
thf(5789,plain,
! [SV1078: $i,SV260: $i > $o,SV1114: $i,SV550: $i > $o] :
( ( ( ! [SY1894: $i] :
( ~ ( SV550 @ SY1894 )
| ( SV1114 = SY1894 ) ) )
= $false )
| ( ( SV550 @ SV1114 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5745]) ).
thf(5790,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1122 )
= $false )
| ( ( ~ ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5746]) ).
thf(5791,plain,
! [SV1079: $i,SV260: $i > $o,SV1115: $i,SV550: $i > $o] :
( ( ( ! [SY1895: $i] :
( ~ ( SV550 @ SY1895 )
| ( SV1115 = SY1895 ) ) )
= $false )
| ( ( SV550 @ SV1115 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5747]) ).
thf(5792,plain,
! [SV1074: $i,SV260: $i > $o,SV1116: $i,SV550: $i > $o] :
( ( ( ! [SY1896: $i] :
( ~ ( SV550 @ SY1896 )
| ( SV1116 = SY1896 ) ) )
= $false )
| ( ( SV550 @ SV1116 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5748]) ).
thf(5793,plain,
! [SV1110: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK190_SY1890 @ SV1074 @ SV260 @ SV1110 @ SV550 ) )
| ( SV1110
= ( sK190_SY1890 @ SV1074 @ SV260 @ SV1110 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1110 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5749]) ).
thf(5794,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5750]) ).
thf(5795,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ~ ! [SY1914: $i] :
( ~ ( SV415 @ SY1914 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1914 ) ) )
= $false )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5750]) ).
thf(5796,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5751]) ).
thf(5797,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ! [SY1907: $i] :
( ~ ( SV415 @ SY1907 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1907 ) ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5752]) ).
thf(5798,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ ( sK189_SY259 @ SV1103 @ SV415 @ SV107 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5753]) ).
thf(5799,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ~ ! [SY1915: $i] :
( ~ ( SV107 @ SY1915 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1915 ) ) )
= $false )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5753]) ).
thf(5800,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK183_SY259 @ SV1103 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5754]) ).
thf(5801,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ! [SY1908: $i] :
( ~ ( SV107 @ SY1908 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1908 ) ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5755]) ).
thf(5802,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5756]) ).
thf(5803,plain,
! [SV107: $i > $o,SV1096: $i,SV415: $i > $o] :
( ( ( ! [SY1909: $i] :
( ~ ( SV415 @ SY1909 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SY1909 ) ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5757]) ).
thf(5804,plain,
! [SV107: $i > $o,SV1096: $i,SV1129: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1129 )
| ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1129 ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5759]) ).
thf(5805,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK185_SY259 @ SV1097 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5760]) ).
thf(5806,plain,
! [SV415: $i > $o,SV1097: $i,SV107: $i > $o] :
( ( ( ! [SY1910: $i] :
( ~ ( SV107 @ SY1910 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SY1910 ) ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5761]) ).
thf(5807,plain,
! [SV415: $i > $o,SV1097: $i,SV1130: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1130 )
| ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1130 ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5763]) ).
thf(5808,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5764]) ).
thf(5809,plain,
! [SV107: $i > $o,SV1098: $i,SV415: $i > $o] :
( ( ( ! [SY1911: $i] :
( ~ ( SV415 @ SY1911 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SY1911 ) ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5765]) ).
thf(5810,plain,
! [SV107: $i > $o,SV1098: $i,SV1131: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1131 )
| ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1131 ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5767]) ).
thf(5811,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK187_SY259 @ SV1099 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5768]) ).
thf(5812,plain,
! [SV415: $i > $o,SV1099: $i,SV107: $i > $o] :
( ( ( ! [SY1912: $i] :
( ~ ( SV107 @ SY1912 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SY1912 ) ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5769]) ).
thf(5813,plain,
! [SV415: $i > $o,SV1099: $i,SV1132: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1132 )
| ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1132 ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5771]) ).
thf(5814,plain,
! [SV107: $i > $o,SV1087: $i,SV1133: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1133 )
| ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1133 ) )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5773]) ).
