%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU784^1 : 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 : n002.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 10:48:16 AM UTC 2026
% Result : Theorem 155.17s 26.24s
% Output : CNFRefutation 155.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 303
% Syntax : Number of formulae : 5640 (1958 unt; 0 typ; 302 def)
% Number of atoms : 51789 (18909 equ; 0 cnn)
% Maximal formula atoms : 306 ( 9 avg)
% Number of connectives : 113500 (18629 ~;18994 |; 231 &;71977 @)
% ( 56 <=>;3613 =>; 0 <=; 0 <~>)
% Maximal formula depth : 315 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2834 (2834 >; 0 *; 0 +; 0 <<)
% Number of symbols : 533 ( 530 usr; 309 con; 0-6 aty)
% Number of variables : 23973 (1420 ^;22366 !; 187 ?;23973 :)
% 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_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_breln1unionIL,type,
breln1unionIL: $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_foundationAx,type,
foundationAx: $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $o ).
thf(tp_if,type,
if: $i > $o > $i > $i > $i ).
thf(tp_ifSingleton,type,
ifSingleton: $o ).
thf(tp_iffalse,type,
iffalse: $o ).
thf(tp_iffalseProp1,type,
iffalseProp1: $o ).
thf(tp_iffalseProp2,type,
iffalseProp2: $o ).
thf(tp_ifp,type,
ifp: $o ).
thf(tp_iftrue,type,
iftrue: $o ).
thf(tp_iftrueProp1,type,
iftrueProp1: $o ).
thf(tp_iftrueProp2,type,
iftrueProp2: $o ).
thf(tp_iftrueorfalse,type,
iftrueorfalse: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inComplementUnionImpInComplement1,type,
inComplementUnionImpInComplement1: $o ).
thf(tp_inComplementUnionImpNotIn1,type,
inComplementUnionImpNotIn1: $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inIntersectImpInIntersectUnions,type,
inIntersectImpInIntersectUnions: $o ).
thf(tp_inIntersectImpInUnion,type,
inIntersectImpInUnion: $o ).
thf(tp_inIntersectImpInUnion2,type,
inIntersectImpInUnion2: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_infuncsetfunc,type,
infuncsetfunc: $o ).
thf(tp_intersectInPowersetIntersectUnions,type,
intersectInPowersetIntersectUnions: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2lamEq,type,
lam2lamEq: $o ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powersetTE1,type,
powersetTE1: $o ).
thf(tp_powersetTI1,type,
powersetTI1: $o ).
thf(tp_powersetT_lem,type,
powersetT_lem: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_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_SY2702,type,
sK100_SY2702: $i > ( $i > $o ) > $i ).
thf(tp_sK101_SY2813,type,
sK101_SY2813: $i > ( $i > $o ) > $i ).
thf(tp_sK102_SY3681,type,
sK102_SY3681: $i > $i > $i > $i ).
thf(tp_sK103_SY2855,type,
sK103_SY2855: $i > ( $i > $o ) > $i ).
thf(tp_sK104_SY2929,type,
sK104_SY2929: $i > ( $i > $o ) > $i ).
thf(tp_sK105_SY3620,type,
sK105_SY3620: $i > $i > $i > $i ).
thf(tp_sK106_SY2813,type,
sK106_SY2813: $i > ( $i > $o ) > $i ).
thf(tp_sK107_SY2813,type,
sK107_SY2813: $i > ( $i > $o ) > $i ).
thf(tp_sK108_SY3718,type,
sK108_SY3718: $i > $i > $i > $i > $i ).
thf(tp_sK109_SY3779,type,
sK109_SY3779: $i > $i > $i > $i > $i > $i ).
thf(tp_sK10_SY3077,type,
sK10_SY3077: ( $i > $o ) > $i > $i ).
thf(tp_sK110_SY3204,type,
sK110_SY3204: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK111_SY2813,type,
sK111_SY2813: $i > ( $i > $o ) > $i ).
thf(tp_sK112_SY3816,type,
sK112_SY3816: $i > $i > $i > $i ).
thf(tp_sK113_SY3681,type,
sK113_SY3681: $i > $i > $i > $i ).
thf(tp_sK114_SY3681,type,
sK114_SY3681: $i > $i > $i > $i ).
thf(tp_sK115_SY3789,type,
sK115_SY3789: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK116_SY3780,type,
sK116_SY3780: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK117_SY3204,type,
sK117_SY3204: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK118_SY3821,type,
sK118_SY3821: $i > $i > $i > $i > $i ).
thf(tp_sK119_SY3718,type,
sK119_SY3718: $i > $i > $i > $i > $i ).
thf(tp_sK11_SY3100,type,
sK11_SY3100: $i > $i > $i ).
thf(tp_sK120_SY3718,type,
sK120_SY3718: $i > $i > $i > $i > $i ).
thf(tp_sK121_SY3681,type,
sK121_SY3681: $i > $i > $i > $i ).
thf(tp_sK122_SY3818,type,
sK122_SY3818: $o > $i > $i > $i > $i > $i > $i ).
thf(tp_sK123_SX0,type,
sK123_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK124_SX0,type,
sK124_SX0: $i > $i > $i > $i > $i > $i ).
thf(tp_sK125_SY3718,type,
sK125_SY3718: $i > $i > $i > $i > $i ).
thf(tp_sK126_SY3827,type,
sK126_SY3827: $i > $i > $i > $i ).
thf(tp_sK127_SY3828,type,
sK127_SY3828: $i > $i > $i > $i ).
thf(tp_sK128_SY3834,type,
sK128_SY3834: $i > $i > $i > $i > $i ).
thf(tp_sK129_SY3835,type,
sK129_SY3835: $i > $i > $i > $i > $i ).
thf(tp_sK12_SY3109,type,
sK12_SY3109: ( $i > $o ) > $i > $i ).
thf(tp_sK130_SY3836,type,
sK130_SY3836: $i > $i > $i > $i ).
thf(tp_sK131_SY3738,type,
sK131_SY3738: $i > $i > $i > $i ).
thf(tp_sK132_SY3812,type,
sK132_SY3812: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK133_SY3813,type,
sK133_SY3813: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK134_SY3840,type,
sK134_SY3840: $i > $i > $i > $i > $i ).
thf(tp_sK135_SY3738,type,
sK135_SY3738: $i > $i > $i > $i ).
thf(tp_sK136_SY3822,type,
sK136_SY3822: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK137_SY3806,type,
sK137_SY3806: $i > $i > $i > $i ).
thf(tp_sK138_SY3847,type,
sK138_SY3847: $i > $i > $i > $i ).
thf(tp_sK139_SY3829,type,
sK139_SY3829: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY3143,type,
sK13_SY3143: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK140_SY3830,type,
sK140_SY3830: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK141_SY3147,type,
sK141_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK142_SY2531,type,
sK142_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK143_SY3855,type,
sK143_SY3855: $i > $i > $i > $i ).
thf(tp_sK144_SY3837,type,
sK144_SY3837: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK145_SY3147,type,
sK145_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK146_SY2531,type,
sK146_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK147_SY3843,type,
sK147_SY3843: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK148_SY3844,type,
sK148_SY3844: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK149_SY3838,type,
sK149_SY3838: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK14_SY3181,type,
sK14_SY3181: ( $i > $o ) > $i > $i ).
thf(tp_sK150_SY3851,type,
sK150_SY3851: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK151_SY3852,type,
sK151_SY3852: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK152_SY3853,type,
sK152_SY3853: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK153_SY3854,type,
sK153_SY3854: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK154_SY3845,type,
sK154_SY3845: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK155_SY3859,type,
sK155_SY3859: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK156_SY3860,type,
sK156_SY3860: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK157_SY3861,type,
sK157_SY3861: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK158_SY3147,type,
sK158_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK159_SY2531,type,
sK159_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK15_SY3201,type,
sK15_SY3201: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK160_SY3865,type,
sK160_SY3865: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK161_SY3147,type,
sK161_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK162_SY2531,type,
sK162_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK163_SY3147,type,
sK163_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK164_SY2531,type,
sK164_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK165_SY3147,type,
sK165_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK166_SY2531,type,
sK166_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK167_SY3147,type,
sK167_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK168_SY2531,type,
sK168_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK169_SY3147,type,
sK169_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK16_SY3216,type,
sK16_SY3216: $i > $i > $i ).
thf(tp_sK170_SY2531,type,
sK170_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK171_SY3147,type,
sK171_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK172_SY2531,type,
sK172_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK173_SY3147,type,
sK173_SY3147: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK174_SY2531,type,
sK174_SY2531: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK175_SY3873,type,
sK175_SY3873: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK176_SY3875,type,
sK176_SY3875: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK177_SY3876,type,
sK177_SY3876: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK178_SY3877,type,
sK178_SY3877: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK179_SY3881,type,
sK179_SY3881: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK17_SY3346,type,
sK17_SY3346: $i > $i > $i ).
thf(tp_sK180_SY3882,type,
sK180_SY3882: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK181_SY3883,type,
sK181_SY3883: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK182_SY3890,type,
sK182_SY3890: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK18_SY3418,type,
sK18_SY3418: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK19_SY3422,type,
sK19_SY3422: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK20_SY3429,type,
sK20_SY3429: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK21_SY3441,type,
sK21_SY3441: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK22_SY3614,type,
sK22_SY3614: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK23_SY3631,type,
sK23_SY3631: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK24_SY3199,type,
sK24_SY3199: ( $i > $o ) > $i > $i ).
thf(tp_sK25_SY3515,type,
sK25_SY3515: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK26_SY3253,type,
sK26_SY3253: $i > $i > $i ).
thf(tp_sK27_SY2868,type,
sK27_SY2868: $i > $i ).
thf(tp_sK28_SY3552,type,
sK28_SY3552: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK29_SY3556,type,
sK29_SY3556: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK2_SY2224,type,
sK2_SY2224: $i > $i ).
thf(tp_sK30_SY2910,type,
sK30_SY2910: $i > $i ).
thf(tp_sK31_SY3607,type,
sK31_SY3607: $i ).
thf(tp_sK32_SY3615,type,
sK32_SY3615: ( $i > $o ) > $i > $i ).
thf(tp_sK33_SY3088,type,
sK33_SY3088: ( $i > $o ) > $i > $i ).
thf(tp_sK34_SY3488,type,
sK34_SY3488: $i > $i > $i > $i ).
thf(tp_sK35_SY3641,type,
sK35_SY3641: ( $i > $o ) > $i > $i ).
thf(tp_sK36_SY3248,type,
sK36_SY3248: $i > $i > $i ).
thf(tp_sK37_SY3674,type,
sK37_SY3674: $i > ( $i > $o ) > $i ).
thf(tp_sK38_SY3333,type,
sK38_SY3333: ( $i > $o ) > $i > $i ).
thf(tp_sK39_SY2254,type,
sK39_SY2254: $i > $i ).
thf(tp_sK3_SY3035,type,
sK3_SY3035: $i ).
thf(tp_sK40_SY3049,type,
sK40_SY3049: $i > $i > $i ).
thf(tp_sK41_SY3632,type,
sK41_SY3632: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK42_SY3649,type,
sK42_SY3649: $o > $i > $i > $i ).
thf(tp_sK43_SX0,type,
sK43_SX0: $i > $i > $i ).
thf(tp_sK44_SX0,type,
sK44_SX0: $i > $i > $i ).
thf(tp_sK45_SY3669,type,
sK45_SY3669: ( $i > $o ) > $i > $i > $i ).
thf(tp_sK46_SY2861,type,
sK46_SY2861: $i > $i > $i ).
thf(tp_sK47_SY3688,type,
sK47_SY3688: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK48_SY2973,type,
sK48_SY2973: $i > $i > $i ).
thf(tp_sK49_SY3731,type,
sK49_SY3731: $i ).
thf(tp_sK4_SY2504,type,
sK4_SY2504: $i > $i ).
thf(tp_sK50_SY2389,type,
sK50_SY2389: $i > ( $i > $o ) > $i ).
thf(tp_sK51_SY3700,type,
sK51_SY3700: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK52_SY3204,type,
sK52_SY3204: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK53_SY3710,type,
sK53_SY3710: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK54_SY3217,type,
sK54_SY3217: $i > $i > $i ).
thf(tp_sK55_SY3420,type,
sK55_SY3420: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK56_SY3033,type,
sK56_SY3033: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK57_SY3767,type,
sK57_SY3767: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY3619,type,
sK58_SY3619: $i > $i > $i > $i ).
thf(tp_sK59_SY3747,type,
sK59_SY3747: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY2645,type,
sK5_SY2645: $i > $i ).
thf(tp_sK60_SY3217,type,
sK60_SY3217: $i > $i > $i ).
thf(tp_sK61_SY3644,type,
sK61_SY3644: $i > $i > $i > $i ).
thf(tp_sK62_SY3278,type,
sK62_SY3278: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK63_SY3661,type,
sK63_SY3661: $i > $i > $i > $i ).
thf(tp_sK64_SY3662,type,
sK64_SY3662: $i > $i > $i > $i ).
thf(tp_sK65_SY3757,type,
sK65_SY3757: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK66_SY3679,type,
sK66_SY3679: $i > $i > $i > $i ).
thf(tp_sK67_SY3590,type,
sK67_SY3590: $i > ( $i > $o ) > $i ).
thf(tp_sK68_SY3762,type,
sK68_SY3762: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK69_SY3692,type,
sK69_SY3692: $i > $i > $i > $i > $i ).
thf(tp_sK6_SY2972,type,
sK6_SY2972: $i > $i > $i ).
thf(tp_sK70_SY3694,type,
sK70_SY3694: $i > $i > $i > $i > $i ).
thf(tp_sK71_SY3617,type,
sK71_SY3617: $i > ( $i > $o ) > $i ).
thf(tp_sK72_SY3768,type,
sK72_SY3768: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK73_SY3627,type,
sK73_SY3627: $i > ( $i > $o ) > $i ).
thf(tp_sK74_SY3703,type,
sK74_SY3703: $i > $i > $i > $i > $i ).
thf(tp_sK75_SY3630,type,
sK75_SY3630: $i > ( $i > $o ) > $i ).
thf(tp_sK76_SY3772,type,
sK76_SY3772: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK77_SY3655,type,
sK77_SY3655: $i > ( $i > $o ) > $i ).
thf(tp_sK78_SY3714,type,
sK78_SY3714: $i > $i > $i > $i > $i ).
thf(tp_sK79_SY3716,type,
sK79_SY3716: $i > $i > $i > $i > $i ).
thf(tp_sK7_SY3000,type,
sK7_SY3000: $i > $i > $i ).
thf(tp_sK80_SY3683,type,
sK80_SY3683: $i > ( $i > $o ) > $i ).
thf(tp_sK81_SY3687,type,
sK81_SY3687: $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY3774,type,
sK82_SY3774: $i > $i > $i > $i ).
thf(tp_sK83_SY3775,type,
sK83_SY3775: $i > $i > $i > $i ).
thf(tp_sK84_SY3732,type,
sK84_SY3732: $i > $i > $i > $i ).
thf(tp_sK85_SY3782,type,
sK85_SY3782: $i > $i > $i > $i > $i ).
thf(tp_sK86_SY3785,type,
sK86_SY3785: $i > $i > $i > $i > $i ).
thf(tp_sK87_SY3736,type,
sK87_SY3736: $i > $i > $i ).
thf(tp_sK88_SY2391,type,
sK88_SY2391: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY2391,type,
sK89_SY2391: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY3448,type,
sK8_SY3448: $i ).
thf(tp_sK90_SY2492,type,
sK90_SY2492: $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY3749,type,
sK91_SY3749: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK92_SY2702,type,
sK92_SY2702: $i > ( $i > $o ) > $i ).
thf(tp_sK93_SY2855,type,
sK93_SY2855: $i > ( $i > $o ) > $i ).
thf(tp_sK94_SY3368,type,
sK94_SY3368: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK95_SY2929,type,
sK95_SY2929: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY2391,type,
sK96_SY2391: $i > ( $i > $o ) > $i ).
thf(tp_sK97_SY3620,type,
sK97_SY3620: $i > $i > $i > $i ).
thf(tp_sK98_SY3620,type,
sK98_SY3620: $i > $i > $i > $i ).
thf(tp_sK99_SY2492,type,
sK99_SY2492: $i > ( $i > $o ) > $i ).
thf(tp_sK9_SY3069,type,
sK9_SY3069: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_sepInPowerset,type,
sepInPowerset: $o ).
thf(tp_sepSubset,type,
sepSubset: $o ).
thf(tp_set2prop,type,
set2prop: $i > $o ).
thf(tp_setOfPairsIsBReln,type,
setOfPairsIsBReln: $o ).
thf(tp_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_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_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(ap2apEq1,definition,
( ap2apEq1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
thf(ap2apEq2,definition,
( ap2apEq2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq2) ).
thf(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(beta1,definition,
( beta1
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta1) ).
thf(beta2,definition,
( beta2
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B
@ ( lam @ A @ B
@ ^ [Xy: $i] : ( Xf @ Xy ) )
@ Xx )
= ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',beta2) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binintersectTELcontra,definition,
( binintersectTELcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTELcontra) ).
thf(binintersectTERcontra,definition,
( binintersectTERcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectTERcontra) ).
thf(binintersectT_lem,definition,
( binintersectT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectT_lem) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(binunionTE,definition,
( binunionTE
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binunion @ X @ Y ) )
=> ( ( ( in @ Xx @ X )
=> Xphi )
=> ( ( ( in @ Xx @ Y )
=> Xphi )
=> Xphi ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTE) ).
thf(binunionTEcontra,definition,
( binunionTEcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ X )
=> ( ~ ( in @ Xx @ Y )
=> ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTEcontra) ).
thf(binunionTILcontra,definition,
( binunionTILcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra) ).
thf(binunionTIRcontra,definition,
( binunionTIRcontra
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
=> ~ ( in @ Xx @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra) ).
thf(binunionT_lem,definition,
( binunionT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem) ).
thf(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(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(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(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(funcGraphProp1,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcGraphProp3,definition,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp4,definition,
( funcGraphProp4
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,definition,
( funcext2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(funcextLem,definition,
( funcextLem
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(ifSingleton,definition,
( ifSingleton
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifSingleton) ).
thf(iffalse,definition,
( iffalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalse) ).
thf(iffalseProp1,definition,
( iffalseProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( in @ Xy
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp1) ).
thf(iffalseProp2,definition,
( iffalseProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iffalseProp2) ).
thf(ifp,definition,
( ifp
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifp) ).
thf(iftrue,definition,
( iftrue
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(iftrueProp1,definition,
( iftrueProp1
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp1) ).
thf(iftrueProp2,definition,
( iftrueProp2
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( dsetconstr @ A
@ ^ [Xz: $i] :
( ( Xphi
& ( Xz = Xx ) )
| ( ~ Xphi
& ( Xz = Xy ) ) ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueProp2) ).
thf(iftrueorfalse,definition,
( iftrueorfalse
= ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrueorfalse) ).
thf(inComplementUnionImpInComplement1,definition,
( inComplementUnionImpInComplement1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpInComplement1) ).
thf(inComplementUnionImpNotIn1,definition,
( inComplementUnionImpNotIn1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inComplementUnionImpNotIn1) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inIntersectImpInIntersectUnions,definition,
( inIntersectImpInIntersectUnions
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions) ).
thf(inIntersectImpInUnion,definition,
( inIntersectImpInUnion
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion) ).
thf(inIntersectImpInUnion2,definition,
( inIntersectImpInUnion2
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(intersectInPowersetIntersectUnions,definition,
( intersectInPowersetIntersectUnions
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Z: $i] :
( ( in @ Z @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersectInPowersetIntersectUnions) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam2lamEq,definition,
( lam2lamEq
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
= ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2lamEq) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powersetTE1,definition,
( powersetTE1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ X @ ( powerset @ Y ) )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTE1) ).
thf(powersetTI1,definition,
( powersetTI1
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ Y ) ) )
=> ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1) ).
thf(powersetT_lem,definition,
( powersetT_lem
= ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetT_lem) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(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(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theeq,definition,
( theeq
= ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(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(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
=> ! [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(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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [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 ) ) )
=> ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) )
=> ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) )
=> ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) )
=> ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [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 ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) )
=> ( ! [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 ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) )
=> ( ! [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 ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [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 ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy )
=> ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) )
=> ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) )
=> ( ! [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 ) )
=> ( ! [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 ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) )
=> ( ! [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 ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) )
=> ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) )
=> ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) )
=> ( ! [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 ) ) ) ) ) ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [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 ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) )
=> ( ! [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 ) ) ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ( ! [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 ) ) ) ) ) )
=> ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) )
=> ( ! [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 ) ) ) ) ) ) )
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(161,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(162,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(163,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(165,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(167,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(168,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(169,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(170,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(171,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(172,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(173,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(174,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(175,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(176,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(177,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(178,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(179,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(180,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(181,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(182,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(183,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(184,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(185,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(186,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(187,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(188,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(189,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(190,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(191,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(192,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(193,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(194,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(195,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(196,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(197,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(198,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(199,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(200,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(201,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(202,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(203,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(204,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(205,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(206,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(207,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(208,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(209,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(210,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(211,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(212,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(213,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(214,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(215,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(216,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(217,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(218,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(219,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(220,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(221,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(222,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(223,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(224,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(225,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(226,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(227,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(228,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(229,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(230,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(231,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(232,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(233,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(234,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(235,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(236,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(237,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(238,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(239,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(240,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(241,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(242,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(243,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(244,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(245,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(246,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(247,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(248,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(249,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(250,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(251,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(252,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(253,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(254,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(255,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(256,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(257,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(258,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(259,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(260,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(261,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(262,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(263,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(264,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(265,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(266,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(267,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(268,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(269,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(270,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(271,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(272,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(273,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(274,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(275,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(276,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(277,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(278,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(279,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(280,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(281,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(282,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(283,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(284,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(285,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(286,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(287,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(288,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(289,plain,
( ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(290,plain,
( ( ! [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 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(291,plain,
( ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(292,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(293,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(294,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(295,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(296,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(297,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(298,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(299,plain,
( ( ! [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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(300,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(301,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(302,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(303,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(304,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(305,plain,
( ( ~ ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[304]) ).
thf(306,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[303]) ).
thf(307,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( binunion @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(308,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(309,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(310,plain,
( ( ! [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 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(311,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [S: $i] :
( ( breln1 @ A @ S )
=> ( breln1 @ A @ ( breln1compset @ A @ R @ S ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(312,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(313,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(314,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ( breln1 @ A @ ( breln1invset @ A @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(315,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(316,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(317,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(318,plain,
( ( ! [A: $i,Xphi: $i > $i > $o] :
( breln1 @ A
@ ( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(319,plain,
( ( ! [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 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(320,plain,
( ( ! [A: $i,R: $i] :
( ( in @ R @ ( breln1Set @ A ) )
=> ( breln1 @ A @ R ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(321,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(322,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(323,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(324,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(325,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(326,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(327,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(328,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(329,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(330,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(331,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ ( binintersect @ X @ Y ) )
=> ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(332,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(333,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(334,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(335,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(336,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(337,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(338,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(339,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(340,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(341,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(342,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(343,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(344,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(345,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
=> ~ ( in @ Xx @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(346,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(347,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(348,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(349,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(350,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(351,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(352,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ ( setminus @ A @ Y ) )
=> ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(353,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(354,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(355,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(356,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(357,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(358,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( X
= ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(359,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(360,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(361,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(362,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(363,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
=> ( subset @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(364,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( ( subset @ X @ Y )
=> ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(365,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(366,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(367,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(368,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(369,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
=> ( in @ Xx @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(370,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ X )
=> ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(371,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(372,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(373,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(374,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(375,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(376,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(377,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(378,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(379,plain,
( ( ! [A: $i,X: $i] :
( ( in @ X @ ( powerset @ A ) )
=> ! [Y: $i] :
( ( in @ Y @ ( powerset @ A ) )
=> ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(380,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(381,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ~ Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(382,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( Xphi
=> ( ( if @ A @ Xphi @ Xx @ Xy )
= Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(383,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(384,plain,
( ( ! [A: $i,Xphi: $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(385,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(386,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(387,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(388,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(389,plain,
( ( ! [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 ) ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(390,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(391,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(392,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(393,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( ( lam @ A @ B
@ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
= Xf ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(394,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(395,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(396,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(397,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(398,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(399,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(400,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(401,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(402,plain,
( ( ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(403,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(404,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(405,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(406,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(407,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(408,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(409,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(410,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(411,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(412,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(413,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(414,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(415,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(416,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(417,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(418,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(419,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(420,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(421,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(422,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(423,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(424,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(425,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(426,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(427,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(428,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(429,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(430,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(431,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(432,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(433,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(434,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(435,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(436,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(437,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(438,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(439,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(440,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(441,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(442,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(443,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(444,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(445,plain,
( ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(446,plain,
( ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(447,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(448,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(449,plain,
( ( ! [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 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(450,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(451,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(452,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[157]) ).
thf(453,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(454,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(455,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(456,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(457,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(458,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(459,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(460,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(461,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(462,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(463,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(464,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(465,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(466,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(467,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(468,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(469,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(470,plain,
( ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(471,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(472,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(473,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(474,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(475,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(476,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(477,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(478,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(479,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(480,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(481,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(482,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(483,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(484,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(485,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(486,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(487,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(488,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(489,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(490,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(491,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(493,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(494,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(495,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(496,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(497,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(498,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(499,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(500,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(502,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(503,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(504,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(505,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(506,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(507,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(508,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(509,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(510,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(511,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(512,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(513,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(514,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(515,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(516,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(517,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(518,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(519,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(520,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(521,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(522,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(523,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(524,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(525,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(526,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(527,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(528,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(529,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(530,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(531,plain,
( ( ! [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 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(532,plain,
( ( ! [SY251: $i > $o,SY252: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY251 @ Xx )
<=> ( SY252 @ Xy ) ) )
=> ( ? [SY256: $i] :
( ( SY251 @ SY256 )
& ! [SY257: $i] :
( ( SY251 @ SY257 )
=> ( SY256 = SY257 ) ) )
=> ( ? [SY259: $i] :
( ( SY252 @ SY259 )
& ! [SY260: $i] :
( ( SY252 @ SY260 )
=> ( SY259 = SY260 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY252 @ Xx ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(533,plain,
( ( ! [SY245: $i > $o] :
( ? [SY247: $i] :
( ( SY245 @ SY247 )
& ! [SY248: $i] :
( ( SY245 @ SY248 )
=> ( SY247 = SY248 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY245 @ Xx )
=> ( ( SY245 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(534,plain,
( ( omega = omega )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(535,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(536,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(537,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(538,plain,
( ( emptyset = emptyset )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(539,plain,
( ( ! [SY227: $i > $o,SY228: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY227 @ Xx )
<=> ( SY228 @ Xy ) ) )
=> ( ? [SY232: $i] :
( ( SY227 @ SY232 )
& ! [SY233: $i] :
( ( SY227 @ SY233 )
=> ( SY232 = SY233 ) ) )
<=> ? [SY235: $i] :
( ( SY228 @ SY235 )
& ! [SY236: $i] :
( ( SY228 @ SY236 )
=> ( SY235 = SY236 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(540,plain,
( ( ! [SY221: $i > $o] :
( ? [SY223: $i] :
( ( SY221 @ SY223 )
& ! [SY224: $i] :
( ( SY221 @ SY224 )
=> ( SY223 = SY224 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY221 @ Xx )
=> ( ( SY221 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(541,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(542,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(543,plain,
( ( ! [SY207: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY207 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY211: $i] :
( ( SY207 @ SY211 )
& ! [SY212: $i] :
( ( SY207 @ SY212 )
=> ( SY211 = SY212 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(544,plain,
( ( ! [SY200: $i > $o] :
( ? [Xx: $i] : ( SY200 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY200 @ Xx )
=> ( ( SY200 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY205: $i] :
( ( SY200 @ SY205 )
& ! [SY206: $i] :
( ( SY200 @ SY206 )
=> ( SY205 = SY206 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(545,plain,
( ( ! [SY194: $i > $o] :
( ? [Xx: $i] :
( ( SY194 @ Xx )
& ! [Xy: $i] :
( ( SY194 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY198: $i] :
( ( SY194 @ SY198 )
& ! [SY199: $i] :
( ( SY194 @ SY199 )
=> ( SY198 = SY199 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(546,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(547,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(548,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(549,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(550,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(551,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(552,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(553,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(554,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(555,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(556,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(557,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(558,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(559,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(560,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(561,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(562,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(563,plain,
( ( ! [SY145: $i] :
( ( SY145 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY145 )
& $true ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(564,plain,
( ( ! [SY139: $i > $o] :
( ? [SY141: $i] :
( ( SY139 @ SY141 )
& ! [SY142: $i] :
( ( SY139 @ SY142 )
=> ( SY141 = SY142 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY139 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(565,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(566,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(567,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(568,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(569,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(570,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(571,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(572,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(573,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(574,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(575,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(576,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(577,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(578,plain,
( ( ! [SY106: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY106 )
=> ( SY106 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(579,plain,
( ( ! [SY102: $i,SY103: $i > $o,SY104: $i] :
( ( in @ SY104 @ SY102 )
=> ( ( SY103 @ SY104 )
=> ( ( dsetconstr @ SY102
@ ^ [Xy: $i] : ( SY103 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(580,plain,
( ( ! [SY100: $i] :
( ( SY100 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY100 ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(581,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(582,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(583,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(584,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(585,plain,
( ( ! [SY83: $i > $o] :
( ? [SY85: $i] :
( ( SY83 @ SY85 )
& ! [SY86: $i] :
( ( SY83 @ SY86 )
=> ( SY85 = SY86 ) ) )
=> ? [Xx: $i] : ( SY83 @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(586,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(587,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(588,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(589,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(590,plain,
( ( ! [SY71: $i > $o] :
( ? [SY73: $i] :
( ( SY71 @ SY73 )
& ! [SY74: $i] :
( ( SY71 @ SY74 )
=> ( SY73 = SY74 ) ) )
=> ? [Xx: $i] :
( ( SY71 @ Xx )
& ! [Xy: $i] :
( ( SY71 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(591,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(592,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(593,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(594,plain,
( ( ! [SY54: $i > $o] :
( ? [SY56: $i] :
( ( SY54 @ SY56 )
& ! [SY57: $i] :
( ( SY54 @ SY57 )
=> ( SY56 = SY57 ) ) )
=> ( SY54
@ ( descr
@ ^ [Xx: $i] : ( SY54 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(595,plain,
( ( ! [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 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(596,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(597,plain,
( ( ! [SY22: $i > $i > $o,SY23: $i] :
( ! [SY24: $i] :
( ( in @ SY24 @ SY23 )
=> ? [SY26: $i] :
( ( SY22 @ SY24 @ SY26 )
& ! [SY27: $i] :
( ( SY22 @ SY24 @ SY27 )
=> ( SY26 = SY27 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY23 )
& ( SY22 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(598,plain,
( ( ! [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 ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(599,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(600,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(601,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(602,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(603,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(604,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(605,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(606,plain,
( ( ~ ! [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 ) ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[305]) ).