thf(5815,plain,
! [SV107: $i > $o,SV1087: $i,SV1125: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1125 ) )
= $true )
| ( ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1125 )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5774]) ).
thf(5816,plain,
! [SV415: $i > $o,SV1088: $i,SV1134: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1134 )
| ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1134 ) )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5776]) ).
thf(5817,plain,
! [SV415: $i > $o,SV1088: $i,SV1126: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1126 ) )
= $true )
| ( ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1126 )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5777]) ).
thf(5818,plain,
! [SV212: $i,SV955: $i,SV1084: $i] :
( ( ( in @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) @ ( sK4_SY557 @ SV212 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5778]) ).
thf(5819,plain,
! [SV1084: $i,SV955: $i,SV212: $i] :
( ( ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV955 )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5779]) ).
thf(5820,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1135: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SV1135 @ SV955 ) ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5780]) ).
thf(5821,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1119: $i,SV1127: $i] :
( ( ( ~ ( in @ SV1127 @ SV1119 ) )
= $true )
| ( ( in @ SV1127 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
= $true )
| ( ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 )
= $true )
| ( ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5781]) ).
thf(5822,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1128: $i] :
( ( ( ~ ( ~ ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SV1128 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5784]) ).
thf(5823,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1113: $i,SV1124: $i] :
( ( ( in @ SV1124 @ SV1113 )
= $false )
| ( ( in @ SV1124 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
= $true )
| ( ( in @ ( sK154_SY1868 @ SV212 @ SV955 @ SV1077 ) @ SV1113 )
= $true )
| ( ( in @ SV1113 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5785]) ).
thf(5824,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( SV550 @ SV1123 )
= $false )
| ( ( ~ ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5786]) ).
thf(5825,plain,
! [SV1085: $i,SV260: $i > $o,SV1120: $i,SV550: $i > $o] :
( ( ( ! [SY1904: $i] :
( ~ ( SV550 @ SY1904 )
| ( SV1120 = SY1904 ) ) )
= $false )
| ( ( SV550 @ SV1120 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5787]) ).
thf(5826,plain,
! [SV1078: $i,SV260: $i > $o,SV1121: $i,SV550: $i > $o] :
( ( ( ! [SY1905: $i] :
( ~ ( SV550 @ SY1905 )
| ( SV1121 = SY1905 ) ) )
= $false )
| ( ( SV550 @ SV1121 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5788]) ).
thf(5827,plain,
! [SV1114: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK191_SY1894 @ SV1078 @ SV260 @ SV1114 @ SV550 ) )
| ( SV1114
= ( sK191_SY1894 @ SV1078 @ SV260 @ SV1114 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1114 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5789]) ).
thf(5828,plain,
! [SV1079: $i,SV260: $i > $o,SV1122: $i,SV550: $i > $o] :
( ( ( ! [SY1906: $i] :
( ~ ( SV550 @ SY1906 )
| ( SV1122 = SY1906 ) ) )
= $false )
| ( ( SV550 @ SV1122 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5790]) ).
thf(5829,plain,
! [SV1115: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK192_SY1895 @ SV1079 @ SV260 @ SV1115 @ SV550 ) )
| ( SV1115
= ( sK192_SY1895 @ SV1079 @ SV260 @ SV1115 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1115 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5791]) ).
thf(5830,plain,
! [SV1116: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK193_SY1896 @ SV1074 @ SV260 @ SV1116 @ SV550 ) )
| ( SV1116
= ( sK193_SY1896 @ SV1074 @ SV260 @ SV1116 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1116 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5792]) ).
thf(5831,plain,
! [SV1110: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK190_SY1890 @ SV1074 @ SV260 @ SV1110 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1110 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5793]) ).
thf(5832,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1074: $i,SV1110: $i] :
( ( ( SV1110
= ( sK190_SY1890 @ SV1074 @ SV260 @ SV1110 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1110 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5793]) ).
thf(5833,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( SV415 @ ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5794]) ).
thf(5834,plain,
! [SV107: $i > $o,SV1102: $i,SV415: $i > $o] :
( ( ( ! [SY1914: $i] :
( ~ ( SV415 @ SY1914 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SY1914 ) ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5795]) ).