thf(607,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)],[336,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[486,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(609,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)],[327,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(610,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)],[594,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[510,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(612,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)],[311,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[524,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(614,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)],[462,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[494,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(616,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)],[531,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(617,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)],[595,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(618,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)],[406,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(619,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[549,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[467,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(621,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)],[410,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(622,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[527,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(624,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)],[598,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(625,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)],[601,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(626,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)],[450,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(627,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)],[411,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(628,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)],[396,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(629,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)],[341,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(630,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)],[436,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(631,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)],[369,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( SX1
= ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[358,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(633,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)],[397,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(634,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)],[352,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(635,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)],[350,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(636,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)],[329,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(637,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)],[367,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(638,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)],[361,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(639,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[571,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(640,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)],[309,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(641,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)],[338,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(642,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)],[394,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(643,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)],[424,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(644,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)],[413,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(645,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)],[418,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(646,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)],[319,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(647,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)],[405,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(648,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)],[546,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(649,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[525,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(650,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)],[606,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(651,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)],[542,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(652,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[515,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(653,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[435,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(654,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)],[402,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(655,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)],[602,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(656,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)],[541,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(657,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[448,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(658,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)],[343,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(659,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)],[504,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(660,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[475,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(661,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(662,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)],[426,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(663,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[414,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(664,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[528,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(665,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)],[428,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(666,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)],[478,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(667,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[477,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(668,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)],[544,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(669,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)],[537,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(670,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)],[532,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(671,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)],[452,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(672,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[589,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(673,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)],[464,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(674,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)],[340,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(675,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)],[363,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(676,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)],[447,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(677,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)],[324,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(678,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)],[533,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(679,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)],[547,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(680,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)],[368,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(681,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)],[380,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[505,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[495,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(684,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)],[374,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(685,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ ( powerset @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ~ ( in @ SX3 @ SX1 )
| ~ ~ ( in @ SX3 @ SX2 )
| ~ ( in @ SX3 @ ( binunion @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[530,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(687,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[483,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(688,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ( breln1 @ SX0 @ ( breln1invset @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(689,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(690,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)],[388,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(691,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)],[331,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[517,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
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)],[552,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(695,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)],[344,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(696,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)],[420,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(697,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[507,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(698,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)],[415,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(699,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)],[407,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(700,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)],[356,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[476,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(702,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)],[590,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[573,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(704,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(705,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)],[333,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[491,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(707,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)],[371,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(708,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(709,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[498,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(710,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)],[398,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(711,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)],[387,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(712,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)],[540,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(713,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)],[593,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(714,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)],[539,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(715,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)],[458,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(716,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)],[355,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(717,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)],[317,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(718,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)],[330,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[490,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(720,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)],[389,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(721,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[587,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(722,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)],[381,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(723,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[499,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(724,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)],[353,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(725,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)],[328,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(726,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(727,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)],[349,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(728,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)],[555,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(729,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)],[357,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( powerset @ SX1 ) @ ( powerset @ ( powerset @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[519,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(732,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)],[449,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(733,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)],[581,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(734,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)],[579,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(735,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[437,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(736,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)],[429,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(737,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[548,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(738,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)],[459,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(739,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)],[354,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(740,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)],[427,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(741,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)],[451,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(742,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)],[603,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(743,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)],[597,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(744,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[516,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(746,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)],[408,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(747,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)],[442,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(748,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[536,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(749,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[468,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(750,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)],[584,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[575,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(752,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)],[438,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(753,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)],[401,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(754,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(755,plain,
( ( ! [SX0: $i] :
( ~ ( singleton @ SX0 )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(756,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)],[322,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(757,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(758,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)],[316,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(759,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[500,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(760,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)],[347,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(761,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)],[312,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(762,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)],[566,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(763,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[360,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(764,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)],[393,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(765,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)],[351,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(766,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)],[337,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(767,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)],[346,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(768,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)],[574,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(769,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(770,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[493,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(771,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[479,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(772,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)],[376,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(773,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)],[409,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(774,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(775,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(776,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)],[379,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(777,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)],[325,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(778,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[514,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(779,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[503,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(780,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)],[545,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(781,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( breln1Set @ SX0 ) )
| ( breln1 @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(782,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[561,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(783,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[513,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(784,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)],[463,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(785,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( breln1 @ SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( breln1 @ SX0 @ SX2 )
| ( breln1 @ SX0 @ ( binunion @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(786,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(787,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)],[382,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(788,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)],[306,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(789,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)],[323,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(790,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)],[419,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(791,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)],[332,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(792,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[474,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(793,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)],[370,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(794,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)],[553,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(795,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[560,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(796,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)],[335,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(797,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[481,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(798,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[523,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(799,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)],[400,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(800,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)],[378,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(801,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(802,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[512,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(803,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[496,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(804,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)],[461,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(805,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)],[373,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(806,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)],[372,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(807,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[558,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(808,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)],[362,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(809,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[522,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(810,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)],[384,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(811,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)],[348,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(812,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)],[592,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(813,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)],[308,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(814,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)],[321,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(815,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)],[345,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(816,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)],[339,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(817,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)],[390,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(818,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( in @ ( setminus @ SX0 @ SX1 ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(819,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[535,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(820,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[485,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(821,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[529,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(822,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)],[421,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(823,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)],[543,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(824,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)],[399,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(825,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)],[366,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(826,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[554,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(827,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[578,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(828,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[487,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(829,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)],[551,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(830,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[565,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(831,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)],[310,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(832,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)],[315,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(833,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[591,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(834,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)],[605,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(835,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)],[417,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(836,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)],[564,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(837,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)],[365,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(838,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)],[596,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(839,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[482,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(840,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(841,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(842,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ ( setminus @ SX0 @ ( setminus @ SX0 @ SX1 ) ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[359,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(843,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[562,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(844,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[432,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(845,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)],[364,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(846,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)],[460,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(847,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)],[395,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(848,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)],[334,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(849,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)],[416,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(850,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)],[404,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(851,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)],[550,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(852,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)],[313,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(853,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)],[391,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(854,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)],[430,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(855,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)],[392,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(856,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)],[326,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(857,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[563,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(858,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[521,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(859,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[484,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(860,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)],[403,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
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)],[385,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(862,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[425,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(863,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(864,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(865,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[559,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(866,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)],[439,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(867,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[488,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(868,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[588,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(869,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)],[386,ap2apEq1,ap2apEq2,ap2p,apProp,app,beta1,beta2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binintersectTELcontra,binintersectTERcontra,binintersectT_lem,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,binunionTE,binunionTEcontra,binunionTILcontra,binunionTIRcontra,binunionT_lem,breln1SetBreln1,breln1all1,breln1all2,breln1compE,breln1compEex,breln1compI,breln1compprop,breln1invE,breln1invI,breln1invprop,breln1unionIL,breln1unionprop,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,choice2fnsingleton,complementImpComplementIntersect,complementInPowersetComplementIntersect,complementSubsetComplementIntersect,complementTE1,complementTI1,complementT_lem,complementTcontraSubset,complementTnotintersectT,complementUnionInPowersetComplement,contraSubsetComplement,contrasubsetT,contrasubsetT1,contrasubsetT2,contrasubsetT3,demorgan1,demorgan1a,demorgan1b,demorgan2,demorgan2a,demorgan2a1,demorgan2a2,demorgan2b,demorgan2b2,descr__Cong,descrp,disjointsetsI1,doubleComplementE1,doubleComplementEq,doubleComplementI1,doubleComplementSub1,doubleComplementSub2,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqbreln1,eqimpsubset1,eqimpsubset2,eqinunit,eta1,eta2,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,ifSingleton,iffalse,iffalseProp1,iffalseProp2,ifp,iftrue,iftrueProp1,iftrueProp2,iftrueorfalse,inComplementUnionImpInComplement1,inComplementUnionImpNotIn1,inCongP,inIntersectImpInIntersectUnions,inIntersectImpInUnion,inIntersectImpInUnion2,inPowerset,in__Cong,infuncsetfunc,intersectInPowersetIntersectUnions,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam2lamEq,lam2p,lamProp,lamp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powersetTE1,powersetTI1,powersetT_lem,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setOfPairsIsBReln,setOfPairsIsBReln1,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextT,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setminusT_lem,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL,setukpairinjL1,setukpairinjL2,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subbreln1,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTI,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theeq,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx,woz13rule0,woz13rule1,woz13rule2,woz13rule3,woz13rule4,woz1_1,woz1_2,woz1_3,woz1_4,woz1_5]) ).
thf(870,plain,
! [SV1: $i] :
( ( ! [SY2161: $i > $i > $o] :
( breln1 @ SV1
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [Xx: $i,Xy: $i] : ( SY2161 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(871,plain,
! [SV2: $i] :
( ( ! [SY2164: $i,SY2165: $i > $i > $o] :
( breln @ SV2 @ SY2164
@ ( dpsetconstr @ SV2 @ SY2164
@ ^ [Xx: $i,Xy: $i] : ( SY2165 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(872,plain,
! [SV3: $i] :
( ( ! [SY2168: $i,SY2169: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV3 @ SY2168
@ ^ [Xx: $i,Xy: $i] : ( SY2169 @ Xx @ Xy ) )
@ ( cartprod @ SV3 @ SY2168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(873,plain,
! [SV4: $i] :
( ( ! [SY2172: $i] :
( ( ksnd @ ( kpair @ SV4 @ SY2172 ) )
= SY2172 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(874,plain,
! [SV5: $i] :
( ( ! [SY2173: $i] :
( ( kfst @ ( kpair @ SV5 @ SY2173 ) )
= SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(875,plain,
! [SV6: $i] :
( ( ( setunion @ ( setadjoin @ SV6 @ emptyset ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(876,plain,
! [SV7: $i] :
( ( subset @ SV7 @ ( setunion @ ( setadjoin @ SV7 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(877,plain,
! [SV8: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV8 @ emptyset ) ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(878,plain,
! [SV9: $i] :
( ( ! [SY2174: $i] : ( iskpair @ ( kpair @ SV9 @ SY2174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(879,plain,
! [SV10: $i] :
( ( ! [SY2175: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SY2175 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(880,plain,
! [SV11: $i] :
( ( ! [SY2176: $i] : ( in @ SY2176 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SY2176 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(881,plain,
! [SV12: $i] :
( ( ! [SY2177: $i] : ( in @ SV12 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SY2177 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(882,plain,
! [SV13: $i] :
( ( ! [SY2178: $i] : ( in @ SY2178 @ ( setadjoin @ SV13 @ ( setadjoin @ SY2178 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(883,plain,
! [SV14: $i] :
( ( ! [SY2179: $i] : ( subset @ ( setminus @ SV14 @ SY2179 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(884,plain,
! [SV15: $i] :
( ( ! [SY2180: $i,SY2181: $i] :
( ( binintersect @ SV15 @ ( binunion @ SY2180 @ SY2181 ) )
= ( binunion @ ( binintersect @ SV15 @ SY2180 ) @ ( binintersect @ SV15 @ SY2181 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(885,plain,
! [SV16: $i] :
( ( ! [SY2182: $i] : ( subset @ ( binintersect @ SV16 @ SY2182 ) @ SY2182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(886,plain,
! [SV17: $i] :
( ( ! [SY2183: $i] : ( subset @ ( binintersect @ SV17 @ SY2183 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(887,plain,
! [SV18: $i] :
( ( ! [SY2184: $i] : ( subset @ SY2184 @ ( binunion @ SV18 @ SY2184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(888,plain,
! [SV19: $i] :
( ( ! [SY2185: $i] : ( subset @ SV19 @ ( binunion @ SV19 @ SY2185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(889,plain,
! [SV20: $i] :
( ( ! [SY2186: $i] : ( in @ SY2186 @ ( setadjoin @ SV20 @ ( setadjoin @ SY2186 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(890,plain,
! [SV21: $i] :
( ( ! [SY2187: $i > $o] :
( subset
@ ( dsetconstr @ SV21
@ ^ [Xx: $i] : ( SY2187 @ Xx ) )
@ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(891,plain,
! [SV22: $i] :
( ( ! [SY2189: $i > $o] :
( in
@ ( dsetconstr @ SV22
@ ^ [Xx: $i] : ( SY2189 @ Xx ) )
@ ( powerset @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(892,plain,
! [SV23: $i] :
( ( in @ SV23 @ ( powerset @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(893,plain,
! [SV24: $i] :
( ( ! [SY2191: $i] : ( subset @ SY2191 @ ( setadjoin @ SV24 @ SY2191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(894,plain,
! [SV25: $i] :
( ( subset @ SV25 @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(895,plain,
! [SV26: $i] :
( ( subset @ emptyset @ SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(896,plain,
! [SV27: $i] :
( ( ! [SY2192: $i] : ( in @ SY2192 @ ( setadjoin @ SV27 @ ( setadjoin @ SY2192 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(897,plain,
! [SV28: $i] :
( ( ! [SY2193: $i] : ( in @ SV28 @ ( setadjoin @ SV28 @ ( setadjoin @ SY2193 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(898,plain,
! [SV29: $i] :
( ( in @ emptyset @ ( powerset @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(899,plain,
! [SV30: $i] :
( ( in @ emptyset @ ( powerset @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(900,plain,
! [SV31: $i] :
( ( ( dsetconstr @ SV31
@ ^ [Xx: $i] : $true )
= SV31 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(901,plain,
! [SV32: $i] :
( ( ! [SY2195: $i] : ( in @ SV32 @ ( setadjoin @ SV32 @ SY2195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(902,plain,
! [SV33: $i] :
( ( ~ ( in @ SV33 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(903,plain,
! [SV34: $i] :
( ( ~ ( in @ SV34 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(904,plain,
! [SV35: $i] :
( ( ! [SY2196: $i] :
( ~ ( in @ SY2196 @ ( powerset @ SV35 ) )
| ! [SY2197: $i] :
( ~ ( in @ SY2197 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SY2196 @ SY2197 ) )
= ( binunion @ ( setminus @ SV35 @ SY2196 ) @ ( setminus @ SV35 @ SY2197 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(905,plain,
! [SV36: $i] :
( ( ! [SY2198: $i,SY2199: $i] :
( ~ ( in @ SY2199 @ ( setminus @ SV36 @ SY2198 ) )
| ~ ( in @ SY2199 @ SY2198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(906,plain,
! [SV37: $i] :
( ( ! [SY2200: $i] :
( ~ ( in @ SY2200 @ ( powerset @ SV37 ) )
| ! [SY2201: $i] :
( ~ ( in @ SY2201 @ ( powerset @ SV37 ) )
| ! [SY2202: $i] :
( ~ ( in @ SY2202 @ ( powerset @ SV37 ) )
| ! [SY2203: $i] :
( ~ ( in @ SY2203 @ ( powerset @ SV37 ) )
| ~ ( subset @ SY2200 @ SY2202 )
| ~ ( subset @ SY2201 @ SY2203 )
| ( subset @ ( binintersect @ SY2200 @ SY2201 ) @ ( binintersect @ SY2202 @ SY2203 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(907,plain,
! [SV38: $i > $o] :
( ( ~ ~ ! [SY2204: $i] :
~ ~ ( ~ ( SV38 @ SY2204 )
| ~ ! [SY2205: $i] :
( ~ ( SV38 @ SY2205 )
| ( SY2204 = SY2205 ) ) )
| ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(908,plain,
! [SV39: $i] :
( ( ! [SY2207: $i] :
( ~ ( subset @ SV39 @ SY2207 )
| ( subset @ ( powerset @ SV39 ) @ ( powerset @ SY2207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(909,plain,
! [SV40: $i] :
( ( ! [SY2208: $i] :
( ~ ( breln1 @ SV40 @ SY2208 )
| ! [SY2209: $i] :
( ~ ( breln1 @ SV40 @ SY2209 )
| ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SY2208 @ SY2209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(910,plain,
! [SV41: $i] :
( ( ! [SY2210: $i,SY2211: $i] :
( ~ ( subset @ SV41 @ SY2210 )
| ~ ~ ( in @ SY2211 @ SY2210 )
| ~ ( in @ SY2211 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(911,plain,
! [SV42: $i] :
( ( ! [SY2212: $i,SY2213: $i] :
( ~ ( in @ SY2213 @ SV42 )
| ! [SY2214: $i] :
( ~ ( in @ SY2214 @ SY2212 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2213 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2213 @ ( setadjoin @ SY2214 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SY2212 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(912,plain,
! [SV43: $i] :
( ( ! [SY2215: $i,SY2216: $i] :
( ~ ( in @ SY2216 @ ( binintersect @ SV43 @ SY2215 ) )
| ( in @ SY2216 @ SY2215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(913,plain,
! [SV44: $i] :
( ( ! [SY2217: $i] :
( ( SV44 != SY2217 )
| ! [SY2218: $i > $o,SY2219: $i > $o] :
( ~ ! [SY2220: $i] :
( ~ ( in @ SY2220 @ SV44 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2217 )
| ( SY2220 != SX5 )
| ~ ( ~ ( ~ ( SY2218 @ SY2220 )
| ( SY2219 @ SX5 ) )
| ~ ( ~ ( SY2219 @ SX5 )
| ( SY2218 @ SY2220 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SX4: $i] : ( SY2218 @ SX4 ) )
= ( dsetconstr @ SY2217
@ ^ [SX4: $i] : ( SY2219 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(914,plain,
! [SV45: $i] :
( ( ~ ! [SY2224: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2225: $i] :
( ~ ( in @ SY2225 @ SY2224 )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY2225 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY2227: $i,SY2228: $i] :
( ~ ~ ( ~ ( in @ SY2227 @ SV45 )
| ~ ( in @ SY2228 @ SV45 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2224 )
| ~ ( ~ ( ~ ( in @ SY2227 @ SX4 )
| ( in @ SY2228 @ SX4 ) )
| ~ ( ~ ( in @ SY2228 @ SX4 )
| ( in @ SY2227 @ SX4 ) ) ) )
| ( SY2227 = SY2228 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2224 )
| ~ ( in @ SX3 @ SY2224 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2234: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY2234 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2234 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2224 )
| ~ ( in @ SX4 @ SY2234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2234 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2224 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(915,plain,
! [SV46: $i] :
( ( ! [SY2242: $i > $o] :
( ~ ( ex1 @ SV46
@ ^ [SX2: $i] : ( SY2242 @ SX2 ) )
| ! [SY2244: $i] :
( ~ ( in @ SY2244 @ SV46 )
| ! [SY2245: $i] :
( ~ ( in @ SY2245 @ SV46 )
| ~ ( SY2242 @ SY2244 )
| ~ ( SY2242 @ SY2245 )
| ( SY2244 = SY2245 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(916,plain,
! [SV47: $o] :
( ( ~ SV47
| ( in @ emptyset @ ( prop2set @ SV47 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[619]) ).
thf(917,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[619]) ).
thf(918,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[619]) ).
thf(919,plain,
! [SV48: $i] :
( ( ! [SY2246: $i] :
( ~ ( in @ SY2246 @ SV48 )
| ( in @ ( setadjoin @ SY2246 @ emptyset ) @ ( powerset @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(920,plain,
! [SV49: $i] :
( ( ! [SY2247: $i,SY2248: $i > $i] :
( ~ ! [SY2249: $i] :
( ~ ( in @ SY2249 @ SV49 )
| ( in @ ( SY2248 @ SY2249 ) @ SY2247 ) )
| ( func @ SV49 @ SY2247
@ ( lam @ SV49 @ SY2247
@ ^ [SX3: $i] : ( SY2248 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(921,plain,
! [SV50: $i] :
( ( ~ ( singleton @ SV50 )
| ! [SY2251: $i] :
( ~ ( in @ SY2251 @ SV50 )
| ( ( setunion @ SV50 )
= SY2251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(922,plain,
! [SV51: $i] :
( ( ! [SY2252: $i] :
( ~ ! [SY2253: $i] :
( ~ ( in @ SY2253 @ SV51 )
| ( in @ SY2253 @ SY2252 ) )
| ( subset @ SV51 @ SY2252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(923,plain,
! [SV52: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) )
| ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(924,plain,
! [SV53: $i] :
( ( ! [SY2256: $i] :
~ ( ~ ( ~ ( in @ SY2256 @ ( setunion @ SV53 ) )
| ~ ! [SY2257: $i] :
~ ~ ( ~ ( in @ SY2256 @ SY2257 )
| ~ ( in @ SY2257 @ SV53 ) ) )
| ~ ( ~ ~ ! [SY2258: $i] :
~ ~ ( ~ ( in @ SY2256 @ SY2258 )
| ~ ( in @ SY2258 @ SV53 ) )
| ( in @ SY2256 @ ( setunion @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(925,plain,
! [SV54: $i] :
( ( ! [SY2259: $i > $o,SY2260: $i] :
( ~ ( in @ SY2260 @ SV54 )
| ~ ( SY2259 @ SY2260 )
| ~ ! [SY2261: $i] :
( ~ ( in @ SY2261 @ SV54 )
| ~ ( SY2259 @ SY2261 )
| ( SY2261 = SY2260 ) )
| ( ex1 @ SV54
@ ^ [SX3: $i] : ( SY2259 @ SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(926,plain,
! [SV55: $i] :
( ( ! [SY2263: $i,SY2264: $i > $i] :
( ~ ! [SY2265: $i] :
( ~ ( in @ SY2265 @ SV55 )
| ( in @ ( SY2264 @ SY2265 ) @ SY2263 ) )
| ( func @ SV55 @ SY2263
@ ( dpsetconstr @ SV55 @ SY2263
@ ^ [SX3: $i,SX4: $i] :
( ( SY2264 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(927,plain,
! [SV56: $i] :
( ( ! [SY2268: $i,SY2269: $i] :
( ~ ( in @ SY2269 @ ( funcSet @ SV56 @ SY2268 ) )
| ! [SY2270: $i] :
( ~ ( in @ SY2270 @ SV56 )
| ( ( ap @ SV56 @ SY2268 @ SY2269 @ SY2270 )
= ( ap @ SV56 @ SY2268 @ SY2269 @ SY2270 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(928,plain,
! [SV57: $i] :
( ( ! [SY2271: $i] :
( ~ ( in @ SY2271 @ ( powerset @ SV57 ) )
| ! [SY2272: $i] :
( ~ ( in @ SY2272 @ ( powerset @ SV57 ) )
| ! [SY2273: $i] :
( ~ ( in @ SY2273 @ SV57 )
| ~ ( in @ SY2273 @ ( setminus @ SV57 @ ( binunion @ SY2271 @ SY2272 ) ) )
| ( in @ SY2273 @ ( setminus @ SV57 @ SY2271 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(929,plain,
! [SV58: $i] :
( ( ! [SY2274: $i,SY2275: $i,SY2276: $i] :
( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SY2274 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2275 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2275 @ ( setadjoin @ SY2276 @ emptyset ) ) @ emptyset ) ) )
| ( SY2274 = SY2276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(930,plain,
! [SV59: $i] :
( ( ! [SY2277: $i] :
( ~ ( in @ SY2277 @ ( powerset @ SV59 ) )
| ! [SY2278: $i] :
( ~ ( in @ SY2278 @ SV59 )
| ~ ~ ( in @ SY2278 @ ( setminus @ SV59 @ SY2277 ) )
| ( in @ SY2278 @ SY2277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(931,plain,
! [SV60: $i] :
( ( ! [SY2279: $i] :
( ~ ( in @ SY2279 @ ( powerset @ SV60 ) )
| ( SY2279
= ( setminus @ SV60 @ ( setminus @ SV60 @ SY2279 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(932,plain,
! [SV61: $i] :
( ( ! [SY2280: $i,SY2281: $i] :
( ~ ( in @ SY2281 @ ( funcSet @ SV61 @ SY2280 ) )
| ! [SY2282: $i] :
( ~ ( in @ SY2282 @ ( funcSet @ SV61 @ SY2280 ) )
| ~ ! [SY2283: $i] :
( ~ ( in @ SY2283 @ SV61 )
| ( ( ap @ SV61 @ SY2280 @ SY2281 @ SY2283 )
= ( ap @ SV61 @ SY2280 @ SY2282 @ SY2283 ) ) )
| ( SY2281 = SY2282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(933,plain,
! [SV62: $i] :
( ( ! [SY2284: $i] :
( ~ ( in @ SY2284 @ ( powerset @ SV62 ) )
| ! [SY2285: $i] :
( ~ ( in @ SY2285 @ ( powerset @ SV62 ) )
| ~ ( subset @ SY2284 @ ( setminus @ SV62 @ SY2285 ) )
| ( subset @ SY2285 @ ( setminus @ SV62 @ SY2284 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(934,plain,
! [SV63: $i] :
( ( ! [SY2286: $i] :
( ~ ( in @ SY2286 @ ( powerset @ SV63 ) )
| ! [SY2287: $i] :
( ~ ( in @ SY2287 @ ( powerset @ SV63 ) )
| ! [SY2288: $i] :
( ~ ( in @ SY2288 @ SV63 )
| ~ ~ ( in @ SY2288 @ ( binunion @ SY2286 @ SY2287 ) )
| ~ ( in @ SY2288 @ SY2287 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(935,plain,
! [SV64: $i] :
( ( ! [SY2289: $i] :
( ~ ( in @ SY2289 @ ( powerset @ SV64 ) )
| ! [SY2290: $i] :
( ~ ( in @ SY2290 @ ( powerset @ SV64 ) )
| ! [SY2291: $i] :
( ~ ( in @ SY2291 @ ( powerset @ SV64 ) )
| ~ ( subset @ SY2290 @ SY2291 )
| ( subset @ ( binintersect @ SY2289 @ SY2290 ) @ SY2291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(936,plain,
! [SV65: $i] :
( ( ! [SY2292: $i] :
( ~ ( in @ SY2292 @ ( powerset @ SV65 ) )
| ! [SY2293: $i] :
( ~ ( in @ SY2293 @ ( powerset @ SV65 ) )
| ! [SY2294: $i] :
( ~ ( in @ SY2294 @ SV65 )
| ~ ~ ( in @ SY2294 @ SY2293 )
| ~ ( in @ SY2294 @ ( binintersect @ SY2292 @ SY2293 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(937,plain,
! [SV66: $i] :
( ( ! [SY2295: $i] :
( ~ ( in @ SY2295 @ ( powerset @ SV66 ) )
| ! [SY2296: $i] :
( ~ ( in @ SY2296 @ SV66 )
| ~ ( in @ SY2296 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SY2295 ) ) )
| ( in @ SY2296 @ SY2295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(938,plain,
! [SV67: $i] :
( ( ! [SY2297: $i] :
( ~ ! [SY2298: $i] :
( ~ ( in @ SY2298 @ SY2297 )
| ( in @ SY2298 @ SV67 ) )
| ( in @ SY2297 @ ( powerset @ SV67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(939,plain,
! [SV68: $i] :
( ( ! [SY2299: $i] :
( ~ ( breln1 @ SV68 @ SY2299 )
| ! [SY2300: $i] :
( ~ ( breln1 @ SV68 @ SY2300 )
| ! [SY2301: $i] :
( ~ ( in @ SY2301 @ SV68 )
| ! [SY2302: $i] :
( ~ ( in @ SY2302 @ SV68 )
| ~ ( in @ ( kpair @ SY2301 @ SY2302 ) @ ( breln1compset @ SV68 @ SY2299 @ SY2300 ) )
| ~ ! [SY2303: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY2303 @ SV68 )
| ~ ( in @ ( kpair @ SY2301 @ SY2303 ) @ SY2299 ) )
| ~ ( in @ ( kpair @ SY2303 @ SY2302 ) @ SY2300 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(940,plain,
! [SV69: $i] :
( ( ! [SY2304: $i] :
( ~ ( in @ SY2304 @ ( powerset @ SV69 ) )
| ! [SY2305: $i] :
( ~ ( in @ SY2305 @ ( powerset @ SV69 ) )
| ! [SY2306: $i] :
( ~ ( in @ SY2306 @ SV69 )
| ~ ( in @ SY2306 @ ( setminus @ SV69 @ ( binintersect @ SY2304 @ SY2305 ) ) )
| ( in @ SY2306 @ ( binunion @ ( setminus @ SV69 @ SY2304 ) @ ( setminus @ SV69 @ SY2305 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(941,plain,
! [SV70: $i] :
( ( ! [SY2307: $i,SY2308: $i > $i] :
( ~ ! [SY2309: $i] :
( ~ ( in @ SY2309 @ SV70 )
| ( in @ ( SY2308 @ SY2309 ) @ SY2307 ) )
| ! [SY2310: $i] :
( ~ ( in @ SY2310 @ SV70 )
| ( ( ap @ SV70 @ SY2307
@ ( lam @ SV70 @ SY2307
@ ^ [SX4: $i] : ( SY2308 @ SX4 ) )
@ SY2310 )
= ( SY2308 @ SY2310 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(942,plain,
! [SV71: $i] :
( ( ! [SY2312: $i,SY2313: $i > $i > $o,SY2314: $i] :
( ~ ( in @ SY2314 @ SV71 )
| ! [SY2315: $i] :
( ~ ( in @ SY2315 @ SY2312 )
| ~ ( SY2313 @ SY2314 @ SY2315 )
| ( in @ ( kpair @ SY2314 @ SY2315 )
@ ( dpsetconstr @ SV71 @ SY2312
@ ^ [SX5: $i,SX6: $i] : ( SY2313 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(943,plain,
! [SV72: $i] :
( ( ! [SY2318: $i,SY2319: $i] :
( ~ ( in @ SY2319 @ ( funcSet @ SV72 @ SY2318 ) )
| ! [SY2320: $i] :
( ~ ( in @ SY2320 @ SV72 )
| ( in @ ( ap @ SV72 @ SY2318 @ SY2319 @ SY2320 ) @ SY2318 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(944,plain,
! [SV73: $i] :
( ( ! [SY2321: $i,SY2322: $i > $i > $o,SY2323: $i,SY2324: $i] :
( ~ ( in @ ( kpair @ SY2323 @ SY2324 )
@ ( dpsetconstr @ SV73 @ SY2321
@ ^ [SX5: $i,SX6: $i] : ( SY2322 @ SX5 @ SX6 ) ) )
| ( SY2322 @ SY2323 @ SY2324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(945,plain,
! [SV74: $i] :
( ( ! [SY2327: $i,SY2328: $i > $i > $o] :
( ~ ! [SY2329: $i] :
( ~ ( in @ SY2329 @ SV74 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY2327 )
| ~ ( SY2328 @ SY2329 @ SX4 ) ) )
| ! [SY2331: $i] :
( ~ ( in @ SY2331 @ ( breln1Set @ SY2327 ) )
| ~ ( reflwellordering @ SY2327 @ SY2331 )
| ! [SY2332: $i] :
( ~ ( in @ SY2332 @ SV74 )
| ( singleton
@ ( dsetconstr @ SY2327
@ ^ [SX5: $i] :
~ ( ~ ( SY2328 @ SY2332 @ SX5 )
| ~ ! [SX6: $i] :
( ~ ( in @ SX6 @ SY2327 )
| ~ ( SY2328 @ SY2332 @ SX6 )
| ( in @ ( kpair @ SX5 @ SX6 ) @ SY2331 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(946,plain,
! [SV75: $i] :
( ( ! [SY2335: $i,SY2336: $i] :
( ~ ( func @ SV75 @ SY2335 @ SY2336 )
| ! [SY2337: $i] :
( ~ ( in @ SY2337 @ SV75 )
| ( in @ ( kpair @ SY2337 @ ( ap @ SV75 @ SY2335 @ SY2336 @ SY2337 ) ) @ SY2336 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(947,plain,
! [SV76: $i] :
( ( ! [SY2338: $i > $o] :
( ~ ~ ! [SY2339: $i] :
( ~ ( in @ SY2339 @ SV76 )
| ( SY2338 @ SY2339 ) )
| ~ ! [SY2340: $i] :
~ ~ ( ~ ( in @ SY2340 @ SV76 )
| ~ ~ ( SY2338 @ SY2340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(948,plain,
! [SV77: $i] :
( ( ! [SY2341: $i,SY2342: $i] :
( ~ ( subset @ SV77 @ SY2341 )
| ~ ( in @ SY2342 @ SV77 )
| ( in @ SY2342 @ SY2341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(949,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 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(950,plain,
! [SV78: $i] :
( ( ! [SY2343: $i] :
( ( SV78 != SY2343 )
| ! [SY2344: $i,SY2345: $i] :
( ( SY2344 != SY2345 )
| ~ ( in @ SY2344 @ SV78 )
| ( in @ SY2345 @ SY2343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(951,plain,
! [SV79: $i] :
( ( ! [SY2346: $i] :
( ~ ( subset @ SV79 @ SY2346 )
| ~ ( subset @ SY2346 @ SV79 )
| ( SV79 = SY2346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(952,plain,
! [SV80: $i] :
( ( ! [SY2347: $i,SY2348: $i,SY2349: $i] :
( ( ( kpair @ SV80 @ SY2347 )
!= ( kpair @ SY2348 @ SY2349 ) )
| ( SY2347 = SY2349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(953,plain,
! [SV81: $i] :
( ( ! [SY2350: $i,SY2351: $i] :
( ~ ( func @ SV81 @ SY2350 @ SY2351 )
| ! [SY2352: $i] :
( ~ ( func @ SV81 @ SY2350 @ SY2352 )
| ~ ! [SY2353: $i] :
( ~ ( in @ SY2353 @ SV81 )
| ( ( ap @ SV81 @ SY2350 @ SY2351 @ SY2353 )
= ( ap @ SV81 @ SY2350 @ SY2352 @ SY2353 ) ) )
| ! [SY2354: $i] :
( ~ ( in @ SY2354 @ SV81 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2350 )
| ~ ( in @ ( kpair @ SY2354 @ SX5 ) @ SY2352 )
| ( in @ ( kpair @ SY2354 @ SX5 ) @ SY2351 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(954,plain,
! [SV82: $i] :
( ( ! [SY2356: $i] :
~ ( ~ ( ~ ( in @ SY2356 @ ( powerset @ SV82 ) )
| ! [SY2357: $i] :
( ~ ( in @ SY2357 @ SY2356 )
| ( in @ SY2357 @ SV82 ) ) )
| ~ ( ~ ! [SY2358: $i] :
( ~ ( in @ SY2358 @ SY2356 )
| ( in @ SY2358 @ SV82 ) )
| ( in @ SY2356 @ ( powerset @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(955,plain,
! [SV83: $i] :
( ( ! [SY2359: $i] :
( ( SV83 != SY2359 )
| ! [SY2360: $i,SY2361: $i] :
( ( SY2360 != SY2361 )
| ~ ( ~ ( ~ ( in @ SY2360 @ SV83 )
| ( in @ SY2361 @ SY2359 ) )
| ~ ( ~ ( in @ SY2361 @ SY2359 )
| ( in @ SY2360 @ SV83 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(956,plain,
! [SV84: $i] :
( ( ! [SY2362: $i] :
( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SY2362 @ emptyset ) )
| ( SV84 = SY2362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(957,plain,
! [SV85: $i] :
( ( ! [SY2363: $i] :
( ~ ( in @ SY2363 @ ( powerset @ SV85 ) )
| ! [SY2364: $i] :
( ~ ( in @ SY2364 @ ( powerset @ SV85 ) )
| ! [SY2365: $o,SY2366: $i] :
( ~ ( in @ SY2366 @ SV85 )
| ~ ( in @ SY2366 @ ( binunion @ SY2363 @ SY2364 ) )
| ~ ( ~ ( in @ SY2366 @ SY2363 )
| SY2365 )
| ~ ( ~ ( in @ SY2366 @ SY2364 )
| SY2365 )
| SY2365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(958,plain,
! [SV86: $i] :
( ( ! [SY2367: $i,SY2368: $i,SY2369: $o] :
( ~ ( in @ SY2368 @ ( binunion @ SV86 @ SY2367 ) )
| ~ ( ~ ( in @ SY2368 @ SV86 )
| SY2369 )
| ~ ( ~ ( in @ SY2368 @ SY2367 )
| SY2369 )
| SY2369 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(959,plain,
! [SV87: $i] :
( ( ! [SY2370: $i,SY2371: $i] :
( ~ ( in @ SY2371 @ SV87 )
| ~ ( in @ SY2371 @ SY2370 )
| ~ ( in @ SY2371 @ ( symdiff @ SV87 @ SY2370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(960,plain,
! [SV88: $i] :
( ( ! [SY2372: $i,SY2373: $i] :
( ~ ( in @ SY2373 @ ( cartprod @ SV88 @ SY2372 ) )
| ( in @ ( ksnd @ SY2373 ) @ SY2372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(961,plain,
! [SV89: $i] :
( ( ! [SY2374: $i,SY2375: $i] :
( ~ ( in @ SY2375 @ SV89 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2374 )
| ( ( ksnd @ ( kpair @ SY2375 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(962,plain,
! [SV90: $i] :
( ( ! [SY2377: $i,SY2378: $i] :
( ~ ( in @ SY2378 @ ( funcSet @ SV90 @ SY2377 ) )
| ( func @ SV90 @ SY2377 @ SY2378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(963,plain,
! [SV91: $i] :
( ( ! [SY2379: $i] :
( ( SV91 != SY2379 )
| ( subset @ SV91 @ SY2379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(964,plain,
! [SV92: $i] :
( ( ! [SY2380: $i,SY2381: $i] :
( ~ ( in @ SY2381 @ SV92 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2380 )
| ( ( kpair @ SY2381 @ SX3 )
= ( kpair @ SY2381 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(965,plain,
! [SV93: $i] :
( ( ! [SY2383: $i,SY2384: $i] :
( ~ ( in @ SY2384 @ ( symdiff @ SV93 @ SY2383 ) )
| ! [SY2385: $o] :
( ~ ( ~ ( in @ SY2384 @ SV93 )
| ~ ~ ( in @ SY2384 @ SY2383 )
| SY2385 )
| ~ ( ~ ~ ( in @ SY2384 @ SV93 )
| ~ ( in @ SY2384 @ SY2383 )
| SY2385 )
| SY2385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(966,plain,
! [SV94: $i] :
( ( ! [SY2386: $i,SY2387: $i] :
( ~ ( in @ SY2387 @ SV94 )
| ~ ~ ( in @ SY2387 @ SY2386 )
| ( in @ SY2387 @ ( symdiff @ SV94 @ SY2386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(967,plain,
! [SV95: $i > $o] :
( ( ~ ~ ! [SY2388: $i] :
~ ( SV95 @ SY2388 )
| ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(968,plain,
! [SV96: $i] :
( ( ! [SY2393: $i] :
( ( SV96 != SY2393 )
| ! [SY2394: $i,SY2395: $i] :
( ( SY2394 != SY2395 )
| ( ( setadjoin @ SV96 @ SY2394 )
= ( setadjoin @ SY2393 @ SY2395 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(969,plain,
! [SV97: $i > $o] :
( ( ! [SY2396: $i > $o] :
( ~ ! [SY2397: $i,SY2398: $i] :
( ( SY2397 != SY2398 )
| ~ ( ~ ( ~ ( SV97 @ SY2397 )
| ( SY2396 @ SY2398 ) )
| ~ ( ~ ( SY2396 @ SY2398 )
| ( SV97 @ SY2397 ) ) ) )
| ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2396 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2396 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SX2: $i] : ( SY2396 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(970,plain,
! [SV98: $i] :
( ( ! [SY2405: $i > $o] :
( ~ ! [SY2406: $i] :
( ~ ( in @ SY2406 @ SV98 )
| ! [SY2407: $i] :
( ~ ( in @ SY2407 @ SV98 )
| ~ ( SY2405 @ SY2406 )
| ~ ( SY2405 @ SY2407 )
| ( SY2406 = SY2407 ) ) )
| ~ ~ ! [SY2408: $i] :
~ ~ ( ~ ( in @ SY2408 @ SV98 )
| ~ ( SY2405 @ SY2408 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SX2: $i] : ( SY2405 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(971,plain,
! [SV99: $o] :
( ( ! [SY2410: $i] :
( ~ ( in @ SY2410 @ ( prop2set @ SV99 ) )
| SV99 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[672]) ).
thf(972,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[672]) ).
thf(973,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[672]) ).
thf(974,plain,
! [SV100: $i] :
( ( ! [SY2411: $i,SY2412: $i] :
( ~ ( in @ SY2412 @ SV100 )
| ! [SY2413: $i] :
( ~ ( in @ SY2413 @ SY2411 )
| ( subset @ ( setadjoin @ SY2412 @ ( setadjoin @ SY2413 @ emptyset ) ) @ ( binunion @ SV100 @ SY2411 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(975,plain,
! [SV101: $i] :
( ( ! [SY2414: $i] :
( ~ ( in @ SY2414 @ ( powerset @ SV101 ) )
| ! [SY2415: $i] :
( ~ ( in @ SY2415 @ ( powerset @ SV101 ) )
| ( in @ ( setminus @ SV101 @ ( binunion @ SY2414 @ SY2415 ) ) @ ( powerset @ ( setminus @ SV101 @ SY2414 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(976,plain,
! [SV102: $i] :
( ( ! [SY2416: $i] :
( ~ ( in @ SY2416 @ ( powerset @ SV102 ) )
| ! [SY2417: $i] :
( ~ ( in @ SY2417 @ ( powerset @ SV102 ) )
| ~ ( subset @ ( setminus @ SV102 @ SY2417 ) @ ( setminus @ SV102 @ SY2416 ) )
| ( subset @ SY2416 @ SY2417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(977,plain,
! [SV103: $i] :
( ( ! [SY2418: $i,SY2419: $i] :
( ~ ( in @ ( setadjoin @ SY2419 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ ( setadjoin @ SY2418 @ emptyset ) ) @ emptyset ) ) )
| ( SV103 = SY2419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(978,plain,
! [SV104: $i] :
( ( ! [SY2420: $i] :
( ~ ( in @ SY2420 @ ( powerset @ SV104 ) )
| ! [SY2421: $i] :
( ~ ( in @ SY2421 @ ( powerset @ SV104 ) )
| ! [SY2422: $i] :
( ~ ( in @ SY2422 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SY2420 @ SY2421 ) @ ( powerset @ ( binintersect @ ( binunion @ SY2420 @ SY2422 ) @ ( binunion @ SY2421 @ SY2422 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(979,plain,
! [SV105: $i > $o] :
( ( ~ ~ ! [SY2423: $i] :
~ ~ ( ~ ( SV105 @ SY2423 )
| ~ ! [SY2424: $i] :
( ~ ( SV105 @ SY2424 )
| ( SY2423 = SY2424 ) ) )
| ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(980,plain,
! [SV106: $i] :
( ( ! [SY2427: $i > $o] :
( ~ ~ ~ ! [SY2428: $i] :
~ ~ ( ~ ( in @ SY2428 @ SV106 )
| ~ ( SY2427 @ SY2428 ) )
| ! [SY2429: $i] :
( ~ ( in @ SY2429 @ SV106 )
| ~ ( SY2427 @ SY2429 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(981,plain,
! [SV107: $i] :
( ( ! [SY2430: $i] :
( ~ ( in @ SY2430 @ ( powerset @ SV107 ) )
| ! [SY2431: $i] :
( ~ ( in @ SY2431 @ ( powerset @ SV107 ) )
| ! [SY2432: $i] :
( ~ ( in @ SY2432 @ SV107 )
| ~ ~ ( in @ SY2432 @ SY2430 )
| ~ ( in @ SY2432 @ ( binintersect @ SY2430 @ SY2431 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(982,plain,
! [SV108: $i] :
( ( ! [SY2433: $o,SY2434: $i] :
( ~ ( in @ SY2434 @ SV108 )
| ! [SY2435: $i] :
( ~ ( in @ SY2435 @ SV108 )
| ( in @ ( if @ SV108 @ SY2433 @ SY2434 @ SY2435 ) @ ( setadjoin @ SY2434 @ ( setadjoin @ SY2435 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(983,plain,
! [SV109: $i] :
( ( ! [SY2436: $i,SY2437: $i] :
( ~ ( in @ SY2437 @ SY2436 )
| ( in @ SY2437 @ ( binunion @ SV109 @ SY2436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(984,plain,
! [SV110: $i] :
( ( ! [SY2438: $i] :
( ( ( binintersect @ SV110 @ SY2438 )
!= SY2438 )
| ( subset @ SY2438 @ SV110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(985,plain,
! [SV111: $i] :
( ( ! [SY2439: $i] :
( ~ ( in @ SY2439 @ ( powerset @ SV111 ) )
| ! [SY2440: $i] :
( ~ ( in @ SY2440 @ ( powerset @ SV111 ) )
| ~ ! [SY2441: $i] :
( ~ ( in @ SY2441 @ SV111 )
| ~ ( in @ SY2441 @ SY2439 )
| ( in @ SY2441 @ SY2440 ) )
| ~ ! [SY2442: $i] :
( ~ ( in @ SY2442 @ SV111 )
| ~ ( in @ SY2442 @ SY2440 )
| ( in @ SY2442 @ SY2439 ) )
| ( SY2439 = SY2440 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(986,plain,
! [SV112: $i] :
( ( ! [SY2443: $i] :
( ~ ( in @ SY2443 @ ( powerset @ SV112 ) )
| ! [SY2444: $i] :
( ~ ( in @ SY2444 @ ( powerset @ SV112 ) )
| ! [SY2445: $i] :
( ~ ( in @ SY2445 @ SV112 )
| ~ ~ ( in @ SY2445 @ SY2443 )
| ~ ~ ( in @ SY2445 @ SY2444 )
| ~ ( in @ SY2445 @ ( binunion @ SY2443 @ SY2444 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(987,plain,
! [SV113: $i] :
( ( ! [SY2446: $i] :
( ~ ! [SY2447: $i] :
( ~ ( in @ SY2447 @ SV113 )
| ( in @ SY2447 @ SY2446 ) )
| ( subset @ SV113 @ SY2446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(988,plain,
! [SV114: $i] :
( ( ! [SY2448: $i,SY2449: $i] :
( ~ ~ ( in @ SY2449 @ ( setminus @ SV114 @ SY2448 ) )
| ~ ~ ( in @ SY2449 @ SY2448 )
| ~ ( in @ SY2449 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(989,plain,
! [SV115: $i] :
( ( ! [SY2450: $i] :
( ~ ( breln1 @ SV115 @ SY2450 )
| ( breln1 @ SV115 @ ( breln1invset @ SV115 @ SY2450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(990,plain,
! [SV116: $i] :
( ( ~ ( in @ SV116 @ omega )
| ( in @ ( setadjoin @ SV116 @ SV116 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(991,plain,
! [SV117: $i] :
( ( ! [SY2451: $o,SY2452: $i] :
( ~ ( in @ SY2452 @ SV117 )
| ! [SY2453: $i] :
( ~ ( in @ SY2453 @ SV117 )
| ~ ~ SY2451
| ( ( dsetconstr @ SV117
@ ^ [SX4: $i] :
( ~ ( ~ SY2451
| ( SX4 != SY2452 ) )
| ~ ( ~ ~ SY2451
| ( SX4 != SY2453 ) ) ) )
= ( setadjoin @ SY2453 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(992,plain,
! [SV118: $i] :
( ( ! [SY2455: $i] :
( ~ ( in @ SY2455 @ ( powerset @ SV118 ) )
| ! [SY2456: $i] :
( ~ ( in @ SY2456 @ ( powerset @ SV118 ) )
| ! [SY2457: $i] :
( ~ ( in @ SY2457 @ ( binintersect @ SY2455 @ SY2456 ) )
| ( in @ SY2457 @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(993,plain,
! [SV119: $i] :
( ( ! [SY2458: $i,SY2459: $i] :
( ~ ( in @ SY2459 @ ( cartprod @ SV119 @ SY2458 ) )
| ( iskpair @ SY2459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(994,plain,
! [SV120: $i] :
( ( ! [SY2460: $i,SY2461: $i] :
( ~ ( subset @ SV120 @ SY2461 )
| ( subset @ SV120 @ ( setadjoin @ SY2460 @ SY2461 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(995,plain,
! [SV121: $i] :
( ( ! [SY2462: $i > $o] :
( ~ ! [SY2463: $i] :
( ~ ( in @ SY2463 @ SV121 )
| ~ ( SY2462 @ SY2463 ) )
| ~ ~ ! [SY2464: $i] :
~ ~ ( ~ ( in @ SY2464 @ SV121 )
| ~ ( SY2462 @ SY2464 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(996,plain,
! [SV122: $i] :
( ( ! [SY2465: $i] :
( ~ ( in @ SY2465 @ ( powerset @ SV122 ) )
| ! [SY2466: $i] :
( ~ ( in @ SY2466 @ ( powerset @ SV122 ) )
| ! [SY2467: $i] :
( ~ ( in @ SY2467 @ SV122 )
| ~ ( in @ SY2467 @ ( setminus @ SV122 @ ( binunion @ SY2465 @ SY2466 ) ) )
| ( in @ SY2467 @ ( setminus @ SV122 @ SY2465 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(997,plain,
! [SV123: $i] :
( ( ! [SY2468: $i,SY2469: $i > $i > $o,SY2470: $i,SY2471: $i] :
( ~ ( in @ ( kpair @ SY2470 @ SY2471 )
@ ( dpsetconstr @ SV123 @ SY2468
@ ^ [SX5: $i,SX6: $i] : ( SY2469 @ SX5 @ SX6 ) ) )
| ( in @ SY2470 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(998,plain,
! [SV124: $i] :
( ( ! [SY2474: $i,SY2475: $i] :
( ~ ( in @ SY2475 @ SV124 )
| ( in @ SY2475 @ ( binunion @ SV124 @ SY2474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(999,plain,
! [SV125: $i] :
( ( ! [SY2476: $i,SY2477: $i] :
( ~ ( func @ SV125 @ SY2476 @ SY2477 )
| ! [SY2478: $i] :
( ~ ( in @ SY2478 @ SV125 )
| ( in @ ( ap @ SV125 @ SY2476 @ SY2477 @ SY2478 ) @ SY2476 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(1000,plain,
! [SV126: $i] :
( ( ! [SY2479: $i,SY2480: $i] :
( ~ ( breln @ SV126 @ SY2479 @ SY2480 )
| ! [SY2481: $i > $o] :
( ~ ! [SY2482: $i] :
( ~ ( in @ SY2482 @ SV126 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2479 )
| ~ ( in @ ( kpair @ SY2482 @ SX5 ) @ SY2480 )
| ( SY2481 @ ( kpair @ SY2482 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2480 )
| ( SY2481 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(1001,plain,
! [SV127: $i] :
( ( ! [SY2485: $i] :
( ~ ( in @ SY2485 @ ( powerset @ SV127 ) )
| ! [SY2486: $i] :
( ~ ( in @ SY2486 @ ( powerset @ SV127 ) )
| ! [SY2487: $i] :
( ~ ( in @ SY2487 @ SV127 )
| ~ ( in @ SY2487 @ ( setminus @ SV127 @ SY2485 ) )
| ( in @ SY2487 @ ( setminus @ SV127 @ ( binintersect @ SY2485 @ SY2486 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(1002,plain,
! [SV128: $i] :
( ( ! [SY2488: $i,SY2489: $i] :
( ~ ~ ( in @ SY2489 @ SV128 )
| ~ ( in @ SY2489 @ SY2488 )
| ( in @ SY2489 @ ( symdiff @ SV128 @ SY2488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(1003,plain,
! [SV129: $i > $o] :
( ( ~ ~ ! [SY2490: $i] :
~ ~ ( ~ ( SV129 @ SY2490 )
| ~ ! [SY2491: $i] :
( ~ ( SV129 @ SY2491 )
| ( SY2490 = SY2491 ) ) )
| ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(1004,plain,
! [SV130: $i] :
( ( ! [SY2494: $i,SY2495: $i] :
( ~ ( in @ SY2495 @ ( setadjoin @ SV130 @ SY2494 ) )
| ( SY2495 = SV130 )
| ( in @ SY2495 @ SY2494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(1005,plain,
! [SV131: $i] :
( ( ~ ( iskpair @ SV131 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV131 )
@ ^ [SY2496: $i] : ( in @ ( setadjoin @ SY2496 @ emptyset ) @ SV131 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(1006,plain,
! [SV132: $i] :
( ( ! [SY2497: $i] :
( ~ ( in @ SY2497 @ ( powerset @ SV132 ) )
| ! [SY2498: $i] :
( ~ ( in @ SY2498 @ ( powerset @ SV132 ) )
| ! [SY2499: $i] :
( ~ ( in @ SY2499 @ SV132 )
| ~ ( in @ SY2499 @ ( binintersect @ ( setminus @ SV132 @ SY2497 ) @ ( setminus @ SV132 @ SY2498 ) ) )
| ( in @ SY2499 @ ( setminus @ SV132 @ ( binunion @ SY2497 @ SY2498 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(1007,plain,
! [SV133: $i] :
( ( ! [SY2500: $i] :
( ~ ( subset @ SY2500 @ SV133 )
| ( ( binintersect @ SV133 @ SY2500 )
= SY2500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(1008,plain,
! [SV134: $i] :
( ( ! [SY2501: $i] :
( ~ ( in @ SY2501 @ ( powerset @ SV134 ) )
| ! [SY2502: $i] :
( ~ ( in @ SY2502 @ ( powerset @ SV134 ) )
| ! [SY2503: $i] :
( ~ ( in @ SY2503 @ SV134 )
| ~ ( in @ SY2501 @ ( powerset @ SY2502 ) )
| ~ ( in @ SY2503 @ SY2501 )
| ( in @ SY2503 @ SY2502 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(1009,plain,
! [SV135: $i] :
( ( ~ ! [SY2504: $i] :
~ ( in @ SY2504 @ SV135 )
| ( SV135 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(1010,plain,
! [SV136: $i] :
( ( ! [SY2505: $i,SY2506: $i] :
( ~ ( in @ SY2506 @ ( binintersect @ SV136 @ SY2505 ) )
| ( in @ SY2506 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(1011,plain,
! [SV137: $i] :
( ( ! [SY2507: $i,SY2508: $i] :
( ~ ( func @ SV137 @ SY2507 @ SY2508 )
| ! [SY2509: $i] :
( ~ ( func @ SV137 @ SY2507 @ SY2509 )
| ~ ! [SY2510: $i] :
( ~ ( in @ SY2510 @ SV137 )
| ( ( ap @ SV137 @ SY2507 @ SY2508 @ SY2510 )
= ( ap @ SV137 @ SY2507 @ SY2509 @ SY2510 ) ) )
| ( SY2508 = SY2509 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(1012,plain,
! [SV138: $i] :
( ( ! [SY2511: $o,SY2512: $i] :
( ~ ( in @ SY2512 @ SV138 )
| ! [SY2513: $i] :
( ~ ( in @ SY2513 @ SV138 )
| ~ SY2511
| ( in @ SY2512
@ ( dsetconstr @ SV138
@ ^ [SX4: $i] :
( ~ ( ~ SY2511
| ( SX4 != SY2512 ) )
| ~ ( ~ ~ SY2511
| ( SX4 != SY2513 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(1013,plain,
! [SV139: $i > $o] :
( ( ~ ~ ! [SY2515: $i] :
~ ~ ( ~ ( SV139 @ SY2515 )
| ~ ! [SY2516: $i] :
( ~ ( SV139 @ SY2516 )
| ( SY2515 = SY2516 ) ) )
| ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(1014,plain,
! [SV140: $i] :
( ( ! [SY2519: $i > $o,SY2520: $i] :
( ~ ( in @ SY2520 @ SV140 )
| ~ ( SY2519 @ SY2520 )
| ( in @ SY2520
@ ( dsetconstr @ SV140
@ ^ [SX3: $i] : ( SY2519 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(1015,plain,
! [SV141: $i > $o] :
( ( ! [SY2522: $i > $o] :
( ~ ! [SY2523: $i,SY2524: $i] :
( ( SY2523 != SY2524 )
| ~ ( ~ ( ~ ( SV141 @ SY2523 )
| ( SY2522 @ SY2524 ) )
| ~ ( ~ ( SY2522 @ SY2524 )
| ( SV141 @ SY2523 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2522 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2522 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY2522 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY2522 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(1016,plain,
! [SV142: $i] :
( ( ! [SY2533: $i,SY2534: $i] :
( ~ ( in @ SY2534 @ ( cartprod @ SV142 @ SY2533 ) )
| ~ ! [SY2535: $i] :
~ ~ ( ~ ( in @ SY2535 @ SV142 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY2533 )
| ( SY2534
!= ( kpair @ SY2535 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(1017,plain,
! [SV143: $i] :
( ( ! [SY2537: $i] :
( ~ ( in @ SY2537 @ ( powerset @ SV143 ) )
| ! [SY2538: $i] :
( ~ ( in @ SY2538 @ ( powerset @ SV143 ) )
| ( subset @ ( setminus @ SV143 @ SY2537 ) @ ( setminus @ SV143 @ ( binintersect @ SY2537 @ SY2538 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(1018,plain,
! [SV144: $i] :
( ( ! [SY2539: $i] :
( ~ ( breln1 @ SV144 @ SY2539 )
| ! [SY2540: $i > $o] :
( ~ ! [SY2541: $i] :
( ~ ( in @ SY2541 @ SV144 )
| ! [SY2542: $i] :
( ~ ( in @ SY2542 @ SV144 )
| ~ ( in @ ( kpair @ SY2541 @ SY2542 ) @ SY2539 )
| ( SY2540 @ ( kpair @ SY2541 @ SY2542 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2539 )
| ( SY2540 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(1019,plain,
! [SV145: $i] :
( ( ! [SY2544: $i] :
( ~ ( in @ SY2544 @ ( powerset @ SV145 ) )
| ! [SY2545: $i] :
( ~ ( in @ SY2545 @ ( powerset @ SV145 ) )
| ! [SY2546: $i] :
( ~ ( in @ SY2546 @ ( powerset @ SV145 ) )
| ~ ( subset @ SY2544 @ SY2546 )
| ( subset @ ( binintersect @ SY2544 @ SY2545 ) @ SY2546 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(1020,plain,
! [SV146: $i] :
( ( ! [SY2547: $i] :
( ( ( binintersect @ SV146 @ SY2547 )
!= SV146 )
| ( subset @ SV146 @ SY2547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(1021,plain,
! [SV147: $i] :
( ( ! [SY2548: $o,SY2549: $i] :
( ~ ( in @ SY2549 @ SV147 )
| ! [SY2550: $i] :
( ~ ( in @ SY2550 @ SV147 )
| ~ ~ SY2548
| ( in @ SY2550
@ ( dsetconstr @ SV147
@ ^ [SX4: $i] :
( ~ ( ~ SY2548
| ( SX4 != SY2549 ) )
| ~ ( ~ ~ SY2548
| ( SX4 != SY2550 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(1022,plain,
! [SV148: $i] :
( ( ~ ( in @ SV148 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(1023,plain,
! [SV149: $i] :
( ( ! [SY2552: $o,SY2553: $i] :
( ~ ( in @ SY2553 @ SV149 )
| ! [SY2554: $i] :
( ~ ( in @ SY2554 @ SV149 )
| ~ ~ SY2552
| ( ( if @ SV149 @ SY2552 @ SY2553 @ SY2554 )
= SY2554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(1024,plain,
! [SV150: $i] :
( ( ! [SY2555: $i,SY2556: $i] :
( ~ ( subset @ SY2556 @ SV150 )
| ~ ( subset @ SY2556 @ SY2555 )
| ( subset @ SY2556 @ ( binintersect @ SV150 @ SY2555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(1025,plain,
! [SV151: $i] :
( ( ! [SY2557: $i] :
( ~ ( in @ SY2557 @ ( powerset @ SV151 ) )
| ! [SY2558: $i] :
( ~ ( in @ SY2558 @ ( powerset @ SV151 ) )
| ~ ( subset @ SY2557 @ ( setminus @ SV151 @ SY2558 ) )
| ! [SY2559: $i] :
( ~ ( in @ SY2559 @ SV151 )
| ~ ( in @ SY2559 @ SY2558 )
| ( in @ SY2559 @ ( setminus @ SV151 @ SY2557 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(1026,plain,
! [SV152: $i] :
( ( ! [SY2560: $i] :
( ~ ( in @ SY2560 @ ( powerset @ SV152 ) )
| ! [SY2561: $i] :
( ~ ( in @ SY2561 @ ( powerset @ SV152 ) )
| ! [SY2562: $i] :
( ~ ( in @ SY2562 @ ( powerset @ SV152 ) )
| ~ ( subset @ SY2560 @ SY2561 )
| ~ ( subset @ SY2560 @ SY2562 )
| ( subset @ SY2560 @ ( binintersect @ SY2561 @ SY2562 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(1027,plain,
! [SV153: $i] :
( ( ~ ( iskpair @ SV153 )
| ( singleton
@ ( dsetconstr @ ( setunion @ SV153 )
@ ^ [SY2563: $i] :
( SV153
= ( kpair @ ( kfst @ SV153 ) @ SY2563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(1028,plain,
! [SV154: $i] :
( ( ! [SY2564: $i] :
( ~ ( in @ SY2564 @ ( powerset @ SV154 ) )
| ! [SY2565: $i] :
( ~ ( in @ SY2565 @ ( powerset @ SV154 ) )
| ! [SY2566: $i] :
( ~ ( in @ SY2566 @ ( powerset @ SV154 ) )
| ! [SY2567: $i] :
( ~ ( in @ SY2567 @ SV154 )
| ~ ( in @ SY2567 @ ( binintersect @ SY2564 @ SY2565 ) )
| ( in @ SY2567 @ ( binunion @ SY2564 @ SY2566 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(1029,plain,
! [SV155: $i] :
( ( ! [SY2568: $i > $o] :
( ~ ~ ! [SY2569: $i] :
~ ~ ( ~ ( in @ SY2569 @ SV155 )
| ~ ( SY2568 @ SY2569 ) )
| ( ( dsetconstr @ SV155
@ ^ [SX2: $i] : ( SY2568 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(1030,plain,
! [SV156: $i] :
( ( ! [SY2571: $i] :
( ~ ( in @ SY2571 @ ( powerset @ SV156 ) )
| ! [SY2572: $i] :
( ~ ( in @ SY2572 @ ( powerset @ SV156 ) )
| ! [SY2573: $i] :
( ~ ( in @ SY2573 @ SV156 )
| ~ ( in @ SY2573 @ ( setminus @ SV156 @ SY2571 ) )
| ~ ( in @ SY2573 @ ( binintersect @ SY2571 @ SY2572 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(1031,plain,
! [SV157: $i] :
( ( ! [SY2574: $i] :
( ~ ( in @ SY2574 @ ( powerset @ SV157 ) )
| ( in @ ( powerset @ SY2574 ) @ ( powerset @ ( powerset @ SV157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(1032,plain,
! [SV158: $i] :
( ( ! [SY2575: $i,SY2576: $i] :
( ~ ( subset @ SV158 @ SY2575 )
| ~ ( subset @ SY2575 @ SY2576 )
| ( subset @ SV158 @ SY2576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(1033,plain,
! [SV159: $i] :
( ( ! [SY2577: $i > $o] :
( ~ ! [SY2578: $i] :
( ~ ( in @ SY2578 @ SV159 )
| ! [SY2579: $i] :
( ~ ( in @ SY2579 @ SV159 )
| ~ ( SY2577 @ SY2578 )
| ~ ( SY2577 @ SY2579 )
| ( SY2578 = SY2579 ) ) )
| ~ ~ ! [SY2580: $i] :
~ ~ ( ~ ( in @ SY2580 @ SV159 )
| ~ ( SY2577 @ SY2580 ) )
| ( ex1 @ SV159
@ ^ [SX2: $i] : ( SY2577 @ SX2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(1034,plain,
! [SV160: $i] :
( ( ! [SY2582: $i > $o,SY2583: $i] :
( ~ ( in @ SY2583 @ SV160 )
| ~ ( ~ ( ~ ( in @ SY2583
@ ( dsetconstr @ SV160
@ ^ [SX3: $i] : ( SY2582 @ SX3 ) ) )
| ( SY2582 @ SY2583 ) )
| ~ ( ~ ( SY2582 @ SY2583 )
| ( in @ SY2583
@ ( dsetconstr @ SV160
@ ^ [SX3: $i] : ( SY2582 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(1035,plain,
! [SV161: $i] :
( ( ! [SY2586: $i > $o,SY2587: $i] :
( ~ ( in @ SY2587 @ SV161 )
| ~ ( SY2586 @ SY2587 )
| ( ( dsetconstr @ SV161
@ ^ [SX3: $i] : ( SY2586 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(1036,plain,
! [SV162: $i] :
( ( ! [SY2589: $i,SY2590: $i] :
( ( ( setadjoin @ SV162 @ ( setadjoin @ SY2589 @ emptyset ) )
!= ( setadjoin @ SY2590 @ emptyset ) )
| ( SV162 = SY2589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(1037,plain,
! [SV163: $i] :
( ( ! [SY2591: $i,SY2592: $i,SY2593: $i] :
( ~ ( in @ ( kpair @ SY2592 @ SY2593 ) @ ( cartprod @ SV163 @ SY2591 ) )
| ( in @ SY2593 @ SY2591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(1038,plain,
! [SV164: $o] :
( ( ~ SV164
| ( set2prop @ ( prop2set @ SV164 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[737]) ).
thf(1039,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[737]) ).
thf(1040,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[737]) ).