thf(5835,plain,
! [SV107: $i > $o,SV1102: $i,SV1136: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1136 )
| ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1136 ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5797]) ).
thf(5836,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( SV107 @ ( sK189_SY259 @ SV1103 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5798]) ).
thf(5837,plain,
! [SV415: $i > $o,SV1103: $i,SV107: $i > $o] :
( ( ( ! [SY1915: $i] :
( ~ ( SV107 @ SY1915 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SY1915 ) ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5799]) ).
thf(5838,plain,
! [SV415: $i > $o,SV1103: $i,SV1137: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1137 )
| ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1137 ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5801]) ).
thf(5839,plain,
! [SV107: $i > $o,SV1096: $i,SV1138: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1138 )
| ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1138 ) )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5803]) ).
thf(5840,plain,
! [SV107: $i > $o,SV1096: $i,SV1129: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1129 ) )
= $true )
| ( ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1129 )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5804]) ).
thf(5841,plain,
! [SV415: $i > $o,SV1097: $i,SV1139: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1139 )
| ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1139 ) )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5806]) ).
thf(5842,plain,
! [SV415: $i > $o,SV1097: $i,SV1130: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1130 ) )
= $true )
| ( ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1130 )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5807]) ).
thf(5843,plain,
! [SV107: $i > $o,SV1098: $i,SV1140: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1140 )
| ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1140 ) )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5809]) ).
thf(5844,plain,
! [SV107: $i > $o,SV1098: $i,SV1131: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1131 ) )
= $true )
| ( ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1131 )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5810]) ).
thf(5845,plain,
! [SV415: $i > $o,SV1099: $i,SV1141: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1141 )
| ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1141 ) )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5812]) ).
thf(5846,plain,
! [SV415: $i > $o,SV1099: $i,SV1132: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1132 ) )
= $true )
| ( ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1132 )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5813]) ).
thf(5847,plain,
! [SV107: $i > $o,SV1087: $i,SV1133: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1133 ) )
= $true )
| ( ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1133 )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5814]) ).
thf(5848,plain,
! [SV107: $i > $o,SV1087: $i,SV1125: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1125 )
= $false )
| ( ( ( sK172_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1125 )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV1087
= ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5815]) ).
thf(5849,plain,
! [SV415: $i > $o,SV1088: $i,SV1134: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1134 ) )
= $true )
| ( ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1134 )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5816]) ).
thf(5850,plain,
! [SV415: $i > $o,SV1088: $i,SV1126: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1126 )
= $false )
| ( ( ( sK173_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1126 )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV1088
= ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5817]) ).
thf(5851,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1135: $i] :
( ( ( ~ ( ~ ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SV1135 @ SV955 ) ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5820]) ).
thf(5852,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1119: $i,SV1127: $i] :
( ( ( in @ SV1127 @ SV1119 )
= $false )
| ( ( in @ SV1127 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
= $true )
| ( ( in @ ( sK159_SY1874 @ SV212 @ SV955 @ SV1084 ) @ SV1119 )
= $true )
| ( ( in @ SV1119 @ ( sK4_SY557 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5821]) ).
thf(5853,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1128: $i] :
( ( ( ~ ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
| ~ ( in @ SV1128 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5822]) ).
thf(5854,plain,
! [SV1085: $i,SV260: $i > $o,SV1123: $i,SV550: $i > $o] :
( ( ( ! [SY1913: $i] :
( ~ ( SV550 @ SY1913 )
| ( SV1123 = SY1913 ) ) )
= $false )
| ( ( SV550 @ SV1123 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5824]) ).
thf(5855,plain,
! [SV1120: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK194_SY1904 @ SV1085 @ SV260 @ SV1120 @ SV550 ) )
| ( SV1120
= ( sK194_SY1904 @ SV1085 @ SV260 @ SV1120 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1120 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5825]) ).
thf(5856,plain,
! [SV1121: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK195_SY1905 @ SV1078 @ SV260 @ SV1121 @ SV550 ) )
| ( SV1121
= ( sK195_SY1905 @ SV1078 @ SV260 @ SV1121 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1121 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5826]) ).