thf(1041,plain,
! [SV165: $i] :
( ( ! [SY2594: $i,SY2595: $i] :
( ~ ( in @ SY2595 @ SV165 )
| ! [SY2596: $i] :
( ~ ( in @ SY2596 @ SY2594 )
| ( in @ ( kpair @ SY2595 @ SY2596 ) @ ( cartprod @ SV165 @ SY2594 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(1042,plain,
! [SV166: $i] :
( ( ! [SY2597: $i] :
( ~ ( in @ SY2597 @ ( powerset @ SV166 ) )
| ! [SY2598: $i] :
( ~ ( in @ SY2598 @ ( powerset @ SV166 ) )
| ( in @ ( setminus @ SV166 @ SY2597 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SY2597 @ SY2598 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(1043,plain,
! [SV167: $i] :
( ( ! [SY2599: $i,SY2600: $i] :
( ~ ( in @ SY2600 @ SV167 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2599 )
| ( ( kfst @ ( kpair @ SY2600 @ SX3 ) )
= SY2600 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(1044,plain,
! [SV168: $i] :
( ( ! [SY2602: $i > $o] :
( ~ ( ex1 @ SV168
@ ^ [SX2: $i] : ( SY2602 @ SX2 ) )
| ~ ! [SY2604: $i] :
~ ~ ( ~ ( in @ SY2604 @ SV168 )
| ~ ( SY2602 @ SY2604 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(1045,plain,
! [SV169: $i] :
( ( ! [SY2605: $i,SY2606: $i] :
~ ( ~ ( ~ ( in @ SY2606 @ ( setadjoin @ SV169 @ SY2605 ) )
| ( SY2606 = SV169 )
| ( in @ SY2606 @ SY2605 ) )
| ~ ( ~ ( ( SY2606 = SV169 )
| ( in @ SY2606 @ SY2605 ) )
| ( in @ SY2606 @ ( setadjoin @ SV169 @ SY2605 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(1046,plain,
! [SV170: $i > $i > $o] :
( ( ! [SY2607: $i] :
( ~ ! [SY2608: $i] :
( ~ ( in @ SY2608 @ SY2607 )
| ~ ! [SY2609: $i] :
~ ~ ( ~ ( SV170 @ SY2608 @ SY2609 )
| ~ ! [SY2610: $i] :
( ~ ( SV170 @ SY2608 @ SY2610 )
| ( SY2609 = SY2610 ) ) ) )
| ~ ! [SY2611: $i] :
~ ! [SY2612: $i] :
~ ( ~ ( ~ ( in @ SY2612 @ SY2611 )
| ~ ! [SY2613: $i] :
~ ~ ( ~ ( in @ SY2613 @ SY2607 )
| ~ ( SV170 @ SY2613 @ SY2612 ) ) )
| ~ ( ~ ~ ! [SY2614: $i] :
~ ~ ( ~ ( in @ SY2614 @ SY2607 )
| ~ ( SV170 @ SY2614 @ SY2612 ) )
| ( in @ SY2612 @ SY2611 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(1047,plain,
! [SV171: $i] :
( ( ! [SY2615: $i,SY2616: $i] :
( ~ ( in @ SY2615 @ SY2616 )
| ~ ( in @ SY2616 @ SV171 )
| ( in @ SY2615 @ ( setunion @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(1048,plain,
! [SV172: $i] :
( ( ! [SY2617: $i] :
( ~ ( subset @ SV172 @ SY2617 )
| ( in @ SV172 @ ( powerset @ SY2617 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(1049,plain,
! [SV173: $i] :
( ( ! [SY2618: $i,SY2619: $i] :
( ~ ( breln @ SV173 @ SY2618 @ SY2619 )
| ! [SY2620: $i > $o] :
( ~ ! [SY2621: $i] :
( ~ ( in @ SY2621 @ SV173 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2618 )
| ~ ( in @ ( kpair @ SY2621 @ SX5 ) @ SY2619 )
| ( SY2620 @ ( kpair @ SY2621 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2619 )
| ( SY2620 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(1050,plain,
! [SV174: $i] :
( ( ! [SY2624: $i,SY2625: $i,SY2626: $i] :
( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SY2624 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2625 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2625 @ ( setadjoin @ SY2626 @ emptyset ) ) @ emptyset ) ) )
| ( SV174 = SY2625 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(1051,plain,
! [SV175: $i] :
( ( ! [SY2627: $i] :
( ( SV175 != SY2627 )
| ( ( powerset @ SV175 )
= ( powerset @ SY2627 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(1052,plain,
! [SV176: $i] :
( ( ! [SY2628: $i] :
( ~ ( in @ SY2628 @ SV176 )
| ( subset @ ( setadjoin @ SY2628 @ emptyset ) @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(1053,plain,
! [SV177: $i] :
( ( ! [SY2629: $i] :
( ~ ! [SY2630: $i] :
( ~ ( in @ SY2630 @ SV177 )
| ( in @ SY2630 @ SY2629 ) )
| ~ ! [SY2631: $i] :
( ~ ( in @ SY2631 @ SY2629 )
| ( in @ SY2631 @ SV177 ) )
| ( SV177 = SY2629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(1054,plain,
! [SV178: $i] :
( ( ! [SY2632: $i,SY2633: $i] :
( ~ ( in @ SY2633 @ SY2632 )
| ( in @ SY2633 @ ( setadjoin @ SV178 @ SY2632 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(1055,plain,
! [SV179: $i] :
( ( ! [SY2634: $i,SY2635: $i,SY2636: $i] :
( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SY2634 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2635 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2635 @ ( setadjoin @ SY2636 @ emptyset ) ) @ emptyset ) ) )
| ( SY2635 != SY2636 )
| ( SY2634 = SY2636 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(1056,plain,
! [SV180: $i] :
( ( ! [SY2637: $i,SY2638: $i] :
( ~ ( in @ SY2638 @ ( funcSet @ SV180 @ SY2637 ) )
| ! [SY2639: $i] :
( ~ ( in @ SY2639 @ SV180 )
| ! [SY2640: $i] :
( ~ ( in @ SY2640 @ SY2637 )
| ~ ( in @ ( kpair @ SY2639 @ SY2640 ) @ SY2638 )
| ( ( ap @ SV180 @ SY2637 @ SY2638 @ SY2639 )
= SY2640 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(1057,plain,
! [SV181: $i] :
( ( ! [SY2641: $i,SY2642: $i] :
( ~ ( in @ SY2642 @ SV181 )
| ( in @ ( setadjoin @ SY2642 @ emptyset ) @ ( powerset @ ( binunion @ SV181 @ SY2641 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(1058,plain,
! [SV182: $i] :
( ( ~ ( singleton @ SV182 )
| ( in @ ( setunion @ SV182 ) @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(1059,plain,
! [SV183: $i] :
( ( ! [SY2643: $i] :
( ~ ( in @ SY2643 @ ( powerset @ SV183 ) )
| ! [SY2644: $i] :
( ~ ( in @ SY2644 @ ( powerset @ SV183 ) )
| ( in @ ( setminus @ SV183 @ ( binunion @ SY2643 @ SY2644 ) ) @ ( powerset @ ( setminus @ SV183 @ SY2643 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(1060,plain,
! [SV184: $i] :
( ( ~ ! [SY2645: $i] :
~ ( in @ SY2645 @ SV184 )
| ( SV184 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(1061,plain,
! [SV185: $i] :
( ( ! [SY2646: $i] :
( ~ ( breln1 @ SV185 @ SY2646 )
| ! [SY2647: $i] :
( ~ ( breln1 @ SV185 @ SY2647 )
| ~ ! [SY2648: $i] :
( ~ ( in @ SY2648 @ SV185 )
| ! [SY2649: $i] :
( ~ ( in @ SY2649 @ SV185 )
| ~ ( in @ ( kpair @ SY2648 @ SY2649 ) @ SY2646 )
| ( in @ ( kpair @ SY2648 @ SY2649 ) @ SY2647 ) ) )
| ( subset @ SY2646 @ SY2647 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(1062,plain,
! [SV186: $i] :
( ( ! [SY2650: $i,SY2651: $i] :
( ~ ( in @ SY2651 @ SV186 )
| ~ ( in @ SY2651 @ SY2650 )
| ( in @ SY2651 @ ( binintersect @ SV186 @ SY2650 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(1063,plain,
! [SV187: $i] :
( ( ! [SY2652: $i] :
( ~ ( in @ SY2652 @ ( powerset @ SV187 ) )
| ! [SY2653: $i] :
( ~ ( in @ SY2653 @ ( powerset @ SV187 ) )
| ! [SY2654: $i] :
( ~ ( in @ SY2654 @ ( powerset @ SV187 ) )
| ! [SY2655: $i] :
( ~ ( in @ SY2655 @ SV187 )
| ~ ( in @ SY2655 @ ( binintersect @ SY2652 @ SY2653 ) )
| ( in @ SY2655 @ ( binintersect @ ( binunion @ SY2652 @ SY2654 ) @ ( binunion @ SY2653 @ SY2654 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(1064,plain,
! [SV188: $i] :
( ( ! [SY2656: $i] :
( ~ ( breln1 @ SV188 @ SY2656 )
| ! [SY2657: $i] :
( ~ ( in @ SY2657 @ SV188 )
| ! [SY2658: $i] :
( ~ ( in @ SY2658 @ SV188 )
| ~ ( in @ ( kpair @ SY2658 @ SY2657 ) @ ( breln1invset @ SV188 @ SY2656 ) )
| ( in @ ( kpair @ SY2657 @ SY2658 ) @ SY2656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(1065,plain,
! [SV189: $i] :
( ( ! [SY2659: $i] :
( ~ ( in @ SY2659 @ ( setunion @ SV189 ) )
| ! [SY2660: $o] :
( ~ ! [SY2661: $i] :
( ~ ( in @ SY2659 @ SY2661 )
| ~ ( in @ SY2661 @ SV189 )
| SY2660 )
| SY2660 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(1066,plain,
! [SV190: $i] :
( ( ! [SY2662: $i] :
( ~ ( in @ SY2662 @ ( powerset @ SV190 ) )
| ( subset @ SY2662 @ ( setminus @ SV190 @ ( setminus @ SV190 @ SY2662 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(1067,plain,
! [SV191: $i] :
( ( ! [SY2663: $i,SY2664: $i] :
( ~ ( func @ SV191 @ SY2663 @ SY2664 )
| ( ( lam @ SV191 @ SY2663
@ ^ [SY2665: $i] : ( ap @ SV191 @ SY2663 @ SY2664 @ SY2665 ) )
= SY2664 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(1068,plain,
! [SV192: $i] :
( ( ! [SY2666: $i] :
( ~ ( in @ SY2666 @ ( powerset @ SV192 ) )
| ! [SY2667: $i] :
( ~ ( in @ SY2667 @ ( powerset @ SV192 ) )
| ! [SY2668: $i] :
( ~ ( in @ SY2668 @ SV192 )
| ~ ~ ( in @ SY2668 @ ( binunion @ SY2666 @ SY2667 ) )
| ~ ( in @ SY2668 @ SY2666 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(1069,plain,
! [SV193: $i] :
( ( ! [SY2669: $i] :
( ~ ( in @ SY2669 @ ( powerset @ SV193 ) )
| ! [SY2670: $i] :
( ~ ( in @ SY2670 @ ( powerset @ SV193 ) )
| ! [SY2671: $i] :
( ~ ( in @ SY2671 @ SV193 )
| ~ ( in @ SY2671 @ ( binunion @ ( setminus @ SV193 @ SY2669 ) @ ( setminus @ SV193 @ SY2670 ) ) )
| ( in @ SY2671 @ ( setminus @ SV193 @ ( binintersect @ SY2669 @ SY2670 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[766]) ).
thf(1070,plain,
! [SV194: $i] :
( ( ! [SY2672: $i] :
( ~ ( in @ SY2672 @ ( powerset @ SV194 ) )
| ! [SY2673: $i] :
( ~ ( in @ SY2673 @ ( powerset @ SV194 ) )
| ! [SY2674: $i] :
( ~ ( in @ SY2674 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SY2672 @ SY2673 ) @ ( powerset @ ( binintersect @ ( binunion @ SY2672 @ SY2674 ) @ ( binunion @ SY2673 @ SY2674 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(1071,plain,
! [SV195: $i] :
( ( ! [SY2675: $i,SY2676: $i] :
( ~ ( in @ SY2676 @ ( setadjoin @ SV195 @ SY2675 ) )
| ! [SY2677: $o] :
( ~ ( ( SY2676 != SV195 )
| SY2677 )
| ~ ( ~ ( in @ SY2676 @ SY2675 )
| SY2677 )
| SY2677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(1072,plain,
! [SV196: $i] :
( ( ! [SY2678: $i,SY2679: $i] :
( ~ ( in @ SY2679 @ ( cartprod @ SV196 @ SY2678 ) )
| ( in @ ( kfst @ SY2679 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(1073,plain,
! [SV197: $i] :
( ( ! [SY2680: $i] :
( ~ ~ ~ ! [SY2681: $i] :
~ ~ ( ~ ( in @ SY2681 @ SV197 )
| ~ ( in @ SY2681 @ SY2680 ) )
| ( ( binintersect @ SV197 @ SY2680 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(1074,plain,
! [SV198: $i] :
( ( ! [SY2682: $i] :
( ( ( setminus @ SV198 @ SY2682 )
!= emptyset )
| ( subset @ SV198 @ SY2682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(1075,plain,
! [SV199: $i] :
( ( ! [SY2683: $i] :
( ~ ( in @ SY2683 @ ( powerset @ SV199 ) )
| ! [SY2684: $i] :
( ~ ( in @ SY2684 @ ( powerset @ SV199 ) )
| ( in @ ( setminus @ SY2683 @ SY2684 ) @ ( powerset @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(1076,plain,
! [SV200: $i] :
( ( ! [SY2685: $i,SY2686: $i > $i] :
( ~ ! [SY2687: $i] :
( ~ ( in @ SY2687 @ SV200 )
| ( in @ ( SY2686 @ SY2687 ) @ SY2685 ) )
| ( in
@ ( lam @ SV200 @ SY2685
@ ^ [SX3: $i] : ( SY2686 @ SX3 ) )
@ ( funcSet @ SV200 @ SY2685 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(1077,plain,
! [SV201: $i] :
( ( ! [SY2689: $i] :
( ~ ( in @ SY2689 @ ( setunion @ SV201 ) )
| ~ ! [SY2690: $i] :
~ ~ ( ~ ( in @ SY2690 @ SV201 )
| ~ ( in @ SY2689 @ SY2690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(1078,plain,
! [SV202: $i] :
( ( ! [SY2691: $i] :
( ( SV202 != SY2691 )
| ( ( setadjoin @ SV202 @ ( setadjoin @ SY2691 @ emptyset ) )
= ( setadjoin @ SV202 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(1079,plain,
! [SV203: $i] :
( ( ! [SY2692: $i] :
( ~ ( in @ SY2692 @ ( powerset @ SV203 ) )
| ! [SY2693: $i] :
( ~ ( in @ SY2693 @ ( powerset @ SV203 ) )
| ( in @ ( binintersect @ SY2692 @ SY2693 ) @ ( powerset @ SV203 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(1080,plain,
! [SV204: $i] :
( ( ! [SY2694: $i] :
( ~ ( in @ SY2694 @ ( powerset @ SV204 ) )
| ! [SY2695: $i] :
( ~ ( in @ SY2695 @ ( powerset @ SV204 ) )
| ! [SY2696: $i] :
( ~ ( in @ SY2696 @ ( powerset @ SV204 ) )
| ! [SY2697: $i] :
( ~ ( in @ SY2697 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SY2694 @ SY2695 ) @ ( binunion @ SY2696 @ SY2697 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SY2694 ) @ ( setminus @ SV204 @ SY2695 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY2696 ) @ ( setminus @ SV204 @ SY2697 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(1081,plain,
! [SV205: $i] :
( ( ~ ( subset @ SV205 @ emptyset )
| ( SV205 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(1082,plain,
! [SV206: $i] :
( ( ! [SY2698: $i,SY2699: $i] :
( ~ ( in @ SY2699 @ ( binunion @ SV206 @ SY2698 ) )
| ( in @ SY2699 @ SV206 )
| ( in @ SY2699 @ SY2698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(1083,plain,
! [SV207: $i > $o] :
( ( ~ ~ ! [SY2700: $i] :
~ ~ ( ~ ( SV207 @ SY2700 )
| ~ ! [SY2701: $i] :
( ~ ( SV207 @ SY2701 )
| ( SY2700 = SY2701 ) ) )
| ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(1084,plain,
! [SV208: $i] :
( ( ! [SY2704: $i] :
( ~ ( in @ SY2704 @ ( breln1Set @ SV208 ) )
| ( breln1 @ SV208 @ SY2704 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(1085,plain,
! [SV209: $i] :
( ( ! [SY2705: $i] :
( ~ ( ( SV209 != SY2705 ) )
| ~ ( in @ SY2705 @ ( setadjoin @ SV209 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(1086,plain,
! [SV210: $i] :
( ( ! [SY2706: $i] :
( ~ ( subset @ SY2706 @ SV210 )
| ( in @ SY2706 @ ( powerset @ SV210 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(1087,plain,
! [SV211: $i] :
( ( ! [SY2707: $i,SY2708: $i] :
( ~ ( in @ SY2708 @ SV211 )
| ! [SY2709: $i] :
( ~ ( in @ SY2709 @ SY2707 )
| ( in @ ( setadjoin @ SY2708 @ ( setadjoin @ SY2709 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SY2707 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(1088,plain,
! [SV212: $i] :
( ( ! [SY2710: $i] :
( ~ ( breln1 @ SV212 @ SY2710 )
| ! [SY2711: $i] :
( ~ ( breln1 @ SV212 @ SY2711 )
| ( breln1 @ SV212 @ ( binunion @ SY2710 @ SY2711 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(1089,plain,
! [SV213: $i] :
( ( ! [SY2712: $i,SY2713: $i] :
( ~ ( func @ SV213 @ SY2712 @ SY2713 )
| ( in @ SY2713 @ ( funcSet @ SV213 @ SY2712 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(1090,plain,
! [SV214: $i] :
( ( ! [SY2714: $o,SY2715: $i] :
( ~ ( in @ SY2715 @ SV214 )
| ! [SY2716: $i] :
( ~ ( in @ SY2716 @ SV214 )
| ~ SY2714
| ( ( if @ SV214 @ SY2714 @ SY2715 @ SY2716 )
= SY2715 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(1091,plain,
! [SV215: $i] :
( ( ! [SY2717: $i] :
( ~ ( breln1 @ SV215 @ SY2717 )
| ! [SY2718: $i] :
( ~ ( breln1 @ SV215 @ SY2718 )
| ! [SY2719: $i] :
( ~ ( in @ SY2719 @ SV215 )
| ! [SY2720: $i] :
( ~ ( in @ SY2720 @ SV215 )
| ~ ( in @ ( kpair @ SY2719 @ SY2720 ) @ SY2717 )
| ( in @ ( kpair @ SY2719 @ SY2720 ) @ ( binunion @ SY2717 @ SY2718 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(1092,plain,
! [SV216: $i] :
( ( ! [SY2721: $i] :
( ~ ( in @ SY2721 @ ( powerset @ SV216 ) )
| ! [SY2722: $i] :
( ~ ( in @ SY2722 @ ( powerset @ SV216 ) )
| ~ ( subset @ SY2721 @ ( setminus @ SV216 @ SY2722 ) )
| ( subset @ SY2722 @ ( setminus @ SV216 @ SY2721 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(1093,plain,
! [SV217: $i] :
( ( ! [SY2723: $i,SY2724: $i > $i > $o,SY2725: $i,SY2726: $i] :
( ~ ( in @ ( kpair @ SY2725 @ SY2726 )
@ ( dpsetconstr @ SV217 @ SY2723
@ ^ [SX5: $i,SX6: $i] : ( SY2724 @ SX5 @ SX6 ) ) )
| ( in @ SY2726 @ SY2723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(1094,plain,
! [SV218: $i] :
( ( ! [SY2729: $i] :
( ~ ( in @ SY2729 @ ( powerset @ SV218 ) )
| ! [SY2730: $i] :
( ~ ( in @ SY2730 @ ( powerset @ SV218 ) )
| ( ( setminus @ SV218 @ ( binunion @ SY2729 @ SY2730 ) )
= ( binintersect @ ( setminus @ SV218 @ SY2729 ) @ ( setminus @ SV218 @ SY2730 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(1095,plain,
! [SV219: $i] :
( ( ! [SY2731: $i,SY2732: $i] :
( ~ ~ ( in @ SY2732 @ SV219 )
| ~ ~ ( in @ SY2732 @ SY2731 )
| ~ ( in @ SY2732 @ ( symdiff @ SV219 @ SY2731 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(1096,plain,
! [SV220: $i] :
( ( ! [SY2733: $i] :
( ~ ( in @ SY2733 @ ( powerset @ SV220 ) )
| ! [SY2734: $i] :
( ~ ( in @ SY2734 @ SV220 )
| ~ ( in @ SY2734 @ SY2733 )
| ~ ( in @ SY2734 @ ( setminus @ SV220 @ SY2733 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(1097,plain,
! [SV221: $i] :
( ( ! [SY2735: $i > $o] :
( ~ ~ ! [SY2736: $i] :
( ~ ( in @ SY2736 @ SV221 )
| ( SY2735 @ SY2736 ) )
| ~ ! [SY2737: $i] :
~ ~ ( ~ ( in @ SY2737 @ SV221 )
| ~ ~ ( SY2735 @ SY2737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(1098,plain,
! [SV222: $i] :
( ( ! [SY2738: $i] :
( ( SV222 != SY2738 )
| ( in @ SV222 @ ( setadjoin @ SY2738 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1099,plain,
! [SV223: $i] :
( ( ! [SY2739: $i] :
( ~ ( in @ SY2739 @ ( powerset @ SV223 ) )
| ! [SY2740: $i] :
( ~ ( in @ SY2740 @ ( powerset @ SV223 ) )
| ! [SY2741: $i] :
( ~ ( in @ SY2741 @ SV223 )
| ~ ( in @ SY2741 @ ( setminus @ SV223 @ ( binunion @ SY2739 @ SY2740 ) ) )
| ( in @ SY2741 @ ( binintersect @ ( setminus @ SV223 @ SY2739 ) @ ( setminus @ SV223 @ SY2740 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1100,plain,
! [SV224: $i] :
( ( ! [SY2742: $i,SY2743: $i] :
( ~ ( in @ SY2743 @ SY2742 )
| ~ ( in @ SY2743 @ ( setminus @ SV224 @ SY2742 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1101,plain,
! [SV225: $i] :
( ( ! [SY2744: $i,SY2745: $i] :
( ~ ( in @ SY2745 @ SV225 )
| ~ ~ ( in @ SY2745 @ SY2744 )
| ~ ( subset @ SV225 @ SY2744 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1102,plain,
! [SV226: $i] :
( ( ! [SY2746: $i,SY2747: $i] :
( ~ ( breln @ SV226 @ SY2746 @ SY2747 )
| ! [SY2748: $i] :
( ~ ( breln @ SV226 @ SY2746 @ SY2748 )
| ~ ! [SY2749: $i] :
( ~ ( in @ SY2749 @ SV226 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2746 )
| ~ ( in @ ( kpair @ SY2749 @ SX5 ) @ SY2747 )
| ( in @ ( kpair @ SY2749 @ SX5 ) @ SY2748 ) ) )
| ( subset @ SY2747 @ SY2748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1103,plain,
! [SV227: $i] :
( ( ! [SY2751: $i] :
( ~ ( in @ SY2751 @ ( powerset @ SV227 ) )
| ! [SY2752: $i] :
( ~ ( in @ SY2752 @ ( powerset @ SV227 ) )
| ( in @ ( binunion @ SY2751 @ SY2752 ) @ ( powerset @ SV227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1104,plain,
! [SV228: $i] :
( ( ! [SY2753: $i,SY2754: $i] :
( ~ ( in @ SY2753 @ ( powerset @ SV228 ) )
| ~ ( in @ SY2754 @ SY2753 )
| ( in @ SY2754 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1105,plain,
! [SV229: $i] :
( ( ! [SY2755: $i] :
( ~ ( in @ SY2755 @ ( powerset @ SV229 ) )
| ( subset @ SY2755 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1106,plain,
! [SV230: $i] :
( ( ! [SY2756: $i] :
( ~ ( subset @ SV230 @ SY2756 )
| ( ( binintersect @ SV230 @ SY2756 )
= SV230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1107,plain,
! [SV231: $i] :
( ( ! [SY2757: $i,SY2758: $i] :
( ~ ( in @ SY2758 @ SV231 )
| ! [SY2759: $i] :
( ~ ( in @ SY2759 @ SY2757 )
| ( in @ ( setadjoin @ ( setadjoin @ SY2758 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2758 @ ( setadjoin @ SY2759 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SY2757 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1108,plain,
! [SV232: $i] :
( ( ! [SY2760: $i] :
( ~ ( in @ SY2760 @ ( powerset @ SV232 ) )
| ! [SY2761: $i] :
( ~ ( in @ SY2761 @ ( powerset @ SV232 ) )
| ~ ! [SY2762: $i] :
( ~ ( in @ SY2762 @ SV232 )
| ~ ( in @ SY2762 @ SY2760 )
| ( in @ SY2762 @ SY2761 ) )
| ( subset @ SY2760 @ SY2761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1109,plain,
! [SV233: $i] :
( ( ! [SY2763: $i] :
( ~ ( in @ SY2763 @ ( powerset @ SV233 ) )
| ! [SY2764: $i] :
( ~ ( in @ SY2764 @ ( powerset @ SV233 ) )
| ~ ! [SY2765: $i] :
( ~ ( in @ SY2765 @ SV233 )
| ~ ( in @ SY2765 @ SY2763 )
| ( in @ SY2765 @ SY2764 ) )
| ( in @ SY2763 @ ( powerset @ SY2764 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1110,plain,
! [SV234: $i] :
( ( ! [SY2766: $i,SY2767: $i] :
( ~ ( in @ SY2767 @ ( setadjoin @ SV234 @ ( setadjoin @ SY2766 @ emptyset ) ) )
| ( SY2767 = SV234 )
| ( SY2767 = SY2766 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1111,plain,
! [SV235: $i] :
( ( ! [SY2768: $i] :
( ~ ( in @ SY2768 @ ( powerset @ SV235 ) )
| ! [SY2769: $i] :
( ~ ( in @ SY2769 @ SV235 )
| ~ ( in @ SY2769 @ SY2768 )
| ( in @ SY2769 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SY2768 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1112,plain,
! [SV236: $i] :
( ( ! [SY2770: $i] :
( ~ ~ ( subset @ SV236 @ SY2770 )
| ( SV236 != SY2770 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1113,plain,
! [SV237: $i] :
( ( ! [SY2771: $o,SY2772: $i] :
( ~ ( in @ SY2772 @ SV237 )
| ! [SY2773: $i] :
( ~ ( in @ SY2773 @ SV237 )
| ( in @ ( if @ SV237 @ SY2771 @ SY2772 @ SY2773 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1114,plain,
! [SV238: $i] :
( ( ! [SY2774: $i] :
( ~ ( in @ SY2774 @ ( powerset @ SV238 ) )
| ! [SY2775: $i] :
( ~ ( in @ SY2775 @ ( powerset @ SV238 ) )
| ! [SY2776: $i] :
( ~ ( in @ SY2776 @ ( powerset @ SV238 ) )
| ! [SY2777: $i] :
( ~ ( in @ SY2777 @ SV238 )
| ~ ( in @ SY2777 @ ( binintersect @ SY2774 @ SY2775 ) )
| ( in @ SY2777 @ ( binunion @ SY2775 @ SY2776 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1115,plain,
! [SV239: $i] :
( ( ! [SY2778: $i > $o,SY2779: $i] :
( ~ ( in @ SY2779
@ ( dsetconstr @ SV239
@ ^ [SX3: $i] : ( SY2778 @ SX3 ) ) )
| ( in @ SY2779 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1116,plain,
! [SV240: $i] :
( ( ! [SY2781: $i] :
( ~ ( breln1 @ SV240 @ SY2781 )
| ! [SY2782: $i] :
( ~ ( breln1 @ SV240 @ SY2782 )
| ! [SY2783: $i] :
( ~ ( in @ SY2783 @ SV240 )
| ! [SY2784: $i] :
( ~ ( in @ SY2784 @ SV240 )
| ~ ( in @ ( kpair @ SY2783 @ SY2784 ) @ ( breln1compset @ SV240 @ SY2781 @ SY2782 ) )
| ! [SY2785: $o] :
( ~ ! [SY2786: $i] :
( ~ ( in @ SY2786 @ SV240 )
| ~ ( in @ ( kpair @ SY2783 @ SY2786 ) @ SY2781 )
| ~ ( in @ ( kpair @ SY2786 @ SY2784 ) @ SY2782 )
| SY2785 )
| SY2785 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1117,plain,
! [SV241: $i] :
( ( ! [SY2787: $i] :
( ~ ( breln1 @ SV241 @ SY2787 )
| ! [SY2788: $i > $o] :
( ~ ! [SY2789: $i] :
( ~ ( in @ SY2789 @ SV241 )
| ! [SY2790: $i] :
( ~ ( in @ SY2790 @ SV241 )
| ~ ( in @ ( kpair @ SY2789 @ SY2790 ) @ SY2787 )
| ( SY2788 @ ( kpair @ SY2789 @ SY2790 ) ) ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY2787 )
| ( SY2788 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1118,plain,
! [SV242: $i] :
( ( ! [SY2792: $i] :
( ~ ( in @ SY2792 @ ( powerset @ SV242 ) )
| ! [SY2793: $i] :
( ~ ( in @ SY2793 @ ( powerset @ SV242 ) )
| ! [SY2794: $i] :
( ~ ( in @ SY2794 @ SV242 )
| ~ ( in @ SY2794 @ ( setminus @ SV242 @ ( binunion @ SY2792 @ SY2793 ) ) )
| ~ ( in @ SY2794 @ SY2792 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(1119,plain,
! [SV243: $i] :
( ( ! [SY2795: $i] :
( ~ ( in @ SY2795 @ ( powerset @ SV243 ) )
| ! [SY2796: $i] :
( ~ ( in @ SY2796 @ ( powerset @ SV243 ) )
| ! [SY2797: $i] :
( ~ ( in @ SY2797 @ SV243 )
| ~ ( in @ SY2797 @ ( setminus @ SV243 @ ( binunion @ SY2795 @ SY2796 ) ) )
| ( in @ SY2797 @ ( setminus @ SV243 @ SY2796 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(1120,plain,
! [SV244: $i] :
( ( ! [SY2798: $i,SY2799: $i] :
( ~ ( in @ SY2799 @ ( funcSet @ SV244 @ SY2798 ) )
| ( ( lam @ SV244 @ SY2798
@ ^ [SY2800: $i] : ( ap @ SV244 @ SY2798 @ SY2799 @ SY2800 ) )
= SY2799 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(1121,plain,
! [SV245: $i] :
( ( ! [SY2801: $i] :
( ~ ( in @ SY2801 @ ( powerset @ SV245 ) )
| ( in @ ( setminus @ SV245 @ SY2801 ) @ ( powerset @ SV245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1122,plain,
! [SV246: $i] :
( ( ! [SY2802: $i] :
( ( SV246 != SY2802 )
| ( ( setunion @ SV246 )
= ( setunion @ SY2802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1123,plain,
! [SV247: $i] :
( ( ! [SY2803: $i] :
( ~ ( subset @ SV247 @ SY2803 )
| ( ( setminus @ SV247 @ SY2803 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1124,plain,
! [SV248: $i] :
( ( ! [SY2804: $i] :
( ( SV248 != SY2804 )
| ( subset @ SY2804 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(1125,plain,
! [SV249: $i] :
( ( ! [SY2805: $i,SY2806: $i > $i > $o,SY2807: $i] :
( ~ ( in @ SY2807 @ SV249 )
| ! [SY2808: $i] :
( ~ ( in @ SY2808 @ SY2805 )
| ~ ( in @ ( kpair @ SY2807 @ SY2808 )
@ ( dpsetconstr @ SV249 @ SY2805
@ ^ [SX5: $i,SX6: $i] : ( SY2806 @ SX5 @ SX6 ) ) )
| ( SY2806 @ SY2807 @ SY2808 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1126,plain,
! [SV250: $i > $o] :
( ( ~ ~ ! [SY2811: $i] :
~ ! [SY2812: $i] :
~ ( ~ ( ~ ( SV250 @ SY2812 )
| ( SY2812 = SY2811 ) )
| ~ ( ( SY2812 != SY2811 )
| ( SV250 @ SY2812 ) ) )
| ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1127,plain,
! [SV251: $i] :
( ( ! [SY2815: $i,SY2816: $i] :
( ~ ( breln @ SV251 @ SY2815 @ SY2816 )
| ! [SY2817: $i] :
( ~ ( breln @ SV251 @ SY2815 @ SY2817 )
| ~ ! [SY2818: $i] :
( ~ ( in @ SY2818 @ SV251 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2815 )
| ~ ( in @ ( kpair @ SY2818 @ SX5 ) @ SY2816 )
| ( in @ ( kpair @ SY2818 @ SX5 ) @ SY2817 ) ) )
| ~ ! [SY2820: $i] :
( ~ ( in @ SY2820 @ SV251 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2815 )
| ~ ( in @ ( kpair @ SY2820 @ SX5 ) @ SY2817 )
| ( in @ ( kpair @ SY2820 @ SX5 ) @ SY2816 ) ) )
| ( SY2816 = SY2817 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1128,plain,
! [SV252: $i] :
( ( ! [SY2822: $i] :
( ~ ( in @ SY2822 @ ( powerset @ SV252 ) )
| ! [SY2823: $i] :
( ~ ( in @ SY2823 @ ( powerset @ SV252 ) )
| ! [SY2824: $i] :
( ~ ( in @ SY2824 @ SV252 )
| ~ ( subset @ SY2822 @ ( setminus @ SV252 @ SY2823 ) )
| ~ ( in @ SY2824 @ SY2823 )
| ~ ( in @ SY2824 @ SY2822 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1129,plain,
! [SV253: $i > $o] :
( ( ! [SY2825: $i] :
( ~ ( in @ SY2825 @ emptyset )
| ( SV253 @ SY2825 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1130,plain,
! [SV254: $i] :
( ( ~ ~ ! [SY2826: $i] :
~ ( in @ SY2826 @ SV254 )
| ( SV254 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1131,plain,
! [SV255: $i] :
( ( ! [SY2827: $i,SY2828: $i] :
( ~ ( in @ SY2828 @ ( setminus @ SV255 @ SY2827 ) )
| ( in @ SY2828 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1132,plain,
! [SV256: $i] :
( ( ! [SY2829: $i > $o] :
( ~ ~ ~ ! [SY2830: $i] :
~ ~ ( ~ ( in @ SY2830 @ SV256 )
| ~ ( SY2829 @ SY2830 ) )
| ! [SY2831: $i] :
( ~ ( in @ SY2831 @ SV256 )
| ~ ( SY2829 @ SY2831 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1133,plain,
! [SV257: $i] :
( ( ! [SY2832: $i] :
( ~ ( in @ SY2832 @ SV257 )
| ( in @ SY2832 @ ( powerset @ ( setunion @ SV257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1134,plain,
! [SV258: $i] :
( ( ! [SY2833: $i] :
( ~ ( breln1 @ SV258 @ SY2833 )
| ! [SY2834: $i] :
( ~ ( breln1 @ SV258 @ SY2834 )
| ! [SY2835: $i] :
( ~ ( in @ SY2835 @ SV258 )
| ! [SY2836: $i] :
( ~ ( in @ SY2836 @ SV258 )
| ! [SY2837: $i] :
( ~ ( in @ SY2837 @ SV258 )
| ~ ( in @ ( kpair @ SY2835 @ SY2837 ) @ SY2833 )
| ~ ( in @ ( kpair @ SY2837 @ SY2836 ) @ SY2834 )
| ( in @ ( kpair @ SY2835 @ SY2836 ) @ ( breln1compset @ SV258 @ SY2833 @ SY2834 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1135,plain,
! [SV259: $i] :
( ( ! [SY2838: $i] :
( ~ ( breln1 @ SV259 @ SY2838 )
| ! [SY2839: $i] :
( ~ ( breln1 @ SV259 @ SY2839 )
| ~ ! [SY2840: $i] :
( ~ ( in @ SY2840 @ SV259 )
| ! [SY2841: $i] :
( ~ ( in @ SY2841 @ SV259 )
| ~ ( in @ ( kpair @ SY2840 @ SY2841 ) @ SY2838 )
| ( in @ ( kpair @ SY2840 @ SY2841 ) @ SY2839 ) ) )
| ~ ! [SY2842: $i] :
( ~ ( in @ SY2842 @ SV259 )
| ! [SY2843: $i] :
( ~ ( in @ SY2843 @ SV259 )
| ~ ( in @ ( kpair @ SY2842 @ SY2843 ) @ SY2839 )
| ( in @ ( kpair @ SY2842 @ SY2843 ) @ SY2838 ) ) )
| ( SY2838 = SY2839 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1136,plain,
! [SV260: $i] :
( ( ! [SY2844: $i > $o,SY2845: $i] :
( ~ ( in @ SY2845
@ ( dsetconstr @ SV260
@ ^ [SX3: $i] : ( SY2844 @ SX3 ) ) )
| ( SY2844 @ SY2845 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1137,plain,
! [SV261: $i] :
( ( ! [SY2847: $i] :
( ~ ! [SY2848: $i] :
~ ( ~ ( ~ ( in @ SY2848 @ SV261 )
| ( in @ SY2848 @ SY2847 ) )
| ~ ( ~ ( in @ SY2848 @ SY2847 )
| ( in @ SY2848 @ SV261 ) ) )
| ( SV261 = SY2847 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1138,plain,
! [SV262: $i] :
( ( ! [SY2849: $i,SY2850: $i] :
( ~ ( func @ SV262 @ SY2849 @ SY2850 )
| ! [SY2851: $i] :
( ~ ( in @ SY2851 @ SV262 )
| ( singleton
@ ( dsetconstr @ SY2849
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2851 @ SX4 ) @ SY2850 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1139,plain,
! [SV263: $i > $o] :
( ( ~ ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV263 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV263 @ SY2854 )
| ( SY2853 = SY2854 ) ) )
| ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(1140,plain,
! [SV264: $i] :
( ( ! [SY2857: $i] :
( ~ ( in @ SY2857 @ ( powerset @ SV264 ) )
| ! [SY2858: $i] :
( ~ ( in @ SY2858 @ ( powerset @ SV264 ) )
| ! [SY2859: $i] :
( ~ ( in @ SY2859 @ SV264 )
| ~ ( subset @ SY2857 @ SY2858 )
| ~ ~ ( in @ SY2859 @ SY2858 )
| ~ ( in @ SY2859 @ SY2857 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1141,plain,
! [SV265: $i] :
( ( ~ ~ ! [SY2860: $i] :
~ ( in @ SY2860 @ SV265 )
| ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1142,plain,
! [SV266: $i] :
( ( ! [SY2863: $i,SY2864: $i] :
( ~ ~ ( in @ SY2864 @ SV266 )
| ~ ( in @ SY2864 @ ( setminus @ SV266 @ SY2863 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1143,plain,
! [SV267: $i] :
( ( ! [SY2865: $i,SY2866: $i,SY2867: $i] :
( ( ( kpair @ SV267 @ SY2865 )
!= ( kpair @ SY2866 @ SY2867 ) )
| ( SV267 = SY2866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1144,plain,
! [SV268: $i] :
( ( ~ ( ( SV268 != emptyset ) )
| ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1145,plain,
! [SV269: $i] :
( ( ! [SY2869: $i] :
( ~ ( in @ SY2869 @ ( powerset @ SV269 ) )
| ( subset @ ( setminus @ SV269 @ ( setminus @ SV269 @ SY2869 ) ) @ SY2869 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(1146,plain,
! [SV270: $i] :
( ( ! [SY2870: $i] :
( ~ ( in @ SV270 @ ( setadjoin @ SY2870 @ emptyset ) )
| ( SV270 = SY2870 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1147,plain,
! [SV271: $i] :
( ( ~ ( iskpair @ SV271 )
| ( ( kpair @ ( kfst @ SV271 ) @ ( ksnd @ SV271 ) )
= SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1148,plain,
! [SV272: $i] :
( ( ! [SY2871: $i] :
( ~ ( in @ SY2871 @ ( powerset @ SV272 ) )
| ! [SY2872: $i] :
( ~ ( in @ SY2872 @ ( powerset @ SV272 ) )
| ~ ( subset @ SY2871 @ SY2872 )
| ( subset @ ( setminus @ SV272 @ SY2872 ) @ ( setminus @ SV272 @ SY2871 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1149,plain,
! [SV273: $i] :
( ( ! [SY2873: $i,SY2874: $i] :
( ~ ( in @ SY2874 @ SV273 )
| ! [SY2875: $i] :
( ~ ( in @ SY2875 @ SY2873 )
| ( in @ ( kpair @ SY2874 @ SY2875 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SY2873 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1150,plain,
! [SV274: $i] :
( ( ! [SY2876: $i,SY2877: $i] :
( ~ ( func @ SV274 @ SY2876 @ SY2877 )
| ! [SY2878: $i] :
( ~ ( in @ SY2878 @ SV274 )
| ( ( ap @ SV274 @ SY2876 @ SY2877 @ SY2878 )
= ( ap @ SV274 @ SY2876 @ SY2877 @ SY2878 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1151,plain,
! [SV275: $i] :
( ( ! [SY2879: $i] :
( ~ ( in @ SY2879 @ ( powerset @ SV275 ) )
| ! [SY2880: $i] :
( ~ ( in @ SY2880 @ ( powerset @ SV275 ) )
| ! [SY2881: $i] :
( ~ ( in @ SY2881 @ SV275 )
| ~ ( in @ SY2881 @ ( setminus @ SV275 @ SY2879 ) )
| ~ ( in @ SY2881 @ ( setminus @ SV275 @ SY2880 ) )
| ( in @ SY2881 @ ( setminus @ SV275 @ ( binunion @ SY2879 @ SY2880 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(1152,plain,
! [SV276: $i] :
( ( ! [SY2882: $i,SY2883: $i] :
( ~ ( func @ SV276 @ SY2882 @ SY2883 )
| ! [SY2884: $i] :
( ~ ( in @ SY2884 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY2882
@ ^ [SX4: $i] : ( in @ ( kpair @ SY2884 @ SX4 ) @ SY2883 ) ) )
@ SY2882 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(1153,plain,
! [SV277: $i] :
( ( ! [SY2886: $i,SY2887: $i] :
( ~ ( in @ SY2887 @ ( funcSet @ SV277 @ SY2886 ) )
| ! [SY2888: $i] :
( ~ ( in @ SY2888 @ SV277 )
| ( in @ ( kpair @ SY2888 @ ( ap @ SV277 @ SY2886 @ SY2887 @ SY2888 ) ) @ SY2887 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(1154,plain,
! [SV278: $i] :
( ( ! [SY2889: $i > $o] :
( ~ ~ ! [SY2890: $i] :
~ ~ ( ~ ( in @ SY2890 @ SV278 )
| ~ ~ ( SY2889 @ SY2890 ) )
| ~ ! [SY2891: $i] :
( ~ ( in @ SY2891 @ SV278 )
| ( SY2889 @ SY2891 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(1155,plain,
! [SV279: $i] :
( ( ! [SY2892: $i] :
( ~ ( breln1 @ SV279 @ SY2892 )
| ! [SY2893: $i] :
( ~ ( in @ SY2893 @ SV279 )
| ! [SY2894: $i] :
( ~ ( in @ SY2894 @ SV279 )
| ~ ( in @ ( kpair @ SY2893 @ SY2894 ) @ SY2892 )
| ( in @ ( kpair @ SY2894 @ SY2893 ) @ ( breln1invset @ SV279 @ SY2892 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1156,plain,
! [SV280: $i] :
( ( ! [SY2895: $i,SY2896: $i > $i] :
( ~ ! [SY2897: $i] :
( ~ ( in @ SY2897 @ SV280 )
| ( in @ ( SY2896 @ SY2897 ) @ SY2895 ) )
| ! [SY2898: $i] :
( ~ ( in @ SY2898 @ SV280 )
| ( ( ap @ SV280 @ SY2895
@ ( lam @ SV280 @ SY2895
@ ^ [SX4: $i] : ( SY2896 @ SX4 ) )
@ SY2898 )
= ( SY2896 @ SY2898 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(1157,plain,
! [SV281: $i] :
( ( ! [SY2900: $i,SY2901: $i,SY2902: $i] :
( ~ ( in @ ( kpair @ SY2901 @ SY2902 ) @ ( cartprod @ SV281 @ SY2900 ) )
| ( in @ SY2901 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1158,plain,
! [SV282: $i] :
( ( ! [SY2903: $i,SY2904: $i > $i] :
( ~ ! [SY2905: $i] :
( ~ ( in @ SY2905 @ SV282 )
| ( in @ ( SY2904 @ SY2905 ) @ SY2903 ) )
| ( ( lam @ SV282 @ SY2903
@ ^ [SX3: $i] : ( SY2904 @ SX3 ) )
= ( lam @ SV282 @ SY2903
@ ^ [SX3: $i] : ( SY2904 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1159,plain,
! [SV283: $i] :
( ( ! [SY2908: $i] :
( ~ ( in @ SY2908 @ ( powerset @ SV283 ) )
| ! [SY2909: $i] :
( ~ ( in @ SY2909 @ ( powerset @ SV283 ) )
| ( in @ ( setminus @ SV283 @ SY2908 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SY2908 @ SY2909 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(1160,plain,
! [SV284: $i] :
( ( ~ ( ( SV284 != emptyset ) )
| ~ ! [SY2910: $i] :
~ ~ ( ~ ( in @ SY2910 @ SV284 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1161,plain,
! [SV285: $i] :
( ( ! [SY2911: $i,SY2912: $i] :
( ~ ( in @ SY2912 @ SV285 )
| ~ ~ ( in @ SY2912 @ SY2911 )
| ( SV285 != SY2911 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(1162,plain,
! [SV286: $i] :
( ( ! [SY2913: $i,SY2914: $i] :
( ~ ~ ( in @ SY2914 @ ( setminus @ SV286 @ SY2913 ) )
| ~ ( in @ SY2914 @ SV286 )
| ( in @ SY2914 @ SY2913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1163,plain,
! [SV287: $i] :
( ( ! [SY2915: $i,SY2916: $i] :
( ~ ( func @ SV287 @ SY2915 @ SY2916 )
| ! [SY2917: $i] :
( ~ ( in @ SY2917 @ SV287 )
| ! [SY2918: $i] :
( ~ ( in @ SY2918 @ SY2915 )
| ~ ( in @ ( kpair @ SY2917 @ SY2918 ) @ SY2916 )
| ( ( ap @ SV287 @ SY2915 @ SY2916 @ SY2917 )
= SY2918 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(1164,plain,
! [SV288: $i] :
( ( ! [SY2919: $o,SY2920: $i] :
( ~ ( in @ SY2920 @ SV288 )
| ! [SY2921: $i] :
( ~ ( in @ SY2921 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SX4: $i] :
( ~ ( ~ SY2919
| ( SX4 != SY2920 ) )
| ~ ( ~ ~ SY2919
| ( SX4 != SY2921 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1165,plain,
! [SV289: $i] :
( ( ! [SY2923: $i,SY2924: $i] :
( ~ ( in @ SY2924 @ ( cartprod @ SV289 @ SY2923 ) )
| ( ( kpair @ ( kfst @ SY2924 ) @ ( ksnd @ SY2924 ) )
= SY2924 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1166,plain,
! [SV290: $i] :
( ( ! [SY2925: $i,SY2926: $i] :
( ~ ( in @ SY2926 @ ( setadjoin @ SV290 @ ( setadjoin @ SY2925 @ emptyset ) ) )
| ( SY2926 = SV290 )
| ( SY2926 = SY2925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(1167,plain,
! [SV291: $i > $o] :
( ( ~ ~ ! [SY2927: $i] :
~ ~ ( ~ ( SV291 @ SY2927 )
| ~ ! [SY2928: $i] :
( ~ ( SV291 @ SY2928 )
| ( SY2927 = SY2928 ) ) )
| ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1168,plain,
! [SV292: $i] :
( ( ! [SY2930: $i] :
( ~ ( in @ SV292 @ ( setadjoin @ SY2930 @ emptyset ) )
| ( in @ SY2930 @ ( setadjoin @ SV292 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1169,plain,
! [SV293: $i] :
( ( ! [SY2931: $i] :
( ( SV293 != SY2931 )
| ( ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV293 @ ( setadjoin @ SY2931 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[866]) ).
thf(1170,plain,
! [SV294: $i] :
( ( ! [SY2932: $i,SY2933: $i] :
( ~ ( in @ SY2933 @ SV294 )
| ~ ~ ( in @ SY2933 @ SY2932 )
| ( in @ SY2933 @ ( setminus @ SV294 @ SY2932 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(1171,plain,
! [SV295: $i] :
( ( ~ ( in @ SV295 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1172,plain,
! [SV296: $i] :
( ( ! [SY2935: $o,SY2936: $i] :
( ~ ( in @ SY2936 @ SV296 )
| ! [SY2937: $i] :
( ~ ( in @ SY2937 @ SV296 )
| ~ SY2935
| ( ( dsetconstr @ SV296
@ ^ [SX4: $i] :
( ~ ( ~ SY2935
| ( SX4 != SY2936 ) )
| ~ ( ~ ~ SY2935
| ( SX4 != SY2937 ) ) ) )
= ( setadjoin @ SY2936 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1173,plain,
! [SV297: $i > $i > $o,SV1: $i] :
( ( breln1 @ SV1
@ ( dpsetconstr @ SV1 @ SV1
@ ^ [SY2939: $i,SY2940: $i] : ( SV297 @ SY2939 @ SY2940 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1174,plain,
! [SV298: $i,SV2: $i] :
( ( ! [SY2941: $i > $i > $o] :
( breln @ SV2 @ SV298
@ ( dpsetconstr @ SV2 @ SV298
@ ^ [Xx: $i,Xy: $i] : ( SY2941 @ Xx @ Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1175,plain,
! [SV299: $i,SV3: $i] :
( ( ! [SY2944: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV3 @ SV299
@ ^ [Xx: $i,Xy: $i] : ( SY2944 @ Xx @ Xy ) )
@ ( cartprod @ SV3 @ SV299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1176,plain,
! [SV300: $i,SV4: $i] :
( ( ( ksnd @ ( kpair @ SV4 @ SV300 ) )
= SV300 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[873]) ).
thf(1177,plain,
! [SV301: $i,SV5: $i] :
( ( ( kfst @ ( kpair @ SV5 @ SV301 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1178,plain,
! [SV302: $i,SV9: $i] :
( ( iskpair @ ( kpair @ SV9 @ SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1179,plain,
! [SV303: $i,SV10: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV10 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV10 @ ( setadjoin @ SV303 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(1180,plain,
! [SV11: $i,SV304: $i] :
( ( in @ SV304 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV11 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV11 @ ( setadjoin @ SV304 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1181,plain,
! [SV305: $i,SV12: $i] :
( ( in @ SV12 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV305 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1182,plain,
! [SV13: $i,SV306: $i] :
( ( in @ SV306 @ ( setadjoin @ SV13 @ ( setadjoin @ SV306 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1183,plain,
! [SV307: $i,SV14: $i] :
( ( subset @ ( setminus @ SV14 @ SV307 ) @ SV14 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(1184,plain,
! [SV308: $i,SV15: $i] :
( ( ! [SY2947: $i] :
( ( binintersect @ SV15 @ ( binunion @ SV308 @ SY2947 ) )
= ( binunion @ ( binintersect @ SV15 @ SV308 ) @ ( binintersect @ SV15 @ SY2947 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(1185,plain,
! [SV309: $i,SV16: $i] :
( ( subset @ ( binintersect @ SV16 @ SV309 ) @ SV309 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(1186,plain,
! [SV310: $i,SV17: $i] :
( ( subset @ ( binintersect @ SV17 @ SV310 ) @ SV17 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1187,plain,
! [SV18: $i,SV311: $i] :
( ( subset @ SV311 @ ( binunion @ SV18 @ SV311 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(1188,plain,
! [SV312: $i,SV19: $i] :
( ( subset @ SV19 @ ( binunion @ SV19 @ SV312 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(1189,plain,
! [SV20: $i,SV313: $i] :
( ( in @ SV313 @ ( setadjoin @ SV20 @ ( setadjoin @ SV313 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1190,plain,
! [SV314: $i > $o,SV21: $i] :
( ( subset
@ ( dsetconstr @ SV21
@ ^ [SY2948: $i] : ( SV314 @ SY2948 ) )
@ SV21 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(1191,plain,
! [SV315: $i > $o,SV22: $i] :
( ( in
@ ( dsetconstr @ SV22
@ ^ [SY2949: $i] : ( SV315 @ SY2949 ) )
@ ( powerset @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1192,plain,
! [SV24: $i,SV316: $i] :
( ( subset @ SV316 @ ( setadjoin @ SV24 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1193,plain,
! [SV27: $i,SV317: $i] :
( ( in @ SV317 @ ( setadjoin @ SV27 @ ( setadjoin @ SV317 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(1194,plain,
! [SV318: $i,SV28: $i] :
( ( in @ SV28 @ ( setadjoin @ SV28 @ ( setadjoin @ SV318 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(1195,plain,
! [SV319: $i,SV32: $i] :
( ( in @ SV32 @ ( setadjoin @ SV32 @ SV319 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(1196,plain,
! [SV33: $i] :
( ( in @ SV33 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(1197,plain,
! [SV34: $i] :
( ( in @ SV34 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(1198,plain,
! [SV35: $i,SV320: $i] :
( ( ~ ( in @ SV320 @ ( powerset @ SV35 ) )
| ! [SY2950: $i] :
( ~ ( in @ SY2950 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SY2950 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SY2950 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[904]) ).
thf(1199,plain,
! [SV321: $i,SV36: $i] :
( ( ! [SY2951: $i] :
( ~ ( in @ SY2951 @ ( setminus @ SV36 @ SV321 ) )
| ~ ( in @ SY2951 @ SV321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(1200,plain,
! [SV37: $i,SV322: $i] :
( ( ~ ( in @ SV322 @ ( powerset @ SV37 ) )
| ! [SY2952: $i] :
( ~ ( in @ SY2952 @ ( powerset @ SV37 ) )
| ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( powerset @ SV37 ) )
| ! [SY2954: $i] :
( ~ ( in @ SY2954 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY2953 )
| ~ ( subset @ SY2952 @ SY2954 )
| ( subset @ ( binintersect @ SV322 @ SY2952 ) @ ( binintersect @ SY2953 @ SY2954 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(1201,plain,
! [SV38: $i > $o] :
( ( ( ~ ~ ! [SY2204: $i] :
~ ~ ( ~ ( SV38 @ SY2204 )
| ~ ! [SY2205: $i] :
( ~ ( SV38 @ SY2205 )
| ( SY2204 = SY2205 ) ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1202,plain,
! [SV323: $i,SV39: $i] :
( ( ~ ( subset @ SV39 @ SV323 )
| ( subset @ ( powerset @ SV39 ) @ ( powerset @ SV323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1203,plain,
! [SV324: $i,SV40: $i] :
( ( ~ ( breln1 @ SV40 @ SV324 )
| ! [SY2955: $i] :
( ~ ( breln1 @ SV40 @ SY2955 )
| ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SY2955 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[909]) ).
thf(1204,plain,
! [SV325: $i,SV41: $i] :
( ( ! [SY2956: $i] :
( ~ ( subset @ SV41 @ SV325 )
| ~ ~ ( in @ SY2956 @ SV325 )
| ~ ( in @ SY2956 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(1205,plain,
! [SV326: $i,SV42: $i] :
( ( ! [SY2957: $i] :
( ~ ( in @ SY2957 @ SV42 )
| ! [SY2958: $i] :
( ~ ( in @ SY2958 @ SV326 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY2957 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2957 @ ( setadjoin @ SY2958 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1206,plain,
! [SV327: $i,SV43: $i] :
( ( ! [SY2959: $i] :
( ~ ( in @ SY2959 @ ( binintersect @ SV43 @ SV327 ) )
| ( in @ SY2959 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[912]) ).
thf(1207,plain,
! [SV328: $i,SV44: $i] :
( ( ( SV44 != SV328 )
| ! [SY2960: $i > $o,SY2961: $i > $o] :
( ~ ! [SY2962: $i] :
( ~ ( in @ SY2962 @ SV44 )
| ! [SY2963: $i] :
( ~ ( in @ SY2963 @ SV328 )
| ( SY2962 != SY2963 )
| ~ ( ~ ( ~ ( SY2960 @ SY2962 )
| ( SY2961 @ SY2963 ) )
| ~ ( ~ ( SY2961 @ SY2963 )
| ( SY2960 @ SY2962 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SX4: $i] : ( SY2960 @ SX4 ) )
= ( dsetconstr @ SV328
@ ^ [SX4: $i] : ( SY2961 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(1208,plain,
! [SV45: $i] :
( ( ! [SY2224: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY2225: $i] :
( ~ ( in @ SY2225 @ SY2224 )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY2225 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY2227: $i,SY2228: $i] :
( ~ ~ ( ~ ( in @ SY2227 @ SV45 )
| ~ ( in @ SY2228 @ SV45 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY2224 )
| ~ ( ~ ( ~ ( in @ SY2227 @ SX4 )
| ( in @ SY2228 @ SX4 ) )
| ~ ( ~ ( in @ SY2228 @ SX4 )
| ( in @ SY2227 @ SX4 ) ) ) )
| ( SY2227 = SY2228 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY2224 )
| ~ ( in @ SX3 @ SY2224 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY2234: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY2234 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY2234 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY2224 )
| ~ ( in @ SX4 @ SY2234 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY2234 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY2224 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(1209,plain,
! [SV329: $i > $o,SV46: $i] :
( ( ~ ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
| ! [SY2967: $i] :
( ~ ( in @ SY2967 @ SV46 )
| ! [SY2968: $i] :
( ~ ( in @ SY2968 @ SV46 )
| ~ ( SV329 @ SY2967 )
| ~ ( SV329 @ SY2968 )
| ( SY2967 = SY2968 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(1210,plain,
! [SV47: $o] :
( ( ( ~ SV47 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1211,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1212,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1213,plain,
! [SV48: $i,SV330: $i] :
( ( ~ ( in @ SV330 @ SV48 )
| ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1214,plain,
! [SV331: $i,SV49: $i] :
( ( ! [SY2969: $i > $i] :
( ~ ! [SY2970: $i] :
( ~ ( in @ SY2970 @ SV49 )
| ( in @ ( SY2969 @ SY2970 ) @ SV331 ) )
| ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SX3: $i] : ( SY2969 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(1215,plain,
! [SV50: $i] :
( ( ( ~ ( singleton @ SV50 ) )
= $true )
| ( ( ! [SY2251: $i] :
( ~ ( in @ SY2251 @ SV50 )
| ( ( setunion @ SV50 )
= SY2251 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1216,plain,
! [SV332: $i,SV51: $i] :
( ( ~ ! [SY2972: $i] :
( ~ ( in @ SY2972 @ SV51 )
| ( in @ SY2972 @ SV332 ) )
| ( subset @ SV51 @ SV332 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1217,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) ) )
= $true )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1218,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ( ~ ( ~ ( in @ SV333 @ ( setunion @ SV53 ) )
| ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
| ~ ( ~ ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) )
| ( in @ SV333 @ ( setunion @ SV53 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1219,plain,
! [SV334: $i > $o,SV54: $i] :
( ( ! [SY2975: $i] :
( ~ ( in @ SY2975 @ SV54 )
| ~ ( SV334 @ SY2975 )
| ~ ! [SY2976: $i] :
( ~ ( in @ SY2976 @ SV54 )
| ~ ( SV334 @ SY2976 )
| ( SY2976 = SY2975 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[925]) ).
thf(1220,plain,
! [SV335: $i,SV55: $i] :
( ( ! [SY2978: $i > $i] :
( ~ ! [SY2979: $i] :
( ~ ( in @ SY2979 @ SV55 )
| ( in @ ( SY2978 @ SY2979 ) @ SV335 ) )
| ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SX3: $i,SX4: $i] :
( ( SY2978 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1221,plain,
! [SV336: $i,SV56: $i] :
( ( ! [SY2982: $i] :
( ~ ( in @ SY2982 @ ( funcSet @ SV56 @ SV336 ) )
| ! [SY2983: $i] :
( ~ ( in @ SY2983 @ SV56 )
| ( ( ap @ SV56 @ SV336 @ SY2982 @ SY2983 )
= ( ap @ SV56 @ SV336 @ SY2982 @ SY2983 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[927]) ).
thf(1222,plain,
! [SV57: $i,SV337: $i] :
( ( ~ ( in @ SV337 @ ( powerset @ SV57 ) )
| ! [SY2984: $i] :
( ~ ( in @ SY2984 @ ( powerset @ SV57 ) )
| ! [SY2985: $i] :
( ~ ( in @ SY2985 @ SV57 )
| ~ ( in @ SY2985 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SY2984 ) ) )
| ( in @ SY2985 @ ( setminus @ SV57 @ SV337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1223,plain,
! [SV338: $i,SV58: $i] :
( ( ! [SY2986: $i,SY2987: $i] :
( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV338 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY2986 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY2986 @ ( setadjoin @ SY2987 @ emptyset ) ) @ emptyset ) ) )
| ( SV338 = SY2987 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1224,plain,
! [SV59: $i,SV339: $i] :
( ( ~ ( in @ SV339 @ ( powerset @ SV59 ) )
| ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV59 )
| ~ ~ ( in @ SY2988 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SY2988 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[930]) ).
thf(1225,plain,
! [SV60: $i,SV340: $i] :
( ( ~ ( in @ SV340 @ ( powerset @ SV60 ) )
| ( SV340
= ( setminus @ SV60 @ ( setminus @ SV60 @ SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1226,plain,
! [SV341: $i,SV61: $i] :
( ( ! [SY2989: $i] :
( ~ ( in @ SY2989 @ ( funcSet @ SV61 @ SV341 ) )
| ! [SY2990: $i] :
( ~ ( in @ SY2990 @ ( funcSet @ SV61 @ SV341 ) )
| ~ ! [SY2991: $i] :
( ~ ( in @ SY2991 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SY2989 @ SY2991 )
= ( ap @ SV61 @ SV341 @ SY2990 @ SY2991 ) ) )
| ( SY2989 = SY2990 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1227,plain,
! [SV62: $i,SV342: $i] :
( ( ~ ( in @ SV342 @ ( powerset @ SV62 ) )
| ! [SY2992: $i] :
( ~ ( in @ SY2992 @ ( powerset @ SV62 ) )
| ~ ( subset @ SV342 @ ( setminus @ SV62 @ SY2992 ) )
| ( subset @ SY2992 @ ( setminus @ SV62 @ SV342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1228,plain,
! [SV63: $i,SV343: $i] :
( ( ~ ( in @ SV343 @ ( powerset @ SV63 ) )
| ! [SY2993: $i] :
( ~ ( in @ SY2993 @ ( powerset @ SV63 ) )
| ! [SY2994: $i] :
( ~ ( in @ SY2994 @ SV63 )
| ~ ~ ( in @ SY2994 @ ( binunion @ SV343 @ SY2993 ) )
| ~ ( in @ SY2994 @ SY2993 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1229,plain,
! [SV64: $i,SV344: $i] :
( ( ~ ( in @ SV344 @ ( powerset @ SV64 ) )
| ! [SY2995: $i] :
( ~ ( in @ SY2995 @ ( powerset @ SV64 ) )
| ! [SY2996: $i] :
( ~ ( in @ SY2996 @ ( powerset @ SV64 ) )
| ~ ( subset @ SY2995 @ SY2996 )
| ( subset @ ( binintersect @ SV344 @ SY2995 ) @ SY2996 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1230,plain,
! [SV65: $i,SV345: $i] :
( ( ~ ( in @ SV345 @ ( powerset @ SV65 ) )
| ! [SY2997: $i] :
( ~ ( in @ SY2997 @ ( powerset @ SV65 ) )
| ! [SY2998: $i] :
( ~ ( in @ SY2998 @ SV65 )
| ~ ~ ( in @ SY2998 @ SY2997 )
| ~ ( in @ SY2998 @ ( binintersect @ SV345 @ SY2997 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1231,plain,
! [SV66: $i,SV346: $i] :
( ( ~ ( in @ SV346 @ ( powerset @ SV66 ) )
| ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV66 )
| ~ ( in @ SY2999 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SY2999 @ SV346 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[937]) ).