thf(5857,plain,
! [SV1114: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK191_SY1894 @ SV1078 @ SV260 @ SV1114 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1114 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5827]) ).
thf(5858,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1078: $i,SV1114: $i] :
( ( ( SV1114
= ( sK191_SY1894 @ SV1078 @ SV260 @ SV1114 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1114 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5827]) ).
thf(5859,plain,
! [SV1122: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK196_SY1906 @ SV1079 @ SV260 @ SV1122 @ SV550 ) )
| ( SV1122
= ( sK196_SY1906 @ SV1079 @ SV260 @ SV1122 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1122 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5828]) ).
thf(5860,plain,
! [SV1115: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK192_SY1895 @ SV1079 @ SV260 @ SV1115 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1115 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5829]) ).
thf(5861,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1079: $i,SV1115: $i] :
( ( ( SV1115
= ( sK192_SY1895 @ SV1079 @ SV260 @ SV1115 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1115 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5829]) ).
thf(5862,plain,
! [SV1116: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK193_SY1896 @ SV1074 @ SV260 @ SV1116 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1116 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5830]) ).
thf(5863,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1074: $i,SV1116: $i] :
( ( ( SV1116
= ( sK193_SY1896 @ SV1074 @ SV260 @ SV1116 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1116 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5830]) ).
thf(5864,plain,
! [SV1110: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK190_SY1890 @ SV1074 @ SV260 @ SV1110 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1110 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV1074
= ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5831]) ).
thf(5865,plain,
! [SV107: $i > $o,SV1102: $i,SV1142: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1142 )
| ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1142 ) )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5834]) ).
thf(5866,plain,
! [SV107: $i > $o,SV1102: $i,SV1136: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1136 ) )
= $true )
| ( ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1136 )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5835]) ).
thf(5867,plain,
! [SV415: $i > $o,SV1103: $i,SV1143: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1143 )
| ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1143 ) )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5837]) ).
thf(5868,plain,
! [SV415: $i > $o,SV1103: $i,SV1137: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1137 ) )
= $true )
| ( ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1137 )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5838]) ).
thf(5869,plain,
! [SV107: $i > $o,SV1096: $i,SV1138: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1138 ) )
= $true )
| ( ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1138 )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5839]) ).
thf(5870,plain,
! [SV107: $i > $o,SV1096: $i,SV1129: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1129 )
= $false )
| ( ( ( sK175_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1129 )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV1096
= ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5840]) ).
thf(5871,plain,
! [SV415: $i > $o,SV1097: $i,SV1139: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1139 ) )
= $true )
| ( ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1139 )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5841]) ).
thf(5872,plain,
! [SV415: $i > $o,SV1097: $i,SV1130: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1130 )
= $false )
| ( ( ( sK176_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1130 )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV1097
= ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5842]) ).
thf(5873,plain,
! [SV107: $i > $o,SV1098: $i,SV1140: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1140 ) )
= $true )
| ( ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1140 )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5843]) ).
thf(5874,plain,
! [SV107: $i > $o,SV1098: $i,SV1131: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1131 )
= $false )
| ( ( ( sK177_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1131 )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV1098
= ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5844]) ).
thf(5875,plain,
! [SV415: $i > $o,SV1099: $i,SV1141: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1141 ) )
= $true )
| ( ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1141 )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5845]) ).
thf(5876,plain,
! [SV415: $i > $o,SV1099: $i,SV1132: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1132 )
= $false )
| ( ( ( sK178_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1132 )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV1099
= ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5846]) ).
thf(5877,plain,
! [SV107: $i > $o,SV1087: $i,SV1133: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1133 )
= $false )
| ( ( ( sK179_SY1012 @ SV1087 @ SV107 @ SV415 )
= SV1133 )
= $true )
| ( ( SV107 @ SV1087 )
= $false )
| ( ( SV107 @ ( sK161_SY1858 @ SV415 @ SV1087 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5847]) ).