thf(1232,plain,
! [SV67: $i,SV347: $i] :
( ( ~ ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV347 )
| ( in @ SY3000 @ SV67 ) )
| ( in @ SV347 @ ( powerset @ SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1233,plain,
! [SV348: $i,SV68: $i] :
( ( ~ ( breln1 @ SV68 @ SV348 )
| ! [SY3001: $i] :
( ~ ( breln1 @ SV68 @ SY3001 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV68 )
| ! [SY3003: $i] :
( ~ ( in @ SY3003 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3003 ) @ ( breln1compset @ SV68 @ SV348 @ SY3001 ) )
| ~ ! [SY3004: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3004 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3004 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3004 @ SY3003 ) @ SY3001 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[939]) ).
thf(1234,plain,
! [SV69: $i,SV349: $i] :
( ( ~ ( in @ SV349 @ ( powerset @ SV69 ) )
| ! [SY3005: $i] :
( ~ ( in @ SY3005 @ ( powerset @ SV69 ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV69 )
| ~ ( in @ SY3006 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SY3005 ) ) )
| ( in @ SY3006 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SY3005 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1235,plain,
! [SV350: $i,SV70: $i] :
( ( ! [SY3007: $i > $i] :
( ~ ! [SY3008: $i] :
( ~ ( in @ SY3008 @ SV70 )
| ( in @ ( SY3007 @ SY3008 ) @ SV350 ) )
| ! [SY3009: $i] :
( ~ ( in @ SY3009 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SX4: $i] : ( SY3007 @ SX4 ) )
@ SY3009 )
= ( SY3007 @ SY3009 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1236,plain,
! [SV351: $i,SV71: $i] :
( ( ! [SY3011: $i > $i > $o,SY3012: $i] :
( ~ ( in @ SY3012 @ SV71 )
| ! [SY3013: $i] :
( ~ ( in @ SY3013 @ SV351 )
| ~ ( SY3011 @ SY3012 @ SY3013 )
| ( in @ ( kpair @ SY3012 @ SY3013 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SX5: $i,SX6: $i] : ( SY3011 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1237,plain,
! [SV352: $i,SV72: $i] :
( ( ! [SY3016: $i] :
( ~ ( in @ SY3016 @ ( funcSet @ SV72 @ SV352 ) )
| ! [SY3017: $i] :
( ~ ( in @ SY3017 @ SV72 )
| ( in @ ( ap @ SV72 @ SV352 @ SY3016 @ SY3017 ) @ SV352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1238,plain,
! [SV353: $i,SV73: $i] :
( ( ! [SY3018: $i > $i > $o,SY3019: $i,SY3020: $i] :
( ~ ( in @ ( kpair @ SY3019 @ SY3020 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SX5: $i,SX6: $i] : ( SY3018 @ SX5 @ SX6 ) ) )
| ( SY3018 @ SY3019 @ SY3020 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[944]) ).
thf(1239,plain,
! [SV354: $i,SV74: $i] :
( ( ! [SY3023: $i > $i > $o] :
( ~ ! [SY3024: $i] :
( ~ ( in @ SY3024 @ SV74 )
| ~ ! [SY3025: $i] :
~ ~ ( ~ ( in @ SY3025 @ SV354 )
| ~ ( SY3023 @ SY3024 @ SY3025 ) ) )
| ! [SY3026: $i] :
( ~ ( in @ SY3026 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3026 )
| ! [SY3027: $i] :
( ~ ( in @ SY3027 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3028: $i] :
~ ( ~ ( SY3023 @ SY3027 @ SY3028 )
| ~ ! [SY3029: $i] :
( ~ ( in @ SY3029 @ SV354 )
| ~ ( SY3023 @ SY3027 @ SY3029 )
| ( in @ ( kpair @ SY3028 @ SY3029 ) @ SY3026 ) ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(1240,plain,
! [SV355: $i,SV75: $i] :
( ( ! [SY3030: $i] :
( ~ ( func @ SV75 @ SV355 @ SY3030 )
| ! [SY3031: $i] :
( ~ ( in @ SY3031 @ SV75 )
| ( in @ ( kpair @ SY3031 @ ( ap @ SV75 @ SV355 @ SY3030 @ SY3031 ) ) @ SY3030 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1241,plain,
! [SV356: $i > $o,SV76: $i] :
( ( ~ ~ ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV76 )
| ( SV356 @ SY3032 ) )
| ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[947]) ).
thf(1242,plain,
! [SV357: $i,SV77: $i] :
( ( ! [SY3034: $i] :
( ~ ( subset @ SV77 @ SV357 )
| ~ ( in @ SY3034 @ SV77 )
| ( in @ SY3034 @ SV357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1243,plain,
( ( ! [SY3035: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY3035 )
| ! [SY3036: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY3036 )
| ! [SY3037: $i] :
( ~ ( in @ SY3037 @ sK1_SX0 )
| ! [SY3038: $i] :
( ~ ( in @ SY3038 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY3037 @ SY3038 ) @ SY3036 )
| ( in @ ( kpair @ SY3037 @ SY3038 ) @ ( binunion @ SY3035 @ SY3036 ) ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[949]) ).
thf(1244,plain,
! [SV358: $i,SV78: $i] :
( ( ( SV78 != SV358 )
| ! [SY3039: $i,SY3040: $i] :
( ( SY3039 != SY3040 )
| ~ ( in @ SY3039 @ SV78 )
| ( in @ SY3040 @ SV358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1245,plain,
! [SV359: $i,SV79: $i] :
( ( ~ ( subset @ SV79 @ SV359 )
| ~ ( subset @ SV359 @ SV79 )
| ( SV79 = SV359 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[951]) ).
thf(1246,plain,
! [SV360: $i,SV80: $i] :
( ( ! [SY3041: $i,SY3042: $i] :
( ( ( kpair @ SV80 @ SV360 )
!= ( kpair @ SY3041 @ SY3042 ) )
| ( SV360 = SY3042 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1247,plain,
! [SV361: $i,SV81: $i] :
( ( ! [SY3043: $i] :
( ~ ( func @ SV81 @ SV361 @ SY3043 )
| ! [SY3044: $i] :
( ~ ( func @ SV81 @ SV361 @ SY3044 )
| ~ ! [SY3045: $i] :
( ~ ( in @ SY3045 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SY3043 @ SY3045 )
= ( ap @ SV81 @ SV361 @ SY3044 @ SY3045 ) ) )
| ! [SY3046: $i] :
( ~ ( in @ SY3046 @ SV81 )
| ! [SY3047: $i] :
( ~ ( in @ SY3047 @ SV361 )
| ~ ( in @ ( kpair @ SY3046 @ SY3047 ) @ SY3044 )
| ( in @ ( kpair @ SY3046 @ SY3047 ) @ SY3043 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[953]) ).
thf(1248,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ( ~ ( ~ ( in @ SV362 @ ( powerset @ SV82 ) )
| ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) )
| ~ ( ~ ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) )
| ( in @ SV362 @ ( powerset @ SV82 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1249,plain,
! [SV363: $i,SV83: $i] :
( ( ( SV83 != SV363 )
| ! [SY3050: $i,SY3051: $i] :
( ( SY3050 != SY3051 )
| ~ ( ~ ( ~ ( in @ SY3050 @ SV83 )
| ( in @ SY3051 @ SV363 ) )
| ~ ( ~ ( in @ SY3051 @ SV363 )
| ( in @ SY3050 @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1250,plain,
! [SV364: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SV364 @ emptyset ) )
| ( SV84 = SV364 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[956]) ).
thf(1251,plain,
! [SV85: $i,SV365: $i] :
( ( ~ ( in @ SV365 @ ( powerset @ SV85 ) )
| ! [SY3052: $i] :
( ~ ( in @ SY3052 @ ( powerset @ SV85 ) )
| ! [SY3053: $o,SY3054: $i] :
( ~ ( in @ SY3054 @ SV85 )
| ~ ( in @ SY3054 @ ( binunion @ SV365 @ SY3052 ) )
| ~ ( ~ ( in @ SY3054 @ SV365 )
| SY3053 )
| ~ ( ~ ( in @ SY3054 @ SY3052 )
| SY3053 )
| SY3053 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1252,plain,
! [SV366: $i,SV86: $i] :
( ( ! [SY3055: $i,SY3056: $o] :
( ~ ( in @ SY3055 @ ( binunion @ SV86 @ SV366 ) )
| ~ ( ~ ( in @ SY3055 @ SV86 )
| SY3056 )
| ~ ( ~ ( in @ SY3055 @ SV366 )
| SY3056 )
| SY3056 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1253,plain,
! [SV367: $i,SV87: $i] :
( ( ! [SY3057: $i] :
( ~ ( in @ SY3057 @ SV87 )
| ~ ( in @ SY3057 @ SV367 )
| ~ ( in @ SY3057 @ ( symdiff @ SV87 @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1254,plain,
! [SV368: $i,SV88: $i] :
( ( ! [SY3058: $i] :
( ~ ( in @ SY3058 @ ( cartprod @ SV88 @ SV368 ) )
| ( in @ ( ksnd @ SY3058 ) @ SV368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[960]) ).
thf(1255,plain,
! [SV369: $i,SV89: $i] :
( ( ! [SY3059: $i] :
( ~ ( in @ SY3059 @ SV89 )
| ! [SY3060: $i] :
( ~ ( in @ SY3060 @ SV369 )
| ( ( ksnd @ ( kpair @ SY3059 @ SY3060 ) )
= SY3060 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1256,plain,
! [SV370: $i,SV90: $i] :
( ( ! [SY3061: $i] :
( ~ ( in @ SY3061 @ ( funcSet @ SV90 @ SV370 ) )
| ( func @ SV90 @ SV370 @ SY3061 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1257,plain,
! [SV371: $i,SV91: $i] :
( ( ( SV91 != SV371 )
| ( subset @ SV91 @ SV371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(1258,plain,
! [SV372: $i,SV92: $i] :
( ( ! [SY3062: $i] :
( ~ ( in @ SY3062 @ SV92 )
| ! [SY3063: $i] :
( ~ ( in @ SY3063 @ SV372 )
| ( ( kpair @ SY3062 @ SY3063 )
= ( kpair @ SY3062 @ SY3063 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[964]) ).
thf(1259,plain,
! [SV373: $i,SV93: $i] :
( ( ! [SY3064: $i] :
( ~ ( in @ SY3064 @ ( symdiff @ SV93 @ SV373 ) )
| ! [SY3065: $o] :
( ~ ( ~ ( in @ SY3064 @ SV93 )
| ~ ~ ( in @ SY3064 @ SV373 )
| SY3065 )
| ~ ( ~ ~ ( in @ SY3064 @ SV93 )
| ~ ( in @ SY3064 @ SV373 )
| SY3065 )
| SY3065 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1260,plain,
! [SV374: $i,SV94: $i] :
( ( ! [SY3066: $i] :
( ~ ( in @ SY3066 @ SV94 )
| ~ ~ ( in @ SY3066 @ SV374 )
| ( in @ SY3066 @ ( symdiff @ SV94 @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1261,plain,
! [SV95: $i > $o] :
( ( ( ~ ~ ! [SY2388: $i] :
~ ( SV95 @ SY2388 ) )
= $true )
| ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1262,plain,
! [SV375: $i,SV96: $i] :
( ( ( SV96 != SV375 )
| ! [SY3067: $i,SY3068: $i] :
( ( SY3067 != SY3068 )
| ( ( setadjoin @ SV96 @ SY3067 )
= ( setadjoin @ SV375 @ SY3068 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1263,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ~ ! [SY3069: $i,SY3070: $i] :
( ( SY3069 != SY3070 )
| ~ ( ~ ( ~ ( SV97 @ SY3069 )
| ( SV376 @ SY3070 ) )
| ~ ( ~ ( SV376 @ SY3070 )
| ( SV97 @ SY3069 ) ) ) )
| ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(1264,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ~ ! [SY3077: $i] :
( ~ ( in @ SY3077 @ SV98 )
| ! [SY3078: $i] :
( ~ ( in @ SY3078 @ SV98 )
| ~ ( SV377 @ SY3077 )
| ~ ( SV377 @ SY3078 )
| ( SY3077 = SY3078 ) ) )
| ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1265,plain,
! [SV99: $o,SV378: $i] :
( ( ~ ( in @ SV378 @ ( prop2set @ SV99 ) )
| SV99 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[971]) ).
thf(1266,plain,
! [SV379: $i] :
( ( ~ ( in @ SV379 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1267,plain,
! [SV380: $i] :
( ( ~ ( in @ SV380 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[973]) ).
thf(1268,plain,
! [SV381: $i,SV100: $i] :
( ( ! [SY3081: $i] :
( ~ ( in @ SY3081 @ SV100 )
| ! [SY3082: $i] :
( ~ ( in @ SY3082 @ SV381 )
| ( subset @ ( setadjoin @ SY3081 @ ( setadjoin @ SY3082 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[974]) ).
thf(1269,plain,
! [SV101: $i,SV382: $i] :
( ( ~ ( in @ SV382 @ ( powerset @ SV101 ) )
| ! [SY3083: $i] :
( ~ ( in @ SY3083 @ ( powerset @ SV101 ) )
| ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SY3083 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[975]) ).
thf(1270,plain,
! [SV102: $i,SV383: $i] :
( ( ~ ( in @ SV383 @ ( powerset @ SV102 ) )
| ! [SY3084: $i] :
( ~ ( in @ SY3084 @ ( powerset @ SV102 ) )
| ~ ( subset @ ( setminus @ SV102 @ SY3084 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SY3084 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1271,plain,
! [SV384: $i,SV103: $i] :
( ( ! [SY3085: $i] :
( ~ ( in @ ( setadjoin @ SY3085 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ ( setadjoin @ SV384 @ emptyset ) ) @ emptyset ) ) )
| ( SV103 = SY3085 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1272,plain,
! [SV104: $i,SV385: $i] :
( ( ~ ( in @ SV385 @ ( powerset @ SV104 ) )
| ! [SY3086: $i] :
( ~ ( in @ SY3086 @ ( powerset @ SV104 ) )
| ! [SY3087: $i] :
( ~ ( in @ SY3087 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SY3086 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3087 ) @ ( binunion @ SY3086 @ SY3087 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[978]) ).
thf(1273,plain,
! [SV105: $i > $o] :
( ( ( ~ ~ ! [SY2423: $i] :
~ ~ ( ~ ( SV105 @ SY2423 )
| ~ ! [SY2424: $i] :
( ~ ( SV105 @ SY2424 )
| ( SY2423 = SY2424 ) ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1274,plain,
! [SV386: $i > $o,SV106: $i] :
( ( ~ ~ ~ ! [SY3088: $i] :
~ ~ ( ~ ( in @ SY3088 @ SV106 )
| ~ ( SV386 @ SY3088 ) )
| ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[980]) ).
thf(1275,plain,
! [SV107: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ ( powerset @ SV107 ) )
| ! [SY3090: $i] :
( ~ ( in @ SY3090 @ ( powerset @ SV107 ) )
| ! [SY3091: $i] :
( ~ ( in @ SY3091 @ SV107 )
| ~ ~ ( in @ SY3091 @ SV387 )
| ~ ( in @ SY3091 @ ( binintersect @ SV387 @ SY3090 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[981]) ).
thf(1276,plain,
! [SV388: $o,SV108: $i] :
( ( ! [SY3092: $i] :
( ~ ( in @ SY3092 @ SV108 )
| ! [SY3093: $i] :
( ~ ( in @ SY3093 @ SV108 )
| ( in @ ( if @ SV108 @ SV388 @ SY3092 @ SY3093 ) @ ( setadjoin @ SY3092 @ ( setadjoin @ SY3093 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[982]) ).
thf(1277,plain,
! [SV108: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV108 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV108 )
| ( in @ ( if @ SV108 @ $true @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[982]) ).
thf(1278,plain,
! [SV108: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV108 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV108 )
| ( in @ ( if @ SV108 @ $false @ SX0 @ SX1 ) @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[982]) ).
thf(1279,plain,
! [SV109: $i,SV389: $i] :
( ( ! [SY3094: $i] :
( ~ ( in @ SY3094 @ SV389 )
| ( in @ SY3094 @ ( binunion @ SV109 @ SV389 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[983]) ).
thf(1280,plain,
! [SV390: $i,SV110: $i] :
( ( ( ( binintersect @ SV110 @ SV390 )
!= SV390 )
| ( subset @ SV390 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[984]) ).
thf(1281,plain,
! [SV111: $i,SV391: $i] :
( ( ~ ( in @ SV391 @ ( powerset @ SV111 ) )
| ! [SY3095: $i] :
( ~ ( in @ SY3095 @ ( powerset @ SV111 ) )
| ~ ! [SY3096: $i] :
( ~ ( in @ SY3096 @ SV111 )
| ~ ( in @ SY3096 @ SV391 )
| ( in @ SY3096 @ SY3095 ) )
| ~ ! [SY3097: $i] :
( ~ ( in @ SY3097 @ SV111 )
| ~ ( in @ SY3097 @ SY3095 )
| ( in @ SY3097 @ SV391 ) )
| ( SV391 = SY3095 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[985]) ).
thf(1282,plain,
! [SV112: $i,SV392: $i] :
( ( ~ ( in @ SV392 @ ( powerset @ SV112 ) )
| ! [SY3098: $i] :
( ~ ( in @ SY3098 @ ( powerset @ SV112 ) )
| ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV112 )
| ~ ~ ( in @ SY3099 @ SV392 )
| ~ ~ ( in @ SY3099 @ SY3098 )
| ~ ( in @ SY3099 @ ( binunion @ SV392 @ SY3098 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[986]) ).
thf(1283,plain,
! [SV393: $i,SV113: $i] :
( ( ~ ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV113 )
| ( in @ SY3100 @ SV393 ) )
| ( subset @ SV113 @ SV393 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[987]) ).
thf(1284,plain,
! [SV394: $i,SV114: $i] :
( ( ! [SY3101: $i] :
( ~ ~ ( in @ SY3101 @ ( setminus @ SV114 @ SV394 ) )
| ~ ~ ( in @ SY3101 @ SV394 )
| ~ ( in @ SY3101 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1285,plain,
! [SV395: $i,SV115: $i] :
( ( ~ ( breln1 @ SV115 @ SV395 )
| ( breln1 @ SV115 @ ( breln1invset @ SV115 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1286,plain,
! [SV116: $i] :
( ( ( ~ ( in @ SV116 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV116 @ SV116 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[990]) ).
thf(1287,plain,
! [SV396: $o,SV117: $i] :
( ( ! [SY3102: $i] :
( ~ ( in @ SY3102 @ SV117 )
| ! [SY3103: $i] :
( ~ ( in @ SY3103 @ SV117 )
| ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3104: $i] :
( ~ ( ~ SV396
| ( SY3104 != SY3102 ) )
| ~ ( ~ ~ SV396
| ( SY3104 != SY3103 ) ) ) )
= ( setadjoin @ SY3103 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[991]) ).
thf(1288,plain,
! [SV117: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV117 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV117 )
| ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[991]) ).
thf(1289,plain,
! [SV117: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV117 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV117 )
| ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[991]) ).
thf(1290,plain,
! [SV118: $i,SV397: $i] :
( ( ~ ( in @ SV397 @ ( powerset @ SV118 ) )
| ! [SY3105: $i] :
( ~ ( in @ SY3105 @ ( powerset @ SV118 ) )
| ! [SY3106: $i] :
( ~ ( in @ SY3106 @ ( binintersect @ SV397 @ SY3105 ) )
| ( in @ SY3106 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[992]) ).
thf(1291,plain,
! [SV398: $i,SV119: $i] :
( ( ! [SY3107: $i] :
( ~ ( in @ SY3107 @ ( cartprod @ SV119 @ SV398 ) )
| ( iskpair @ SY3107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[993]) ).
thf(1292,plain,
! [SV399: $i,SV120: $i] :
( ( ! [SY3108: $i] :
( ~ ( subset @ SV120 @ SY3108 )
| ( subset @ SV120 @ ( setadjoin @ SV399 @ SY3108 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[994]) ).
thf(1293,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ~ ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV121 )
| ~ ( SV400 @ SY3109 ) )
| ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[995]) ).
thf(1294,plain,
! [SV122: $i,SV401: $i] :
( ( ~ ( in @ SV401 @ ( powerset @ SV122 ) )
| ! [SY3111: $i] :
( ~ ( in @ SY3111 @ ( powerset @ SV122 ) )
| ! [SY3112: $i] :
( ~ ( in @ SY3112 @ SV122 )
| ~ ( in @ SY3112 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SY3111 ) ) )
| ( in @ SY3112 @ ( setminus @ SV122 @ SV401 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1295,plain,
! [SV402: $i,SV123: $i] :
( ( ! [SY3113: $i > $i > $o,SY3114: $i,SY3115: $i] :
( ~ ( in @ ( kpair @ SY3114 @ SY3115 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SX5: $i,SX6: $i] : ( SY3113 @ SX5 @ SX6 ) ) )
| ( in @ SY3114 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[997]) ).
thf(1296,plain,
! [SV403: $i,SV124: $i] :
( ( ! [SY3118: $i] :
( ~ ( in @ SY3118 @ SV124 )
| ( in @ SY3118 @ ( binunion @ SV124 @ SV403 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[998]) ).
thf(1297,plain,
! [SV404: $i,SV125: $i] :
( ( ! [SY3119: $i] :
( ~ ( func @ SV125 @ SV404 @ SY3119 )
| ! [SY3120: $i] :
( ~ ( in @ SY3120 @ SV125 )
| ( in @ ( ap @ SV125 @ SV404 @ SY3119 @ SY3120 ) @ SV404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[999]) ).
thf(1298,plain,
! [SV405: $i,SV126: $i] :
( ( ! [SY3121: $i] :
( ~ ( breln @ SV126 @ SV405 @ SY3121 )
| ! [SY3122: $i > $o] :
( ~ ! [SY3123: $i] :
( ~ ( in @ SY3123 @ SV126 )
| ! [SY3124: $i] :
( ~ ( in @ SY3124 @ SV405 )
| ~ ( in @ ( kpair @ SY3123 @ SY3124 ) @ SY3121 )
| ( SY3122 @ ( kpair @ SY3123 @ SY3124 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3121 )
| ( SY3122 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1299,plain,
! [SV127: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ ( powerset @ SV127 ) )
| ! [SY3126: $i] :
( ~ ( in @ SY3126 @ ( powerset @ SV127 ) )
| ! [SY3127: $i] :
( ~ ( in @ SY3127 @ SV127 )
| ~ ( in @ SY3127 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3127 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SY3126 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1300,plain,
! [SV407: $i,SV128: $i] :
( ( ! [SY3128: $i] :
( ~ ~ ( in @ SY3128 @ SV128 )
| ~ ( in @ SY3128 @ SV407 )
| ( in @ SY3128 @ ( symdiff @ SV128 @ SV407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1301,plain,
! [SV129: $i > $o] :
( ( ( ~ ~ ! [SY2490: $i] :
~ ~ ( ~ ( SV129 @ SY2490 )
| ~ ! [SY2491: $i] :
( ~ ( SV129 @ SY2491 )
| ( SY2490 = SY2491 ) ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1302,plain,
! [SV408: $i,SV130: $i] :
( ( ! [SY3129: $i] :
( ~ ( in @ SY3129 @ ( setadjoin @ SV130 @ SV408 ) )
| ( SY3129 = SV130 )
| ( in @ SY3129 @ SV408 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1303,plain,
! [SV131: $i] :
( ( ( ~ ( iskpair @ SV131 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV131 )
@ ^ [SY2496: $i] : ( in @ ( setadjoin @ SY2496 @ emptyset ) @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1304,plain,
! [SV132: $i,SV409: $i] :
( ( ~ ( in @ SV409 @ ( powerset @ SV132 ) )
| ! [SY3130: $i] :
( ~ ( in @ SY3130 @ ( powerset @ SV132 ) )
| ! [SY3131: $i] :
( ~ ( in @ SY3131 @ SV132 )
| ~ ( in @ SY3131 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SY3130 ) ) )
| ( in @ SY3131 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SY3130 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1006]) ).
thf(1305,plain,
! [SV133: $i,SV410: $i] :
( ( ~ ( subset @ SV410 @ SV133 )
| ( ( binintersect @ SV133 @ SV410 )
= SV410 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1306,plain,
! [SV134: $i,SV411: $i] :
( ( ~ ( in @ SV411 @ ( powerset @ SV134 ) )
| ! [SY3132: $i] :
( ~ ( in @ SY3132 @ ( powerset @ SV134 ) )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SY3132 ) )
| ~ ( in @ SY3133 @ SV411 )
| ( in @ SY3133 @ SY3132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1307,plain,
! [SV135: $i] :
( ( ( ~ ! [SY2504: $i] :
~ ( in @ SY2504 @ SV135 ) )
= $true )
| ( ( SV135 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1308,plain,
! [SV412: $i,SV136: $i] :
( ( ! [SY3134: $i] :
( ~ ( in @ SY3134 @ ( binintersect @ SV136 @ SV412 ) )
| ( in @ SY3134 @ SV136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1309,plain,
! [SV413: $i,SV137: $i] :
( ( ! [SY3135: $i] :
( ~ ( func @ SV137 @ SV413 @ SY3135 )
| ! [SY3136: $i] :
( ~ ( func @ SV137 @ SV413 @ SY3136 )
| ~ ! [SY3137: $i] :
( ~ ( in @ SY3137 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SY3135 @ SY3137 )
= ( ap @ SV137 @ SV413 @ SY3136 @ SY3137 ) ) )
| ( SY3135 = SY3136 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1011]) ).
thf(1310,plain,
! [SV414: $o,SV138: $i] :
( ( ! [SY3138: $i] :
( ~ ( in @ SY3138 @ SV138 )
| ! [SY3139: $i] :
( ~ ( in @ SY3139 @ SV138 )
| ~ SV414
| ( in @ SY3138
@ ( dsetconstr @ SV138
@ ^ [SY3140: $i] :
( ~ ( ~ SV414
| ( SY3140 != SY3138 ) )
| ~ ( ~ ~ SV414
| ( SY3140 != SY3139 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1012]) ).
thf(1311,plain,
! [SV138: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV138 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV138 )
| ~ $true
| ( in @ SX0
@ ( dsetconstr @ SV138
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1012]) ).
thf(1312,plain,
! [SV138: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV138 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV138 )
| ~ $false
| ( in @ SX0
@ ( dsetconstr @ SV138
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1012]) ).
thf(1313,plain,
! [SV139: $i > $o] :
( ( ( ~ ~ ! [SY2515: $i] :
~ ~ ( ~ ( SV139 @ SY2515 )
| ~ ! [SY2516: $i] :
( ~ ( SV139 @ SY2516 )
| ( SY2515 = SY2516 ) ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1314,plain,
! [SV415: $i > $o,SV140: $i] :
( ( ! [SY3141: $i] :
( ~ ( in @ SY3141 @ SV140 )
| ~ ( SV415 @ SY3141 )
| ( in @ SY3141
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1014]) ).
thf(1315,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ~ ! [SY3143: $i,SY3144: $i] :
( ( SY3143 != SY3144 )
| ~ ( ~ ( ~ ( SV141 @ SY3143 )
| ( SV416 @ SY3144 ) )
| ~ ( ~ ( SV416 @ SY3144 )
| ( SV141 @ SY3143 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1015]) ).
thf(1316,plain,
! [SV417: $i,SV142: $i] :
( ( ! [SY3153: $i] :
( ~ ( in @ SY3153 @ ( cartprod @ SV142 @ SV417 ) )
| ~ ! [SY3154: $i] :
~ ~ ( ~ ( in @ SY3154 @ SV142 )
| ~ ~ ! [SY3155: $i] :
~ ~ ( ~ ( in @ SY3155 @ SV417 )
| ( SY3153
!= ( kpair @ SY3154 @ SY3155 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1016]) ).
thf(1317,plain,
! [SV143: $i,SV418: $i] :
( ( ~ ( in @ SV418 @ ( powerset @ SV143 ) )
| ! [SY3156: $i] :
( ~ ( in @ SY3156 @ ( powerset @ SV143 ) )
| ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SY3156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1017]) ).
thf(1318,plain,
! [SV419: $i,SV144: $i] :
( ( ~ ( breln1 @ SV144 @ SV419 )
| ! [SY3157: $i > $o] :
( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV144 )
| ! [SY3159: $i] :
( ~ ( in @ SY3159 @ SV144 )
| ~ ( in @ ( kpair @ SY3158 @ SY3159 ) @ SV419 )
| ( SY3157 @ ( kpair @ SY3158 @ SY3159 ) ) ) )
| ! [SY3160: $i] :
( ~ ( in @ SY3160 @ SV419 )
| ( SY3157 @ SY3160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1319,plain,
! [SV145: $i,SV420: $i] :
( ( ~ ( in @ SV420 @ ( powerset @ SV145 ) )
| ! [SY3161: $i] :
( ~ ( in @ SY3161 @ ( powerset @ SV145 ) )
| ! [SY3162: $i] :
( ~ ( in @ SY3162 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3162 )
| ( subset @ ( binintersect @ SV420 @ SY3161 ) @ SY3162 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1019]) ).
thf(1320,plain,
! [SV421: $i,SV146: $i] :
( ( ( ( binintersect @ SV146 @ SV421 )
!= SV146 )
| ( subset @ SV146 @ SV421 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1321,plain,
! [SV422: $o,SV147: $i] :
( ( ! [SY3163: $i] :
( ~ ( in @ SY3163 @ SV147 )
| ! [SY3164: $i] :
( ~ ( in @ SY3164 @ SV147 )
| ~ ~ SV422
| ( in @ SY3164
@ ( dsetconstr @ SV147
@ ^ [SY3165: $i] :
( ~ ( ~ SV422
| ( SY3165 != SY3163 ) )
| ~ ( ~ ~ SV422
| ( SY3165 != SY3164 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1021]) ).
thf(1322,plain,
! [SV147: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV147 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV147 )
| ~ ~ $true
| ( in @ SX1
@ ( dsetconstr @ SV147
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1021]) ).
thf(1323,plain,
! [SV147: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV147 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV147 )
| ~ ~ $false
| ( in @ SX1
@ ( dsetconstr @ SV147
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1021]) ).
thf(1324,plain,
! [SV148: $i] :
( ( ( ~ ( in @ SV148 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1022]) ).
thf(1325,plain,
! [SV423: $o,SV149: $i] :
( ( ! [SY3166: $i] :
( ~ ( in @ SY3166 @ SV149 )
| ! [SY3167: $i] :
( ~ ( in @ SY3167 @ SV149 )
| ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SY3166 @ SY3167 )
= SY3167 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1023]) ).
thf(1326,plain,
! [SV149: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV149 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV149 )
| ~ ~ $true
| ( ( if @ SV149 @ $true @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1023]) ).
thf(1327,plain,
! [SV149: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV149 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV149 )
| ~ ~ $false
| ( ( if @ SV149 @ $false @ SX0 @ SX1 )
= SX1 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1023]) ).
thf(1328,plain,
! [SV424: $i,SV150: $i] :
( ( ! [SY3168: $i] :
( ~ ( subset @ SY3168 @ SV150 )
| ~ ( subset @ SY3168 @ SV424 )
| ( subset @ SY3168 @ ( binintersect @ SV150 @ SV424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1024]) ).
thf(1329,plain,
! [SV151: $i,SV425: $i] :
( ( ~ ( in @ SV425 @ ( powerset @ SV151 ) )
| ! [SY3169: $i] :
( ~ ( in @ SY3169 @ ( powerset @ SV151 ) )
| ~ ( subset @ SV425 @ ( setminus @ SV151 @ SY3169 ) )
| ! [SY3170: $i] :
( ~ ( in @ SY3170 @ SV151 )
| ~ ( in @ SY3170 @ SY3169 )
| ( in @ SY3170 @ ( setminus @ SV151 @ SV425 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1330,plain,
! [SV152: $i,SV426: $i] :
( ( ~ ( in @ SV426 @ ( powerset @ SV152 ) )
| ! [SY3171: $i] :
( ~ ( in @ SY3171 @ ( powerset @ SV152 ) )
| ! [SY3172: $i] :
( ~ ( in @ SY3172 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SY3171 )
| ~ ( subset @ SV426 @ SY3172 )
| ( subset @ SV426 @ ( binintersect @ SY3171 @ SY3172 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1026]) ).