thf(5878,plain,
! [SV415: $i > $o,SV1088: $i,SV1134: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1134 )
= $false )
| ( ( ( sK180_SY259 @ SV1088 @ SV415 @ SV107 )
= SV1134 )
= $true )
| ( ( SV415 @ SV1088 )
= $false )
| ( ( SV415 @ ( sK162_SY1859 @ SV107 @ SV1088 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5849]) ).
thf(5879,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1135: $i] :
( ( ( ~ ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
| ~ ( in @ SV1135 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5851]) ).
thf(5880,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1128: $i] :
( ( ( ~ ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) ) )
= $true )
| ( ( ~ ( in @ SV1128 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5853]) ).
thf(5881,plain,
! [SV1123: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK197_SY1913 @ SV1085 @ SV260 @ SV1123 @ SV550 ) )
| ( SV1123
= ( sK197_SY1913 @ SV1085 @ SV260 @ SV1123 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1123 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5854]) ).
thf(5882,plain,
! [SV1120: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK194_SY1904 @ SV1085 @ SV260 @ SV1120 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1120 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5855]) ).
thf(5883,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1085: $i,SV1120: $i] :
( ( ( SV1120
= ( sK194_SY1904 @ SV1085 @ SV260 @ SV1120 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1120 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5855]) ).
thf(5884,plain,
! [SV1121: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK195_SY1905 @ SV1078 @ SV260 @ SV1121 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1121 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5856]) ).
thf(5885,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1078: $i,SV1121: $i] :
( ( ( SV1121
= ( sK195_SY1905 @ SV1078 @ SV260 @ SV1121 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1121 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5856]) ).
thf(5886,plain,
! [SV1114: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK191_SY1894 @ SV1078 @ SV260 @ SV1114 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1114 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV1078
= ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5857]) ).
thf(5887,plain,
! [SV1122: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK196_SY1906 @ SV1079 @ SV260 @ SV1122 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1122 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5859]) ).
thf(5888,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1079: $i,SV1122: $i] :
( ( ( SV1122
= ( sK196_SY1906 @ SV1079 @ SV260 @ SV1122 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1122 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5859]) ).
thf(5889,plain,
! [SV1115: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK192_SY1895 @ SV1079 @ SV260 @ SV1115 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1115 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV1079
= ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5860]) ).
thf(5890,plain,
! [SV1116: $i,SV260: $i > $o,SV1074: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK193_SY1896 @ SV1074 @ SV260 @ SV1116 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1116 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1074 )
= $false )
| ( ( SV260 @ ( sK150_SY1843 @ SV550 @ SV1074 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5862]) ).
thf(5891,plain,
! [SV107: $i > $o,SV1102: $i,SV1142: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV1142 ) )
= $true )
| ( ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1142 )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5865]) ).
thf(5892,plain,
! [SV107: $i > $o,SV1102: $i,SV1136: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1136 )
= $false )
| ( ( ( sK182_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1136 )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV1102
= ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5866]) ).
thf(5893,plain,
! [SV415: $i > $o,SV1103: $i,SV1143: $i,SV107: $i > $o] :
( ( ( ~ ( SV107 @ SV1143 ) )
= $true )
| ( ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1143 )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5867]) ).
thf(5894,plain,
! [SV415: $i > $o,SV1103: $i,SV1137: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1137 )
= $false )
| ( ( ( sK183_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1137 )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV1103
= ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $false )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5868]) ).
thf(5895,plain,
! [SV107: $i > $o,SV1096: $i,SV1138: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1138 )
= $false )
| ( ( ( sK184_SY1012 @ SV1096 @ SV107 @ SV415 )
= SV1138 )
= $true )
| ( ( SV107 @ SV1096 )
= $false )
| ( ( SV107 @ ( sK164_SY1864 @ SV415 @ SV1096 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5869]) ).
thf(5896,plain,
! [SV415: $i > $o,SV1097: $i,SV1139: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1139 )
= $false )
| ( ( ( sK185_SY259 @ SV1097 @ SV415 @ SV107 )
= SV1139 )
= $true )
| ( ( SV415 @ SV1097 )
= $false )
| ( ( SV415 @ ( sK165_SY1865 @ SV107 @ SV1097 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5871]) ).
thf(5897,plain,
! [SV107: $i > $o,SV1098: $i,SV1140: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1140 )
= $false )
| ( ( ( sK186_SY1012 @ SV1098 @ SV107 @ SV415 )
= SV1140 )
= $true )
| ( ( SV107 @ SV1098 )
= $false )
| ( ( SV107 @ ( sK166_SY1866 @ SV415 @ SV1098 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5873]) ).
thf(5898,plain,
! [SV415: $i > $o,SV1099: $i,SV1141: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1141 )
= $false )
| ( ( ( sK187_SY259 @ SV1099 @ SV415 @ SV107 )
= SV1141 )
= $true )
| ( ( SV415 @ SV1099 )
= $false )
| ( ( SV415 @ ( sK167_SY1867 @ SV107 @ SV1099 @ SV415 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $false )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5875]) ).
thf(5899,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1135: $i] :
( ( ( ~ ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) ) )
= $true )
| ( ( ~ ( in @ SV1135 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5879]) ).
thf(5900,plain,
! [SV212: $i,SV955: $i,SV1077: $i,SV1128: $i] :
( ( ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
= $false )
| ( ( ~ ( in @ SV1128 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5880]) ).
thf(5901,plain,
! [SV1123: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( ~ ( SV550 @ ( sK197_SY1913 @ SV1085 @ SV260 @ SV1123 @ SV550 ) ) )
= $false )
| ( ( SV550 @ SV1123 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5881]) ).
thf(5902,plain,
! [SV550: $i > $o,SV260: $i > $o,SV1085: $i,SV1123: $i] :
( ( ( SV1123
= ( sK197_SY1913 @ SV1085 @ SV260 @ SV1123 @ SV550 ) )
= $false )
| ( ( SV550 @ SV1123 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5881]) ).
thf(5903,plain,
! [SV1120: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK194_SY1904 @ SV1085 @ SV260 @ SV1120 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1120 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV1085
= ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $false )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5882]) ).
thf(5904,plain,
! [SV1121: $i,SV260: $i > $o,SV1078: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK195_SY1905 @ SV1078 @ SV260 @ SV1121 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1121 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1078 )
= $false )
| ( ( SV260 @ ( sK155_SY1851 @ SV550 @ SV1078 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5884]) ).
thf(5905,plain,
! [SV1122: $i,SV260: $i > $o,SV1079: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK196_SY1906 @ SV1079 @ SV260 @ SV1122 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1122 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1079 )
= $false )
| ( ( SV260 @ ( sK156_SY1852 @ SV550 @ SV1079 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $false )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5887]) ).
thf(5906,plain,
! [SV107: $i > $o,SV1102: $i,SV1142: $i,SV415: $i > $o] :
( ( ( SV415 @ SV1142 )
= $false )
| ( ( ( sK188_SY1012 @ SV1102 @ SV107 @ SV415 )
= SV1142 )
= $true )
| ( ( SV107 @ SV1102 )
= $false )
| ( ( SV107 @ ( sK169_SY1872 @ SV415 @ SV1102 @ SV107 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5891]) ).
thf(5907,plain,
! [SV415: $i > $o,SV1103: $i,SV1143: $i,SV107: $i > $o] :
( ( ( SV107 @ SV1143 )
= $false )
| ( ( ( sK189_SY259 @ SV1103 @ SV415 @ SV107 )
= SV1143 )
= $true )
| ( ( SV415 @ SV1103 )
= $false )
| ( ( SV415 @ ( sK170_SY1873 @ SV107 @ SV1103 @ SV415 ) )
= $true )
| ( ( SV107 @ ( sK13_SY1008 @ SV415 @ SV107 ) )
= $true )
| ( ( SV415 @ ( sK26_SY1601 @ SV107 @ SV415 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5893]) ).
thf(5908,plain,
! [SV212: $i,SV955: $i,SV1084: $i,SV1135: $i] :
( ( ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
= $false )
| ( ( ~ ( in @ SV1135 @ SV955 ) )
= $true )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5899]) ).