thf(1331,plain,
! [SV153: $i] :
( ( ( ~ ( iskpair @ SV153 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV153 )
@ ^ [SY2563: $i] :
( SV153
= ( kpair @ ( kfst @ SV153 ) @ SY2563 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1332,plain,
! [SV154: $i,SV427: $i] :
( ( ~ ( in @ SV427 @ ( powerset @ SV154 ) )
| ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( powerset @ SV154 ) )
| ! [SY3174: $i] :
( ~ ( in @ SY3174 @ ( powerset @ SV154 ) )
| ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV154 )
| ~ ( in @ SY3175 @ ( binintersect @ SV427 @ SY3173 ) )
| ( in @ SY3175 @ ( binunion @ SV427 @ SY3174 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1333,plain,
! [SV428: $i > $o,SV155: $i] :
( ( ~ ~ ! [SY3176: $i] :
~ ~ ( ~ ( in @ SY3176 @ SV155 )
| ~ ( SV428 @ SY3176 ) )
| ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1029]) ).
thf(1334,plain,
! [SV156: $i,SV429: $i] :
( ( ~ ( in @ SV429 @ ( powerset @ SV156 ) )
| ! [SY3178: $i] :
( ~ ( in @ SY3178 @ ( powerset @ SV156 ) )
| ! [SY3179: $i] :
( ~ ( in @ SY3179 @ SV156 )
| ~ ( in @ SY3179 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3179 @ ( binintersect @ SV429 @ SY3178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1335,plain,
! [SV157: $i,SV430: $i] :
( ( ~ ( in @ SV430 @ ( powerset @ SV157 ) )
| ( in @ ( powerset @ SV430 ) @ ( powerset @ ( powerset @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1336,plain,
! [SV431: $i,SV158: $i] :
( ( ! [SY3180: $i] :
( ~ ( subset @ SV158 @ SV431 )
| ~ ( subset @ SV431 @ SY3180 )
| ( subset @ SV158 @ SY3180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1337,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ~ ! [SY3181: $i] :
( ~ ( in @ SY3181 @ SV159 )
| ! [SY3182: $i] :
( ~ ( in @ SY3182 @ SV159 )
| ~ ( SV432 @ SY3181 )
| ~ ( SV432 @ SY3182 )
| ( SY3181 = SY3182 ) ) )
| ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1033]) ).
thf(1338,plain,
! [SV433: $i > $o,SV160: $i] :
( ( ! [SY3185: $i] :
( ~ ( in @ SY3185 @ SV160 )
| ~ ( ~ ( ~ ( in @ SY3185
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SY3185 ) )
| ~ ( ~ ( SV433 @ SY3185 )
| ( in @ SY3185
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1034]) ).
thf(1339,plain,
! [SV434: $i > $o,SV161: $i] :
( ( ! [SY3188: $i] :
( ~ ( in @ SY3188 @ SV161 )
| ~ ( SV434 @ SY3188 )
| ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1340,plain,
! [SV435: $i,SV162: $i] :
( ( ! [SY3190: $i] :
( ( ( setadjoin @ SV162 @ ( setadjoin @ SV435 @ emptyset ) )
!= ( setadjoin @ SY3190 @ emptyset ) )
| ( SV162 = SV435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1036]) ).
thf(1341,plain,
! [SV436: $i,SV163: $i] :
( ( ! [SY3191: $i,SY3192: $i] :
( ~ ( in @ ( kpair @ SY3191 @ SY3192 ) @ ( cartprod @ SV163 @ SV436 ) )
| ( in @ SY3192 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1342,plain,
! [SV164: $o] :
( ( ( ~ SV164 ) = $true )
| ( ( set2prop @ ( prop2set @ SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1038]) ).
thf(1343,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1039]) ).
thf(1344,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1345,plain,
! [SV437: $i,SV165: $i] :
( ( ! [SY3193: $i] :
( ~ ( in @ SY3193 @ SV165 )
| ! [SY3194: $i] :
( ~ ( in @ SY3194 @ SV437 )
| ( in @ ( kpair @ SY3193 @ SY3194 ) @ ( cartprod @ SV165 @ SV437 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1041]) ).
thf(1346,plain,
! [SV166: $i,SV438: $i] :
( ( ~ ( in @ SV438 @ ( powerset @ SV166 ) )
| ! [SY3195: $i] :
( ~ ( in @ SY3195 @ ( powerset @ SV166 ) )
| ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SY3195 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1347,plain,
! [SV439: $i,SV167: $i] :
( ( ! [SY3196: $i] :
( ~ ( in @ SY3196 @ SV167 )
| ! [SY3197: $i] :
( ~ ( in @ SY3197 @ SV439 )
| ( ( kfst @ ( kpair @ SY3196 @ SY3197 ) )
= SY3196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1348,plain,
! [SV440: $i > $o,SV168: $i] :
( ( ~ ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
| ~ ! [SY3199: $i] :
~ ~ ( ~ ( in @ SY3199 @ SV168 )
| ~ ( SV440 @ SY3199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1349,plain,
! [SV441: $i,SV169: $i] :
( ( ! [SY3200: $i] :
~ ( ~ ( ~ ( in @ SY3200 @ ( setadjoin @ SV169 @ SV441 ) )
| ( SY3200 = SV169 )
| ( in @ SY3200 @ SV441 ) )
| ~ ( ~ ( ( SY3200 = SV169 )
| ( in @ SY3200 @ SV441 ) )
| ( in @ SY3200 @ ( setadjoin @ SV169 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1350,plain,
! [SV170: $i > $i > $o,SV442: $i] :
( ( ~ ! [SY3201: $i] :
( ~ ( in @ SY3201 @ SV442 )
| ~ ! [SY2609: $i] :
~ ~ ( ~ ( SV170 @ SY3201 @ SY2609 )
| ~ ! [SY2610: $i] :
( ~ ( SV170 @ SY3201 @ SY2610 )
| ( SY2609 = SY2610 ) ) ) )
| ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1351,plain,
! [SV171: $i,SV443: $i] :
( ( ! [SY3208: $i] :
( ~ ( in @ SV443 @ SY3208 )
| ~ ( in @ SY3208 @ SV171 )
| ( in @ SV443 @ ( setunion @ SV171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1352,plain,
! [SV444: $i,SV172: $i] :
( ( ~ ( subset @ SV172 @ SV444 )
| ( in @ SV172 @ ( powerset @ SV444 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1353,plain,
! [SV445: $i,SV173: $i] :
( ( ! [SY3209: $i] :
( ~ ( breln @ SV173 @ SV445 @ SY3209 )
| ! [SY3210: $i > $o] :
( ~ ! [SY3211: $i] :
( ~ ( in @ SY3211 @ SV173 )
| ! [SY3212: $i] :
( ~ ( in @ SY3212 @ SV445 )
| ~ ( in @ ( kpair @ SY3211 @ SY3212 ) @ SY3209 )
| ( SY3210 @ ( kpair @ SY3211 @ SY3212 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3209 )
| ( SY3210 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1354,plain,
! [SV446: $i,SV174: $i] :
( ( ! [SY3214: $i,SY3215: $i] :
( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3214 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3214 @ ( setadjoin @ SY3215 @ emptyset ) ) @ emptyset ) ) )
| ( SV174 = SY3214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1355,plain,
! [SV447: $i,SV175: $i] :
( ( ( SV175 != SV447 )
| ( ( powerset @ SV175 )
= ( powerset @ SV447 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1356,plain,
! [SV176: $i,SV448: $i] :
( ( ~ ( in @ SV448 @ SV176 )
| ( subset @ ( setadjoin @ SV448 @ emptyset ) @ SV176 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1052]) ).
thf(1357,plain,
! [SV449: $i,SV177: $i] :
( ( ~ ! [SY3216: $i] :
( ~ ( in @ SY3216 @ SV177 )
| ( in @ SY3216 @ SV449 ) )
| ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1053]) ).
thf(1358,plain,
! [SV178: $i,SV450: $i] :
( ( ! [SY3218: $i] :
( ~ ( in @ SY3218 @ SV450 )
| ( in @ SY3218 @ ( setadjoin @ SV178 @ SV450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1359,plain,
! [SV451: $i,SV179: $i] :
( ( ! [SY3219: $i,SY3220: $i] :
( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY3219 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3219 @ ( setadjoin @ SY3220 @ emptyset ) ) @ emptyset ) ) )
| ( SY3219 != SY3220 )
| ( SV451 = SY3220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1055]) ).
thf(1360,plain,
! [SV452: $i,SV180: $i] :
( ( ! [SY3221: $i] :
( ~ ( in @ SY3221 @ ( funcSet @ SV180 @ SV452 ) )
| ! [SY3222: $i] :
( ~ ( in @ SY3222 @ SV180 )
| ! [SY3223: $i] :
( ~ ( in @ SY3223 @ SV452 )
| ~ ( in @ ( kpair @ SY3222 @ SY3223 ) @ SY3221 )
| ( ( ap @ SV180 @ SV452 @ SY3221 @ SY3222 )
= SY3223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1056]) ).
thf(1361,plain,
! [SV453: $i,SV181: $i] :
( ( ! [SY3224: $i] :
( ~ ( in @ SY3224 @ SV181 )
| ( in @ ( setadjoin @ SY3224 @ emptyset ) @ ( powerset @ ( binunion @ SV181 @ SV453 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1057]) ).
thf(1362,plain,
! [SV182: $i] :
( ( ( ~ ( singleton @ SV182 ) )
= $true )
| ( ( in @ ( setunion @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1058]) ).
thf(1363,plain,
! [SV183: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ ( powerset @ SV183 ) )
| ! [SY3225: $i] :
( ~ ( in @ SY3225 @ ( powerset @ SV183 ) )
| ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SY3225 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1364,plain,
! [SV184: $i] :
( ( ( ~ ! [SY2645: $i] :
~ ( in @ SY2645 @ SV184 ) )
= $true )
| ( ( SV184 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1365,plain,
! [SV455: $i,SV185: $i] :
( ( ~ ( breln1 @ SV185 @ SV455 )
| ! [SY3226: $i] :
( ~ ( breln1 @ SV185 @ SY3226 )
| ~ ! [SY3227: $i] :
( ~ ( in @ SY3227 @ SV185 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SV185 )
| ~ ( in @ ( kpair @ SY3227 @ SY3228 ) @ SV455 )
| ( in @ ( kpair @ SY3227 @ SY3228 ) @ SY3226 ) ) )
| ( subset @ SV455 @ SY3226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1061]) ).
thf(1366,plain,
! [SV456: $i,SV186: $i] :
( ( ! [SY3229: $i] :
( ~ ( in @ SY3229 @ SV186 )
| ~ ( in @ SY3229 @ SV456 )
| ( in @ SY3229 @ ( binintersect @ SV186 @ SV456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1062]) ).
thf(1367,plain,
! [SV187: $i,SV457: $i] :
( ( ~ ( in @ SV457 @ ( powerset @ SV187 ) )
| ! [SY3230: $i] :
( ~ ( in @ SY3230 @ ( powerset @ SV187 ) )
| ! [SY3231: $i] :
( ~ ( in @ SY3231 @ ( powerset @ SV187 ) )
| ! [SY3232: $i] :
( ~ ( in @ SY3232 @ SV187 )
| ~ ( in @ SY3232 @ ( binintersect @ SV457 @ SY3230 ) )
| ( in @ SY3232 @ ( binintersect @ ( binunion @ SV457 @ SY3231 ) @ ( binunion @ SY3230 @ SY3231 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1368,plain,
! [SV458: $i,SV188: $i] :
( ( ~ ( breln1 @ SV188 @ SV458 )
| ! [SY3233: $i] :
( ~ ( in @ SY3233 @ SV188 )
| ! [SY3234: $i] :
( ~ ( in @ SY3234 @ SV188 )
| ~ ( in @ ( kpair @ SY3234 @ SY3233 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SY3233 @ SY3234 ) @ SV458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1064]) ).
thf(1369,plain,
! [SV189: $i,SV459: $i] :
( ( ~ ( in @ SV459 @ ( setunion @ SV189 ) )
| ! [SY3235: $o] :
( ~ ! [SY3236: $i] :
( ~ ( in @ SV459 @ SY3236 )
| ~ ( in @ SY3236 @ SV189 )
| SY3235 )
| SY3235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1370,plain,
! [SV190: $i,SV460: $i] :
( ( ~ ( in @ SV460 @ ( powerset @ SV190 ) )
| ( subset @ SV460 @ ( setminus @ SV190 @ ( setminus @ SV190 @ SV460 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1371,plain,
! [SV461: $i,SV191: $i] :
( ( ! [SY3237: $i] :
( ~ ( func @ SV191 @ SV461 @ SY3237 )
| ( ( lam @ SV191 @ SV461
@ ^ [SY3238: $i] : ( ap @ SV191 @ SV461 @ SY3237 @ SY3238 ) )
= SY3237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1067]) ).
thf(1372,plain,
! [SV192: $i,SV462: $i] :
( ( ~ ( in @ SV462 @ ( powerset @ SV192 ) )
| ! [SY3239: $i] :
( ~ ( in @ SY3239 @ ( powerset @ SV192 ) )
| ! [SY3240: $i] :
( ~ ( in @ SY3240 @ SV192 )
| ~ ~ ( in @ SY3240 @ ( binunion @ SV462 @ SY3239 ) )
| ~ ( in @ SY3240 @ SV462 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1068]) ).
thf(1373,plain,
! [SV193: $i,SV463: $i] :
( ( ~ ( in @ SV463 @ ( powerset @ SV193 ) )
| ! [SY3241: $i] :
( ~ ( in @ SY3241 @ ( powerset @ SV193 ) )
| ! [SY3242: $i] :
( ~ ( in @ SY3242 @ SV193 )
| ~ ( in @ SY3242 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SY3241 ) ) )
| ( in @ SY3242 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SY3241 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1069]) ).
thf(1374,plain,
! [SV194: $i,SV464: $i] :
( ( ~ ( in @ SV464 @ ( powerset @ SV194 ) )
| ! [SY3243: $i] :
( ~ ( in @ SY3243 @ ( powerset @ SV194 ) )
| ! [SY3244: $i] :
( ~ ( in @ SY3244 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SY3243 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3244 ) @ ( binunion @ SY3243 @ SY3244 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1070]) ).
thf(1375,plain,
! [SV465: $i,SV195: $i] :
( ( ! [SY3245: $i] :
( ~ ( in @ SY3245 @ ( setadjoin @ SV195 @ SV465 ) )
| ! [SY3246: $o] :
( ~ ( ( SY3245 != SV195 )
| SY3246 )
| ~ ( ~ ( in @ SY3245 @ SV465 )
| SY3246 )
| SY3246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1071]) ).
thf(1376,plain,
! [SV466: $i,SV196: $i] :
( ( ! [SY3247: $i] :
( ~ ( in @ SY3247 @ ( cartprod @ SV196 @ SV466 ) )
| ( in @ ( kfst @ SY3247 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1072]) ).
thf(1377,plain,
! [SV467: $i,SV197: $i] :
( ( ~ ~ ~ ! [SY3248: $i] :
~ ~ ( ~ ( in @ SY3248 @ SV197 )
| ~ ( in @ SY3248 @ SV467 ) )
| ( ( binintersect @ SV197 @ SV467 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1073]) ).
thf(1378,plain,
! [SV468: $i,SV198: $i] :
( ( ( ( setminus @ SV198 @ SV468 )
!= emptyset )
| ( subset @ SV198 @ SV468 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1074]) ).
thf(1379,plain,
! [SV199: $i,SV469: $i] :
( ( ~ ( in @ SV469 @ ( powerset @ SV199 ) )
| ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( powerset @ SV199 ) )
| ( in @ ( setminus @ SV469 @ SY3249 ) @ ( powerset @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1075]) ).
thf(1380,plain,
! [SV470: $i,SV200: $i] :
( ( ! [SY3250: $i > $i] :
( ~ ! [SY3251: $i] :
( ~ ( in @ SY3251 @ SV200 )
| ( in @ ( SY3250 @ SY3251 ) @ SV470 ) )
| ( in
@ ( lam @ SV200 @ SV470
@ ^ [SX3: $i] : ( SY3250 @ SX3 ) )
@ ( funcSet @ SV200 @ SV470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1076]) ).
thf(1381,plain,
! [SV201: $i,SV471: $i] :
( ( ~ ( in @ SV471 @ ( setunion @ SV201 ) )
| ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ SV201 )
| ~ ( in @ SV471 @ SY3253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1077]) ).
thf(1382,plain,
! [SV472: $i,SV202: $i] :
( ( ( SV202 != SV472 )
| ( ( setadjoin @ SV202 @ ( setadjoin @ SV472 @ emptyset ) )
= ( setadjoin @ SV202 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1078]) ).
thf(1383,plain,
! [SV203: $i,SV473: $i] :
( ( ~ ( in @ SV473 @ ( powerset @ SV203 ) )
| ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( powerset @ SV203 ) )
| ( in @ ( binintersect @ SV473 @ SY3254 ) @ ( powerset @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1079]) ).
thf(1384,plain,
! [SV204: $i,SV474: $i] :
( ( ~ ( in @ SV474 @ ( powerset @ SV204 ) )
| ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV204 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV204 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SY3255 ) @ ( binunion @ SY3256 @ SY3257 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SY3255 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3256 ) @ ( setminus @ SV204 @ SY3257 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1080]) ).
thf(1385,plain,
! [SV205: $i] :
( ( ( ~ ( subset @ SV205 @ emptyset ) )
= $true )
| ( ( SV205 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1386,plain,
! [SV475: $i,SV206: $i] :
( ( ! [SY3258: $i] :
( ~ ( in @ SY3258 @ ( binunion @ SV206 @ SV475 ) )
| ( in @ SY3258 @ SV206 )
| ( in @ SY3258 @ SV475 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1387,plain,
! [SV207: $i > $o] :
( ( ( ~ ~ ! [SY2700: $i] :
~ ~ ( ~ ( SV207 @ SY2700 )
| ~ ! [SY2701: $i] :
( ~ ( SV207 @ SY2701 )
| ( SY2700 = SY2701 ) ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1388,plain,
! [SV208: $i,SV476: $i] :
( ( ~ ( in @ SV476 @ ( breln1Set @ SV208 ) )
| ( breln1 @ SV208 @ SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1084]) ).
thf(1389,plain,
! [SV477: $i,SV209: $i] :
( ( ~ ( ( SV209 != SV477 ) )
| ~ ( in @ SV477 @ ( setadjoin @ SV209 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1085]) ).
thf(1390,plain,
! [SV210: $i,SV478: $i] :
( ( ~ ( subset @ SV478 @ SV210 )
| ( in @ SV478 @ ( powerset @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1391,plain,
! [SV479: $i,SV211: $i] :
( ( ! [SY3259: $i] :
( ~ ( in @ SY3259 @ SV211 )
| ! [SY3260: $i] :
( ~ ( in @ SY3260 @ SV479 )
| ( in @ ( setadjoin @ SY3259 @ ( setadjoin @ SY3260 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1087]) ).
thf(1392,plain,
! [SV480: $i,SV212: $i] :
( ( ~ ( breln1 @ SV212 @ SV480 )
| ! [SY3261: $i] :
( ~ ( breln1 @ SV212 @ SY3261 )
| ( breln1 @ SV212 @ ( binunion @ SV480 @ SY3261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1088]) ).
thf(1393,plain,
! [SV481: $i,SV213: $i] :
( ( ! [SY3262: $i] :
( ~ ( func @ SV213 @ SV481 @ SY3262 )
| ( in @ SY3262 @ ( funcSet @ SV213 @ SV481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1394,plain,
! [SV482: $o,SV214: $i] :
( ( ! [SY3263: $i] :
( ~ ( in @ SY3263 @ SV214 )
| ! [SY3264: $i] :
( ~ ( in @ SY3264 @ SV214 )
| ~ SV482
| ( ( if @ SV214 @ SV482 @ SY3263 @ SY3264 )
= SY3263 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1090]) ).
thf(1395,plain,
! [SV214: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV214 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV214 )
| ~ $true
| ( ( if @ SV214 @ $true @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1090]) ).
thf(1396,plain,
! [SV214: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV214 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV214 )
| ~ $false
| ( ( if @ SV214 @ $false @ SX0 @ SX1 )
= SX0 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1090]) ).
thf(1397,plain,
! [SV483: $i,SV215: $i] :
( ( ~ ( breln1 @ SV215 @ SV483 )
| ! [SY3265: $i] :
( ~ ( breln1 @ SV215 @ SY3265 )
| ! [SY3266: $i] :
( ~ ( in @ SY3266 @ SV215 )
| ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV215 )
| ~ ( in @ ( kpair @ SY3266 @ SY3267 ) @ SV483 )
| ( in @ ( kpair @ SY3266 @ SY3267 ) @ ( binunion @ SV483 @ SY3265 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1091]) ).
thf(1398,plain,
! [SV216: $i,SV484: $i] :
( ( ~ ( in @ SV484 @ ( powerset @ SV216 ) )
| ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( powerset @ SV216 ) )
| ~ ( subset @ SV484 @ ( setminus @ SV216 @ SY3268 ) )
| ( subset @ SY3268 @ ( setminus @ SV216 @ SV484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1092]) ).
thf(1399,plain,
! [SV485: $i,SV217: $i] :
( ( ! [SY3269: $i > $i > $o,SY3270: $i,SY3271: $i] :
( ~ ( in @ ( kpair @ SY3270 @ SY3271 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SX5: $i,SX6: $i] : ( SY3269 @ SX5 @ SX6 ) ) )
| ( in @ SY3271 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1093]) ).
thf(1400,plain,
! [SV218: $i,SV486: $i] :
( ( ~ ( in @ SV486 @ ( powerset @ SV218 ) )
| ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( powerset @ SV218 ) )
| ( ( setminus @ SV218 @ ( binunion @ SV486 @ SY3274 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SY3274 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1094]) ).
thf(1401,plain,
! [SV487: $i,SV219: $i] :
( ( ! [SY3275: $i] :
( ~ ~ ( in @ SY3275 @ SV219 )
| ~ ~ ( in @ SY3275 @ SV487 )
| ~ ( in @ SY3275 @ ( symdiff @ SV219 @ SV487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1402,plain,
! [SV220: $i,SV488: $i] :
( ( ~ ( in @ SV488 @ ( powerset @ SV220 ) )
| ! [SY3276: $i] :
( ~ ( in @ SY3276 @ SV220 )
| ~ ( in @ SY3276 @ SV488 )
| ~ ( in @ SY3276 @ ( setminus @ SV220 @ SV488 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1403,plain,
! [SV489: $i > $o,SV221: $i] :
( ( ~ ~ ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV221 )
| ( SV489 @ SY3277 ) )
| ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1404,plain,
! [SV490: $i,SV222: $i] :
( ( ( SV222 != SV490 )
| ( in @ SV222 @ ( setadjoin @ SV490 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1098]) ).
thf(1405,plain,
! [SV223: $i,SV491: $i] :
( ( ~ ( in @ SV491 @ ( powerset @ SV223 ) )
| ! [SY3279: $i] :
( ~ ( in @ SY3279 @ ( powerset @ SV223 ) )
| ! [SY3280: $i] :
( ~ ( in @ SY3280 @ SV223 )
| ~ ( in @ SY3280 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SY3279 ) ) )
| ( in @ SY3280 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SY3279 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1099]) ).
thf(1406,plain,
! [SV224: $i,SV492: $i] :
( ( ! [SY3281: $i] :
( ~ ( in @ SY3281 @ SV492 )
| ~ ( in @ SY3281 @ ( setminus @ SV224 @ SV492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1407,plain,
! [SV493: $i,SV225: $i] :
( ( ! [SY3282: $i] :
( ~ ( in @ SY3282 @ SV225 )
| ~ ~ ( in @ SY3282 @ SV493 )
| ~ ( subset @ SV225 @ SV493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1408,plain,
! [SV494: $i,SV226: $i] :
( ( ! [SY3283: $i] :
( ~ ( breln @ SV226 @ SV494 @ SY3283 )
| ! [SY3284: $i] :
( ~ ( breln @ SV226 @ SV494 @ SY3284 )
| ~ ! [SY3285: $i] :
( ~ ( in @ SY3285 @ SV226 )
| ! [SY3286: $i] :
( ~ ( in @ SY3286 @ SV494 )
| ~ ( in @ ( kpair @ SY3285 @ SY3286 ) @ SY3283 )
| ( in @ ( kpair @ SY3285 @ SY3286 ) @ SY3284 ) ) )
| ( subset @ SY3283 @ SY3284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1102]) ).
thf(1409,plain,
! [SV227: $i,SV495: $i] :
( ( ~ ( in @ SV495 @ ( powerset @ SV227 ) )
| ! [SY3287: $i] :
( ~ ( in @ SY3287 @ ( powerset @ SV227 ) )
| ( in @ ( binunion @ SV495 @ SY3287 ) @ ( powerset @ SV227 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1103]) ).
thf(1410,plain,
! [SV228: $i,SV496: $i] :
( ( ! [SY3288: $i] :
( ~ ( in @ SV496 @ ( powerset @ SV228 ) )
| ~ ( in @ SY3288 @ SV496 )
| ( in @ SY3288 @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1411,plain,
! [SV229: $i,SV497: $i] :
( ( ~ ( in @ SV497 @ ( powerset @ SV229 ) )
| ( subset @ SV497 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1412,plain,
! [SV498: $i,SV230: $i] :
( ( ~ ( subset @ SV230 @ SV498 )
| ( ( binintersect @ SV230 @ SV498 )
= SV230 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1106]) ).
thf(1413,plain,
! [SV499: $i,SV231: $i] :
( ( ! [SY3289: $i] :
( ~ ( in @ SY3289 @ SV231 )
| ! [SY3290: $i] :
( ~ ( in @ SY3290 @ SV499 )
| ( in @ ( setadjoin @ ( setadjoin @ SY3289 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY3289 @ ( setadjoin @ SY3290 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1107]) ).
thf(1414,plain,
! [SV232: $i,SV500: $i] :
( ( ~ ( in @ SV500 @ ( powerset @ SV232 ) )
| ! [SY3291: $i] :
( ~ ( in @ SY3291 @ ( powerset @ SV232 ) )
| ~ ! [SY3292: $i] :
( ~ ( in @ SY3292 @ SV232 )
| ~ ( in @ SY3292 @ SV500 )
| ( in @ SY3292 @ SY3291 ) )
| ( subset @ SV500 @ SY3291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1108]) ).
thf(1415,plain,
! [SV233: $i,SV501: $i] :
( ( ~ ( in @ SV501 @ ( powerset @ SV233 ) )
| ! [SY3293: $i] :
( ~ ( in @ SY3293 @ ( powerset @ SV233 ) )
| ~ ! [SY3294: $i] :
( ~ ( in @ SY3294 @ SV233 )
| ~ ( in @ SY3294 @ SV501 )
| ( in @ SY3294 @ SY3293 ) )
| ( in @ SV501 @ ( powerset @ SY3293 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1109]) ).
thf(1416,plain,
! [SV502: $i,SV234: $i] :
( ( ! [SY3295: $i] :
( ~ ( in @ SY3295 @ ( setadjoin @ SV234 @ ( setadjoin @ SV502 @ emptyset ) ) )
| ( SY3295 = SV234 )
| ( SY3295 = SV502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1110]) ).
thf(1417,plain,
! [SV235: $i,SV503: $i] :
( ( ~ ( in @ SV503 @ ( powerset @ SV235 ) )
| ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV235 )
| ~ ( in @ SY3296 @ SV503 )
| ( in @ SY3296 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1111]) ).
thf(1418,plain,
! [SV504: $i,SV236: $i] :
( ( ~ ~ ( subset @ SV236 @ SV504 )
| ( SV236 != SV504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1112]) ).
thf(1419,plain,
! [SV505: $o,SV237: $i] :
( ( ! [SY3297: $i] :
( ~ ( in @ SY3297 @ SV237 )
| ! [SY3298: $i] :
( ~ ( in @ SY3298 @ SV237 )
| ( in @ ( if @ SV237 @ SV505 @ SY3297 @ SY3298 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1113]) ).
thf(1420,plain,
! [SV237: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV237 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV237 )
| ( in @ ( if @ SV237 @ $true @ SX0 @ SX1 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1113]) ).
thf(1421,plain,
! [SV237: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV237 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV237 )
| ( in @ ( if @ SV237 @ $false @ SX0 @ SX1 ) @ SV237 ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1113]) ).
thf(1422,plain,
! [SV238: $i,SV506: $i] :
( ( ~ ( in @ SV506 @ ( powerset @ SV238 ) )
| ! [SY3299: $i] :
( ~ ( in @ SY3299 @ ( powerset @ SV238 ) )
| ! [SY3300: $i] :
( ~ ( in @ SY3300 @ ( powerset @ SV238 ) )
| ! [SY3301: $i] :
( ~ ( in @ SY3301 @ SV238 )
| ~ ( in @ SY3301 @ ( binintersect @ SV506 @ SY3299 ) )
| ( in @ SY3301 @ ( binunion @ SY3299 @ SY3300 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1114]) ).
thf(1423,plain,
! [SV507: $i > $o,SV239: $i] :
( ( ! [SY3302: $i] :
( ~ ( in @ SY3302
@ ( dsetconstr @ SV239
@ ^ [SY3303: $i] : ( SV507 @ SY3303 ) ) )
| ( in @ SY3302 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1424,plain,
! [SV508: $i,SV240: $i] :
( ( ~ ( breln1 @ SV240 @ SV508 )
| ! [SY3304: $i] :
( ~ ( breln1 @ SV240 @ SY3304 )
| ! [SY3305: $i] :
( ~ ( in @ SY3305 @ SV240 )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3306 ) @ ( breln1compset @ SV240 @ SV508 @ SY3304 ) )
| ! [SY3307: $o] :
( ~ ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3308 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3308 @ SY3306 ) @ SY3304 )
| SY3307 )
| SY3307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1425,plain,
! [SV509: $i,SV241: $i] :
( ( ~ ( breln1 @ SV241 @ SV509 )
| ! [SY3309: $i > $o] :
( ~ ! [SY3310: $i] :
( ~ ( in @ SY3310 @ SV241 )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ SV241 )
| ~ ( in @ ( kpair @ SY3310 @ SY3311 ) @ SV509 )
| ( SY3309 @ ( kpair @ SY3310 @ SY3311 ) ) ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV509 )
| ( SY3309 @ SY3312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1117]) ).
thf(1426,plain,
! [SV242: $i,SV510: $i] :
( ( ~ ( in @ SV510 @ ( powerset @ SV242 ) )
| ! [SY3313: $i] :
( ~ ( in @ SY3313 @ ( powerset @ SV242 ) )
| ! [SY3314: $i] :
( ~ ( in @ SY3314 @ SV242 )
| ~ ( in @ SY3314 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SY3313 ) ) )
| ~ ( in @ SY3314 @ SV510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1118]) ).
thf(1427,plain,
! [SV243: $i,SV511: $i] :
( ( ~ ( in @ SV511 @ ( powerset @ SV243 ) )
| ! [SY3315: $i] :
( ~ ( in @ SY3315 @ ( powerset @ SV243 ) )
| ! [SY3316: $i] :
( ~ ( in @ SY3316 @ SV243 )
| ~ ( in @ SY3316 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SY3315 ) ) )
| ( in @ SY3316 @ ( setminus @ SV243 @ SY3315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1119]) ).
thf(1428,plain,
! [SV512: $i,SV244: $i] :
( ( ! [SY3317: $i] :
( ~ ( in @ SY3317 @ ( funcSet @ SV244 @ SV512 ) )
| ( ( lam @ SV244 @ SV512
@ ^ [SY3318: $i] : ( ap @ SV244 @ SV512 @ SY3317 @ SY3318 ) )
= SY3317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1120]) ).
thf(1429,plain,
! [SV245: $i,SV513: $i] :
( ( ~ ( in @ SV513 @ ( powerset @ SV245 ) )
| ( in @ ( setminus @ SV245 @ SV513 ) @ ( powerset @ SV245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1121]) ).