thf(5909,plain,
! [SV212: $i,SV1077: $i,SV955: $i,SV1128: $i] :
( ( ( in @ SV1128 @ SV955 )
= $false )
| ( ( in @ SV1128 @ ( sK147_SY1756 @ SV1077 @ SV955 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV212 )
= $false )
| ( ( in @ SV1077 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5900]) ).
thf(5910,plain,
! [SV1123: $i,SV260: $i > $o,SV1085: $i,SV550: $i > $o] :
( ( ( SV550 @ ( sK197_SY1913 @ SV1085 @ SV260 @ SV1123 @ SV550 ) )
= $true )
| ( ( SV550 @ SV1123 )
= $false )
| ( ( ( descr
@ ^ [SY698: $i] : ( SV260 @ SY698 ) )
= ( descr
@ ^ [SY1273: $i] : ( SV550 @ SY1273 ) ) )
= $true )
| ( ( SV260 @ SV1085 )
= $false )
| ( ( SV260 @ ( sK160_SY1857 @ SV550 @ SV1085 @ SV260 ) )
= $true )
| ( ( SV260 @ ( sK21_SY1266 @ SV550 @ SV260 ) )
= $true )
| ( ( SV550 @ ( sK34_SY1652 @ SV260 @ SV550 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5901]) ).
thf(5911,plain,
! [SV212: $i,SV1084: $i,SV955: $i,SV1135: $i] :
( ( ( in @ SV1135 @ SV955 )
= $false )
| ( ( in @ SV1135 @ ( sK149_SY1756 @ SV1084 @ SV955 @ SV212 ) )
= $false )
| ( ( in @ ( sK104_SY1754 @ SV212 @ SV955 ) @ SV955 )
= $true )
| ( ( in @ SV1084 @ SV955 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5908]) ).
thf(5912,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[674,5911,5910,5909,5907,5906,5905,5904,5903,5902,5898,5897,5896,5895,5894,5892,5890,5889,5888,5886,5885,5883,5878,5877,5876,5874,5872,5870,5864,5863,5861,5858,5852,5850,5848,5836,5833,5832,5823,5819,5818,5811,5808,5805,5802,5800,5796,5783,5782,5775,5772,5770,5766,5762,5758,5734,5732,5728,5701,5694,5693,5691,5690,5689,5670,5669,5660,5659,5651,5648,5646,5645,5626,5624,5614,5603,5602,5537,5534,5498,5494,5443,5437,5436,5412,5405,5382,5381,5380,5371,5370,5355,5354,5353,5346,5345,5343,5342,5340,5339,5329,5328,5327,5325,5324,5322,5321,5306,5305,5304,5301,5300,5299,5297,5296,5289,5286,5283,5280,5270,5269,5268,5264,5262,5259,5257,5256,5255,5254,5253,5238,5236,5235,5233,5232,5230,5228,5227,5226,5225,5223,5222,5220,5217,5215,5187,5183,5180,5179,5178,5175,5173,5172,5168,5155,5152,5149,5148,5146,5145,5144,5142,5141,5139,5138,5134,5133,5128,5125,5112,5111,5099,5097,5093,5089,5088,5086,5073,5072,5071,5054,5051,5049,5046,5043,5038,5037,5033,5029,5028,5026,5013,5011,5004,4998,4979,4975,4974,4972,4967,4966,4965,4963,4938,4915,4894,4889,4885,4883,4880,4879,4877,4876,4871,4869,4867,4863,4830,4806,4786,4784,4781,4779,4770,4768,4767,4762,4761,4747,4746,4745,4744,4743,4742,4740,4738,4735,4728,4727,4726,4725,4721,4703,4701,4700,4698,4692,4687,4685,4671,4663,4646,4631,4628,4625,4622,4618,4616,4609,4607,4605,4603,4599,4598,4580,4570,4569,4568,4567,4558,4553,4543,4541,4535,4533,4517,4507,4506,4503,4502,4501,4500,4497,4496,4495,4494,4491,4490,4488,4485,4484,4483,4481,4480,4479,4478,4472,4467,4466,4465,4458,4457,4456,4452,4432,4422,4420,4419,4413,4409,4403,4401,4400,4363,4355,4351,4348,4344,4341,4337,4333,4331,4327,4324,4323,4322,4320,4315,4311,4308,4307,4305,4303,4299,4298,4297,4295,4294,4292,4291,4286,4284,4282,4281,4279,4278,4276,4275,4273,4268,4257,4246,4208,4205,4198,4194,4188,4178,4145,4141,4140,4133,4132,4124,4123,4119,4112,4110,4109,4106,4103,4100,4099,4096,4092,4090,4088,4085,4082,4073,4069,4064,4063,4054,4053,4041,4038,4034,4003,3999,3992,3991,3990,3979,3957,3946,3945,3930,3928,3917,3900,3899,3898,3887,3868,3867,3866,3863,3862,3837,3829,3828,3827,3819,3818,3805,3804,3803,3802,3790,3767,3766,3765,3763,3720,3719,3697,3696,3695,3692,3686,3681,3680,3669,3647,3646,3645,3643,3642,3641,3640,3638,3630,3623,3616,3615,3606,3604,3603,3601,3600,3598,3597,3596,3595,3594,3583,3582,3564,3563,3562,3553,3551,3539,3527,3478,3468,3455,3444,3441,3435,3415,3392,3381,3338,3337,3328,3327,3326,3321,3313,3311,3304,3279,3272,3266,3256,3255,3254,3253,3241,3240,3239,3238,3230,3225,3224,3223,3218,3210,3200,3199,3193,3176,3168,3164,3143,3142,3141,3140,3139,3137,3134,3118,3108,3099,3097,3096,3094,3093,3090,3087,3086,3085,3074,3072,3070,3062,3025,3022,3016,3015,3001,3000,2994,2985,2961,2959,2947,2944,2934,2927,2924,2917,2906,2900,2895,2893,2882,2871,2868,2863,2862,2849,2842,2826,2778,2769,2745,2739,2730,2694,2690,2671,2670,2669,2655,2650,2635,2627,2621,2620,2611,2608,2601,2578,2542,2537,2534,2532,2527,2523,2521,2518,2516,2508,2497,2489,2488,2470,2469,2451,2426,2409,2407,2389,2386,2382,2379,2334,2323,2314,2308,2306,2300,2291,2286,2278,2266,2255,2250,2240,2231,2230,2229,2223,2207,2199,2197,2196,2188,2178,2175,2144,2132,2128,2118,2104,2093,2085,2083,2073,2070,2065,2051,2043,2022,2016,2015,2014,2012,2006,1994,1958,1950,1917,1874,1858,1857,1856,1774,1770,1760,1742,1741,1740,1735,1706,1694,1690,1685,1642,1640,1623,1613,1588,1586,1566,1549,1544,1538,1511,1507,1487,1471,1466,1444,1437,1428,1418,1404,1402,1361,1343,1297,1226,1221,1220,1180,1061,1047,1036,1027,767,765,691]) ).
thf(5913,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU814^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:36:55 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 215.31/36.34 ..
% 215.31/36.34
% 215.31/36.34 No.of.Axioms: 0
% 215.31/36.34
% 215.31/36.34 Length.of.Defs: 80318
% 215.31/36.34
% 215.31/36.34 Contains.Choice.Funs: true
% 215.31/36.34 ..................................................................................................................................................................................................................................
% 215.31/36.34
% 215.31/36.34 ********************************
% 215.31/36.34 * All subproblems solved! *
% 215.31/36.34 ********************************
% 215.31/36.34 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:330,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:5912,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 215.31/36.34
% 215.31/36.34 %**** Beginning of derivation protocol ****
% 215.31/36.34 % SZS output start CNFRefutation
% See solution above
% 35.79/36.41
% 35.79/36.41 %**** End of derivation protocol ****
% 35.79/36.41 %**** no. of clauses in derivation: 5913 ****
% 35.79/36.41 %**** clause counter: 5912 ****
% 35.79/36.41
% 35.79/36.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:330,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:5912,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------