thf(1430,plain,
! [SV514: $i,SV246: $i] :
( ( ( SV246 != SV514 )
| ( ( setunion @ SV246 )
= ( setunion @ SV514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1431,plain,
! [SV515: $i,SV247: $i] :
( ( ~ ( subset @ SV247 @ SV515 )
| ( ( setminus @ SV247 @ SV515 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1432,plain,
! [SV516: $i,SV248: $i] :
( ( ( SV248 != SV516 )
| ( subset @ SV516 @ SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1433,plain,
! [SV517: $i,SV249: $i] :
( ( ! [SY3319: $i > $i > $o,SY3320: $i] :
( ~ ( in @ SY3320 @ SV249 )
| ! [SY3321: $i] :
( ~ ( in @ SY3321 @ SV517 )
| ~ ( in @ ( kpair @ SY3320 @ SY3321 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SX5: $i,SX6: $i] : ( SY3319 @ SX5 @ SX6 ) ) )
| ( SY3319 @ SY3320 @ SY3321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1434,plain,
! [SV250: $i > $o] :
( ( ( ~ ~ ! [SY2811: $i] :
~ ! [SY2812: $i] :
~ ( ~ ( ~ ( SV250 @ SY2812 )
| ( SY2812 = SY2811 ) )
| ~ ( ( SY2812 != SY2811 )
| ( SV250 @ SY2812 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1435,plain,
! [SV518: $i,SV251: $i] :
( ( ! [SY3324: $i] :
( ~ ( breln @ SV251 @ SV518 @ SY3324 )
| ! [SY3325: $i] :
( ~ ( breln @ SV251 @ SV518 @ SY3325 )
| ~ ! [SY3326: $i] :
( ~ ( in @ SY3326 @ SV251 )
| ! [SY3327: $i] :
( ~ ( in @ SY3327 @ SV518 )
| ~ ( in @ ( kpair @ SY3326 @ SY3327 ) @ SY3324 )
| ( in @ ( kpair @ SY3326 @ SY3327 ) @ SY3325 ) ) )
| ~ ! [SY3328: $i] :
( ~ ( in @ SY3328 @ SV251 )
| ! [SY3329: $i] :
( ~ ( in @ SY3329 @ SV518 )
| ~ ( in @ ( kpair @ SY3328 @ SY3329 ) @ SY3325 )
| ( in @ ( kpair @ SY3328 @ SY3329 ) @ SY3324 ) ) )
| ( SY3324 = SY3325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1436,plain,
! [SV252: $i,SV519: $i] :
( ( ~ ( in @ SV519 @ ( powerset @ SV252 ) )
| ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV252 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SY3330 ) )
| ~ ( in @ SY3331 @ SY3330 )
| ~ ( in @ SY3331 @ SV519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1128]) ).
thf(1437,plain,
! [SV253: $i > $o,SV520: $i] :
( ( ~ ( in @ SV520 @ emptyset )
| ( SV253 @ SV520 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1129]) ).
thf(1438,plain,
! [SV254: $i] :
( ( ( ~ ~ ! [SY2826: $i] :
~ ( in @ SY2826 @ SV254 ) )
= $true )
| ( ( SV254 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1130]) ).
thf(1439,plain,
! [SV521: $i,SV255: $i] :
( ( ! [SY3332: $i] :
( ~ ( in @ SY3332 @ ( setminus @ SV255 @ SV521 ) )
| ( in @ SY3332 @ SV255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1131]) ).
thf(1440,plain,
! [SV522: $i > $o,SV256: $i] :
( ( ~ ~ ~ ! [SY3333: $i] :
~ ~ ( ~ ( in @ SY3333 @ SV256 )
| ~ ( SV522 @ SY3333 ) )
| ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1132]) ).
thf(1441,plain,
! [SV257: $i,SV523: $i] :
( ( ~ ( in @ SV523 @ SV257 )
| ( in @ SV523 @ ( powerset @ ( setunion @ SV257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1133]) ).
thf(1442,plain,
! [SV524: $i,SV258: $i] :
( ( ~ ( breln1 @ SV258 @ SV524 )
| ! [SY3335: $i] :
( ~ ( breln1 @ SV258 @ SY3335 )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV258 )
| ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV258 )
| ! [SY3338: $i] :
( ~ ( in @ SY3338 @ SV258 )
| ~ ( in @ ( kpair @ SY3336 @ SY3338 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3338 @ SY3337 ) @ SY3335 )
| ( in @ ( kpair @ SY3336 @ SY3337 ) @ ( breln1compset @ SV258 @ SV524 @ SY3335 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1134]) ).
thf(1443,plain,
! [SV525: $i,SV259: $i] :
( ( ~ ( breln1 @ SV259 @ SV525 )
| ! [SY3339: $i] :
( ~ ( breln1 @ SV259 @ SY3339 )
| ~ ! [SY3340: $i] :
( ~ ( in @ SY3340 @ SV259 )
| ! [SY3341: $i] :
( ~ ( in @ SY3341 @ SV259 )
| ~ ( in @ ( kpair @ SY3340 @ SY3341 ) @ SV525 )
| ( in @ ( kpair @ SY3340 @ SY3341 ) @ SY3339 ) ) )
| ~ ! [SY3342: $i] :
( ~ ( in @ SY3342 @ SV259 )
| ! [SY3343: $i] :
( ~ ( in @ SY3343 @ SV259 )
| ~ ( in @ ( kpair @ SY3342 @ SY3343 ) @ SY3339 )
| ( in @ ( kpair @ SY3342 @ SY3343 ) @ SV525 ) ) )
| ( SV525 = SY3339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1135]) ).
thf(1444,plain,
! [SV526: $i > $o,SV260: $i] :
( ( ! [SY3344: $i] :
( ~ ( in @ SY3344
@ ( dsetconstr @ SV260
@ ^ [SY3345: $i] : ( SV526 @ SY3345 ) ) )
| ( SV526 @ SY3344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1136]) ).
thf(1445,plain,
! [SV527: $i,SV261: $i] :
( ( ~ ! [SY3346: $i] :
~ ( ~ ( ~ ( in @ SY3346 @ SV261 )
| ( in @ SY3346 @ SV527 ) )
| ~ ( ~ ( in @ SY3346 @ SV527 )
| ( in @ SY3346 @ SV261 ) ) )
| ( SV261 = SV527 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1137]) ).
thf(1446,plain,
! [SV528: $i,SV262: $i] :
( ( ! [SY3347: $i] :
( ~ ( func @ SV262 @ SV528 @ SY3347 )
| ! [SY3348: $i] :
( ~ ( in @ SY3348 @ SV262 )
| ( singleton
@ ( dsetconstr @ SV528
@ ^ [SX4: $i] : ( in @ ( kpair @ SY3348 @ SX4 ) @ SY3347 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1447,plain,
! [SV263: $i > $o] :
( ( ( ~ ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV263 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV263 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1139]) ).
thf(1448,plain,
! [SV264: $i,SV529: $i] :
( ( ~ ( in @ SV529 @ ( powerset @ SV264 ) )
| ! [SY3350: $i] :
( ~ ( in @ SY3350 @ ( powerset @ SV264 ) )
| ! [SY3351: $i] :
( ~ ( in @ SY3351 @ SV264 )
| ~ ( subset @ SV529 @ SY3350 )
| ~ ~ ( in @ SY3351 @ SY3350 )
| ~ ( in @ SY3351 @ SV529 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1140]) ).
thf(1449,plain,
! [SV265: $i] :
( ( ( ~ ~ ! [SY2860: $i] :
~ ( in @ SY2860 @ SV265 ) )
= $true )
| ( ( ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1450,plain,
! [SV530: $i,SV266: $i] :
( ( ! [SY3352: $i] :
( ~ ~ ( in @ SY3352 @ SV266 )
| ~ ( in @ SY3352 @ ( setminus @ SV266 @ SV530 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1451,plain,
! [SV531: $i,SV267: $i] :
( ( ! [SY3353: $i,SY3354: $i] :
( ( ( kpair @ SV267 @ SV531 )
!= ( kpair @ SY3353 @ SY3354 ) )
| ( SV267 = SY3353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1143]) ).
thf(1452,plain,
! [SV268: $i] :
( ( ( ~ ( ( SV268 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1453,plain,
! [SV269: $i,SV532: $i] :
( ( ~ ( in @ SV532 @ ( powerset @ SV269 ) )
| ( subset @ ( setminus @ SV269 @ ( setminus @ SV269 @ SV532 ) ) @ SV532 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1145]) ).
thf(1454,plain,
! [SV533: $i,SV270: $i] :
( ( ~ ( in @ SV270 @ ( setadjoin @ SV533 @ emptyset ) )
| ( SV270 = SV533 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1146]) ).
thf(1455,plain,
! [SV271: $i] :
( ( ( ~ ( iskpair @ SV271 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV271 ) @ ( ksnd @ SV271 ) )
= SV271 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1147]) ).
thf(1456,plain,
! [SV272: $i,SV534: $i] :
( ( ~ ( in @ SV534 @ ( powerset @ SV272 ) )
| ! [SY3355: $i] :
( ~ ( in @ SY3355 @ ( powerset @ SV272 ) )
| ~ ( subset @ SV534 @ SY3355 )
| ( subset @ ( setminus @ SV272 @ SY3355 ) @ ( setminus @ SV272 @ SV534 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1148]) ).
thf(1457,plain,
! [SV535: $i,SV273: $i] :
( ( ! [SY3356: $i] :
( ~ ( in @ SY3356 @ SV273 )
| ! [SY3357: $i] :
( ~ ( in @ SY3357 @ SV535 )
| ( in @ ( kpair @ SY3356 @ SY3357 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1149]) ).
thf(1458,plain,
! [SV536: $i,SV274: $i] :
( ( ! [SY3358: $i] :
( ~ ( func @ SV274 @ SV536 @ SY3358 )
| ! [SY3359: $i] :
( ~ ( in @ SY3359 @ SV274 )
| ( ( ap @ SV274 @ SV536 @ SY3358 @ SY3359 )
= ( ap @ SV274 @ SV536 @ SY3358 @ SY3359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1150]) ).
thf(1459,plain,
! [SV275: $i,SV537: $i] :
( ( ~ ( in @ SV537 @ ( powerset @ SV275 ) )
| ! [SY3360: $i] :
( ~ ( in @ SY3360 @ ( powerset @ SV275 ) )
| ! [SY3361: $i] :
( ~ ( in @ SY3361 @ SV275 )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SY3360 ) )
| ( in @ SY3361 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SY3360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1151]) ).
thf(1460,plain,
! [SV538: $i,SV276: $i] :
( ( ! [SY3362: $i] :
( ~ ( func @ SV276 @ SV538 @ SY3362 )
| ! [SY3363: $i] :
( ~ ( in @ SY3363 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SX4: $i] : ( in @ ( kpair @ SY3363 @ SX4 ) @ SY3362 ) ) )
@ SV538 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1152]) ).
thf(1461,plain,
! [SV539: $i,SV277: $i] :
( ( ! [SY3365: $i] :
( ~ ( in @ SY3365 @ ( funcSet @ SV277 @ SV539 ) )
| ! [SY3366: $i] :
( ~ ( in @ SY3366 @ SV277 )
| ( in @ ( kpair @ SY3366 @ ( ap @ SV277 @ SV539 @ SY3365 @ SY3366 ) ) @ SY3365 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1153]) ).
thf(1462,plain,
! [SV540: $i > $o,SV278: $i] :
( ( ~ ~ ! [SY3367: $i] :
~ ~ ( ~ ( in @ SY3367 @ SV278 )
| ~ ~ ( SV540 @ SY3367 ) )
| ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1154]) ).
thf(1463,plain,
! [SV541: $i,SV279: $i] :
( ( ~ ( breln1 @ SV279 @ SV541 )
| ! [SY3369: $i] :
( ~ ( in @ SY3369 @ SV279 )
| ! [SY3370: $i] :
( ~ ( in @ SY3370 @ SV279 )
| ~ ( in @ ( kpair @ SY3369 @ SY3370 ) @ SV541 )
| ( in @ ( kpair @ SY3370 @ SY3369 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1464,plain,
! [SV542: $i,SV280: $i] :
( ( ! [SY3371: $i > $i] :
( ~ ! [SY3372: $i] :
( ~ ( in @ SY3372 @ SV280 )
| ( in @ ( SY3371 @ SY3372 ) @ SV542 ) )
| ! [SY3373: $i] :
( ~ ( in @ SY3373 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SX4: $i] : ( SY3371 @ SX4 ) )
@ SY3373 )
= ( SY3371 @ SY3373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1465,plain,
! [SV543: $i,SV281: $i] :
( ( ! [SY3375: $i,SY3376: $i] :
( ~ ( in @ ( kpair @ SY3375 @ SY3376 ) @ ( cartprod @ SV281 @ SV543 ) )
| ( in @ SY3375 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1157]) ).
thf(1466,plain,
! [SV544: $i,SV282: $i] :
( ( ! [SY3377: $i > $i] :
( ~ ! [SY3378: $i] :
( ~ ( in @ SY3378 @ SV282 )
| ( in @ ( SY3377 @ SY3378 ) @ SV544 ) )
| ( ( lam @ SV282 @ SV544
@ ^ [SX3: $i] : ( SY3377 @ SX3 ) )
= ( lam @ SV282 @ SV544
@ ^ [SX3: $i] : ( SY3377 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1158]) ).
thf(1467,plain,
! [SV283: $i,SV545: $i] :
( ( ~ ( in @ SV545 @ ( powerset @ SV283 ) )
| ! [SY3381: $i] :
( ~ ( in @ SY3381 @ ( powerset @ SV283 ) )
| ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SY3381 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1159]) ).
thf(1468,plain,
! [SV284: $i] :
( ( ( ~ ( ( SV284 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY2910: $i] :
~ ~ ( ~ ( in @ SY2910 @ SV284 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1469,plain,
! [SV546: $i,SV285: $i] :
( ( ! [SY3382: $i] :
( ~ ( in @ SY3382 @ SV285 )
| ~ ~ ( in @ SY3382 @ SV546 )
| ( SV285 != SV546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1161]) ).
thf(1470,plain,
! [SV547: $i,SV286: $i] :
( ( ! [SY3383: $i] :
( ~ ~ ( in @ SY3383 @ ( setminus @ SV286 @ SV547 ) )
| ~ ( in @ SY3383 @ SV286 )
| ( in @ SY3383 @ SV547 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1162]) ).
thf(1471,plain,
! [SV548: $i,SV287: $i] :
( ( ! [SY3384: $i] :
( ~ ( func @ SV287 @ SV548 @ SY3384 )
| ! [SY3385: $i] :
( ~ ( in @ SY3385 @ SV287 )
| ! [SY3386: $i] :
( ~ ( in @ SY3386 @ SV548 )
| ~ ( in @ ( kpair @ SY3385 @ SY3386 ) @ SY3384 )
| ( ( ap @ SV287 @ SV548 @ SY3384 @ SY3385 )
= SY3386 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1163]) ).
thf(1472,plain,
! [SV549: $o,SV288: $i] :
( ( ! [SY3387: $i] :
( ~ ( in @ SY3387 @ SV288 )
| ! [SY3388: $i] :
( ~ ( in @ SY3388 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3389: $i] :
( ~ ( ~ SV549
| ( SY3389 != SY3387 ) )
| ~ ( ~ ~ SV549
| ( SY3389 != SY3388 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1164]) ).
thf(1473,plain,
! [SV288: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV288 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1164]) ).
thf(1474,plain,
! [SV288: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV288 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1164]) ).
thf(1475,plain,
! [SV550: $i,SV289: $i] :
( ( ! [SY3390: $i] :
( ~ ( in @ SY3390 @ ( cartprod @ SV289 @ SV550 ) )
| ( ( kpair @ ( kfst @ SY3390 ) @ ( ksnd @ SY3390 ) )
= SY3390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1165]) ).
thf(1476,plain,
! [SV551: $i,SV290: $i] :
( ( ! [SY3391: $i] :
( ~ ( in @ SY3391 @ ( setadjoin @ SV290 @ ( setadjoin @ SV551 @ emptyset ) ) )
| ( SY3391 = SV290 )
| ( SY3391 = SV551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1166]) ).
thf(1477,plain,
! [SV291: $i > $o] :
( ( ( ~ ~ ! [SY2927: $i] :
~ ~ ( ~ ( SV291 @ SY2927 )
| ~ ! [SY2928: $i] :
( ~ ( SV291 @ SY2928 )
| ( SY2927 = SY2928 ) ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1478,plain,
! [SV552: $i,SV292: $i] :
( ( ~ ( in @ SV292 @ ( setadjoin @ SV552 @ emptyset ) )
| ( in @ SV552 @ ( setadjoin @ SV292 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1168]) ).
thf(1479,plain,
! [SV553: $i,SV293: $i] :
( ( ( SV293 != SV553 )
| ( ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV293 @ ( setadjoin @ SV553 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1169]) ).
thf(1480,plain,
! [SV554: $i,SV294: $i] :
( ( ! [SY3392: $i] :
( ~ ( in @ SY3392 @ SV294 )
| ~ ~ ( in @ SY3392 @ SV554 )
| ( in @ SY3392 @ ( setminus @ SV294 @ SV554 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1170]) ).
thf(1481,plain,
! [SV295: $i] :
( ( ( ~ ( in @ SV295 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1482,plain,
! [SV555: $o,SV296: $i] :
( ( ! [SY3393: $i] :
( ~ ( in @ SY3393 @ SV296 )
| ! [SY3394: $i] :
( ~ ( in @ SY3394 @ SV296 )
| ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3395: $i] :
( ~ ( ~ SV555
| ( SY3395 != SY3393 ) )
| ~ ( ~ ~ SV555
| ( SY3395 != SY3394 ) ) ) )
= ( setadjoin @ SY3393 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1172]) ).
thf(1483,plain,
! [SV296: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV296 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV296 )
| ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SX2: $i] :
( ~ ( ~ $true
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $true
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1172]) ).
thf(1484,plain,
! [SV296: $i] :
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV296 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SV296 )
| ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SX2: $i] :
( ~ ( ~ $false
| ( SX2 != SX0 ) )
| ~ ( ~ ~ $false
| ( SX2 != SX1 ) ) ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1172]) ).
thf(1485,plain,
! [SV556: $i > $i > $o,SV298: $i,SV2: $i] :
( ( breln @ SV2 @ SV298
@ ( dpsetconstr @ SV2 @ SV298
@ ^ [SY3396: $i,SY3397: $i] : ( SV556 @ SY3396 @ SY3397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1174]) ).
thf(1486,plain,
! [SV557: $i > $i > $o,SV299: $i,SV3: $i] :
( ( subset
@ ( dpsetconstr @ SV3 @ SV299
@ ^ [SY3398: $i,SY3399: $i] : ( SV557 @ SY3398 @ SY3399 ) )
@ ( cartprod @ SV3 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1175]) ).
thf(1487,plain,
! [SV558: $i,SV308: $i,SV15: $i] :
( ( ( binintersect @ SV15 @ ( binunion @ SV308 @ SV558 ) )
= ( binunion @ ( binintersect @ SV15 @ SV308 ) @ ( binintersect @ SV15 @ SV558 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1184]) ).
thf(1488,plain,
! [SV35: $i,SV320: $i] :
( ( ( ~ ( in @ SV320 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ! [SY2950: $i] :
( ~ ( in @ SY2950 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SY2950 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SY2950 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1489,plain,
! [SV321: $i,SV36: $i,SV559: $i] :
( ( ~ ( in @ SV559 @ ( setminus @ SV36 @ SV321 ) )
| ~ ( in @ SV559 @ SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1199]) ).
thf(1490,plain,
! [SV37: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ! [SY2952: $i] :
( ~ ( in @ SY2952 @ ( powerset @ SV37 ) )
| ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( powerset @ SV37 ) )
| ! [SY2954: $i] :
( ~ ( in @ SY2954 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY2953 )
| ~ ( subset @ SY2952 @ SY2954 )
| ( subset @ ( binintersect @ SV322 @ SY2952 ) @ ( binintersect @ SY2953 @ SY2954 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1200]) ).
thf(1491,plain,
! [SV38: $i > $o] :
( ( ( ~ ! [SY2204: $i] :
~ ~ ( ~ ( SV38 @ SY2204 )
| ~ ! [SY2205: $i] :
( ~ ( SV38 @ SY2205 )
| ( SY2204 = SY2205 ) ) ) )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1201]) ).
thf(1492,plain,
! [SV323: $i,SV39: $i] :
( ( ( ~ ( subset @ SV39 @ SV323 ) )
= $true )
| ( ( subset @ ( powerset @ SV39 ) @ ( powerset @ SV323 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1493,plain,
! [SV324: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV324 ) )
= $true )
| ( ( ! [SY2955: $i] :
( ~ ( breln1 @ SV40 @ SY2955 )
| ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SY2955 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1494,plain,
! [SV560: $i,SV325: $i,SV41: $i] :
( ( ~ ( subset @ SV41 @ SV325 )
| ~ ~ ( in @ SV560 @ SV325 )
| ~ ( in @ SV560 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1204]) ).
thf(1495,plain,
! [SV326: $i,SV42: $i,SV561: $i] :
( ( ~ ( in @ SV561 @ SV42 )
| ! [SY3400: $i] :
( ~ ( in @ SY3400 @ SV326 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SY3400 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1205]) ).
thf(1496,plain,
! [SV327: $i,SV43: $i,SV562: $i] :
( ( ~ ( in @ SV562 @ ( binintersect @ SV43 @ SV327 ) )
| ( in @ SV562 @ SV327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1206]) ).
thf(1497,plain,
! [SV328: $i,SV44: $i] :
( ( ( SV44 != SV328 )
= $true )
| ( ( ! [SY2960: $i > $o,SY2961: $i > $o] :
( ~ ! [SY2962: $i] :
( ~ ( in @ SY2962 @ SV44 )
| ! [SY2963: $i] :
( ~ ( in @ SY2963 @ SV328 )
| ( SY2962 != SY2963 )
| ~ ( ~ ( ~ ( SY2960 @ SY2962 )
| ( SY2961 @ SY2963 ) )
| ~ ( ~ ( SY2961 @ SY2963 )
| ( SY2960 @ SY2962 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SX4: $i] : ( SY2960 @ SX4 ) )
= ( dsetconstr @ SV328
@ ^ [SX4: $i] : ( SY2961 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1207]) ).
thf(1498,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
| ~ ! [SY3410: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY3410 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3410 ) )
| ~ ! [SY3413: $i] :
~ ~ ! [SY3414: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3413 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3414 @ SY3410 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3413 )
| ~ ( in @ SX5 @ SY3410 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3413 ) )
| ( in @ SY3414 @ SY3416 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1208]) ).
thf(1499,plain,
! [SV329: $i > $o,SV46: $i] :
( ( ( ~ ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) ) )
= $true )
| ( ( ! [SY2967: $i] :
( ~ ( in @ SY2967 @ SV46 )
| ! [SY2968: $i] :
( ~ ( in @ SY2968 @ SV46 )
| ~ ( SV329 @ SY2967 )
| ~ ( SV329 @ SY2968 )
| ( SY2967 = SY2968 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1500,plain,
! [SV47: $o] :
( ( SV47 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1501,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1502,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1503,plain,
! [SV48: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV48 ) )
= $true )
| ( ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV48 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1213]) ).
thf(1504,plain,
! [SV331: $i,SV563: $i > $i,SV49: $i] :
( ( ~ ! [SY3418: $i] :
( ~ ( in @ SY3418 @ SV49 )
| ( in @ ( SV563 @ SY3418 ) @ SV331 ) )
| ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1214]) ).
thf(1505,plain,
! [SV50: $i] :
( ( ( singleton @ SV50 )
= $false )
| ( ( ! [SY2251: $i] :
( ~ ( in @ SY2251 @ SV50 )
| ( ( setunion @ SV50 )
= SY2251 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1506,plain,
! [SV332: $i,SV51: $i] :
( ( ( ~ ! [SY2972: $i] :
( ~ ( in @ SY2972 @ SV51 )
| ( in @ SY2972 @ SV332 ) ) )
= $true )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1507,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) ) )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1508,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ( ~ ( in @ SV333 @ ( setunion @ SV53 ) )
| ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
| ~ ( ~ ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) )
| ( in @ SV333 @ ( setunion @ SV53 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1218]) ).
thf(1509,plain,
! [SV334: $i > $o,SV54: $i,SV564: $i] :
( ( ~ ( in @ SV564 @ SV54 )
| ~ ( SV334 @ SV564 )
| ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1219]) ).
thf(1510,plain,
! [SV335: $i,SV565: $i > $i,SV55: $i] :
( ( ~ ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV55 )
| ( in @ ( SV565 @ SY3422 ) @ SV335 ) )
| ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1511,plain,
! [SV336: $i,SV56: $i,SV566: $i] :
( ( ~ ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) )
| ! [SY3425: $i] :
( ~ ( in @ SY3425 @ SV56 )
| ( ( ap @ SV56 @ SV336 @ SV566 @ SY3425 )
= ( ap @ SV56 @ SV336 @ SV566 @ SY3425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1512,plain,
! [SV57: $i,SV337: $i] :
( ( ( ~ ( in @ SV337 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( ! [SY2984: $i] :
( ~ ( in @ SY2984 @ ( powerset @ SV57 ) )
| ! [SY2985: $i] :
( ~ ( in @ SY2985 @ SV57 )
| ~ ( in @ SY2985 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SY2984 ) ) )
| ( in @ SY2985 @ ( setminus @ SV57 @ SV337 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1513,plain,
! [SV567: $i,SV338: $i,SV58: $i] :
( ( ! [SY3426: $i] :
( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV338 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV567 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV567 @ ( setadjoin @ SY3426 @ emptyset ) ) @ emptyset ) ) )
| ( SV338 = SY3426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1514,plain,
! [SV59: $i,SV339: $i] :
( ( ( ~ ( in @ SV339 @ ( powerset @ SV59 ) ) )
= $true )
| ( ( ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV59 )
| ~ ~ ( in @ SY2988 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SY2988 @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1224]) ).
thf(1515,plain,
! [SV60: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( powerset @ SV60 ) ) )
= $true )
| ( ( SV340
= ( setminus @ SV60 @ ( setminus @ SV60 @ SV340 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1516,plain,
! [SV341: $i,SV61: $i,SV568: $i] :
( ( ~ ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
| ! [SY3427: $i] :
( ~ ( in @ SY3427 @ ( funcSet @ SV61 @ SV341 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3428 )
= ( ap @ SV61 @ SV341 @ SY3427 @ SY3428 ) ) )
| ( SV568 = SY3427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1226]) ).
thf(1517,plain,
! [SV62: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ! [SY2992: $i] :
( ~ ( in @ SY2992 @ ( powerset @ SV62 ) )
| ~ ( subset @ SV342 @ ( setminus @ SV62 @ SY2992 ) )
| ( subset @ SY2992 @ ( setminus @ SV62 @ SV342 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1518,plain,
! [SV63: $i,SV343: $i] :
( ( ( ~ ( in @ SV343 @ ( powerset @ SV63 ) ) )
= $true )
| ( ( ! [SY2993: $i] :
( ~ ( in @ SY2993 @ ( powerset @ SV63 ) )
| ! [SY2994: $i] :
( ~ ( in @ SY2994 @ SV63 )
| ~ ~ ( in @ SY2994 @ ( binunion @ SV343 @ SY2993 ) )
| ~ ( in @ SY2994 @ SY2993 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1519,plain,
! [SV64: $i,SV344: $i] :
( ( ( ~ ( in @ SV344 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ! [SY2995: $i] :
( ~ ( in @ SY2995 @ ( powerset @ SV64 ) )
| ! [SY2996: $i] :
( ~ ( in @ SY2996 @ ( powerset @ SV64 ) )
| ~ ( subset @ SY2995 @ SY2996 )
| ( subset @ ( binintersect @ SV344 @ SY2995 ) @ SY2996 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1520,plain,
! [SV65: $i,SV345: $i] :
( ( ( ~ ( in @ SV345 @ ( powerset @ SV65 ) ) )
= $true )
| ( ( ! [SY2997: $i] :
( ~ ( in @ SY2997 @ ( powerset @ SV65 ) )
| ! [SY2998: $i] :
( ~ ( in @ SY2998 @ SV65 )
| ~ ~ ( in @ SY2998 @ SY2997 )
| ~ ( in @ SY2998 @ ( binintersect @ SV345 @ SY2997 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1521,plain,
! [SV66: $i,SV346: $i] :
( ( ( ~ ( in @ SV346 @ ( powerset @ SV66 ) ) )
= $true )
| ( ( ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV66 )
| ~ ( in @ SY2999 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SY2999 @ SV346 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1231]) ).
thf(1522,plain,
! [SV67: $i,SV347: $i] :
( ( ( ~ ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV347 )
| ( in @ SY3000 @ SV67 ) ) )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1523,plain,
! [SV348: $i,SV68: $i] :
( ( ( ~ ( breln1 @ SV68 @ SV348 ) )
= $true )
| ( ( ! [SY3001: $i] :
( ~ ( breln1 @ SV68 @ SY3001 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV68 )
| ! [SY3003: $i] :
( ~ ( in @ SY3003 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3003 ) @ ( breln1compset @ SV68 @ SV348 @ SY3001 ) )
| ~ ! [SY3004: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3004 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3004 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3004 @ SY3003 ) @ SY3001 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1524,plain,
! [SV69: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ! [SY3005: $i] :
( ~ ( in @ SY3005 @ ( powerset @ SV69 ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV69 )
| ~ ( in @ SY3006 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SY3005 ) ) )
| ( in @ SY3006 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SY3005 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1234]) ).
thf(1525,plain,
! [SV350: $i,SV569: $i > $i,SV70: $i] :
( ( ~ ! [SY3429: $i] :
( ~ ( in @ SY3429 @ SV70 )
| ( in @ ( SV569 @ SY3429 ) @ SV350 ) )
| ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1526,plain,
! [SV570: $i > $i > $o,SV351: $i,SV71: $i] :
( ( ! [SY3432: $i] :
( ~ ( in @ SY3432 @ SV71 )
| ! [SY3433: $i] :
( ~ ( in @ SY3433 @ SV351 )
| ~ ( SV570 @ SY3432 @ SY3433 )
| ( in @ ( kpair @ SY3432 @ SY3433 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1236]) ).
thf(1527,plain,
! [SV352: $i,SV72: $i,SV571: $i] :
( ( ~ ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) )
| ! [SY3436: $i] :
( ~ ( in @ SY3436 @ SV72 )
| ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SY3436 ) @ SV352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1237]) ).
thf(1528,plain,
! [SV572: $i > $i > $o,SV353: $i,SV73: $i] :
( ( ! [SY3437: $i,SY3438: $i] :
( ~ ( in @ ( kpair @ SY3437 @ SY3438 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SY3439: $i,SY3440: $i] : ( SV572 @ SY3439 @ SY3440 ) ) )
| ( SV572 @ SY3437 @ SY3438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1238]) ).
thf(1529,plain,
! [SV573: $i > $i > $o,SV354: $i,SV74: $i] :
( ( ~ ! [SY3441: $i] :
( ~ ( in @ SY3441 @ SV74 )
| ~ ! [SY3442: $i] :
~ ~ ( ~ ( in @ SY3442 @ SV354 )
| ~ ( SV573 @ SY3441 @ SY3442 ) ) )
| ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1530,plain,
! [SV574: $i,SV355: $i,SV75: $i] :
( ( ~ ( func @ SV75 @ SV355 @ SV574 )
| ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV75 )
| ( in @ ( kpair @ SY3447 @ ( ap @ SV75 @ SV355 @ SV574 @ SY3447 ) ) @ SV574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1240]) ).
thf(1531,plain,
! [SV356: $i > $o,SV76: $i] :
( ( ( ~ ~ ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV76 )
| ( SV356 @ SY3032 ) ) )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1532,plain,
! [SV575: $i,SV357: $i,SV77: $i] :
( ( ~ ( subset @ SV77 @ SV357 )
| ~ ( in @ SV575 @ SV77 )
| ( in @ SV575 @ SV357 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1242]) ).
thf(1533,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK3_SY3035 )
| ! [SY3448: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY3448 )
| ! [SY3449: $i] :
( ~ ( in @ SY3449 @ sK1_SX0 )
| ! [SY3450: $i] :
( ~ ( in @ SY3450 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY3449 @ SY3450 ) @ SY3448 )
| ( in @ ( kpair @ SY3449 @ SY3450 ) @ ( binunion @ sK3_SY3035 @ SY3448 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1243]) ).
thf(1534,plain,
! [SV358: $i,SV78: $i] :
( ( ( SV78 != SV358 )
= $true )
| ( ( ! [SY3039: $i,SY3040: $i] :
( ( SY3039 != SY3040 )
| ~ ( in @ SY3039 @ SV78 )
| ( in @ SY3040 @ SV358 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1535,plain,
! [SV359: $i,SV79: $i] :
( ( ( ~ ( subset @ SV79 @ SV359 ) )
= $true )
| ( ( ~ ( subset @ SV359 @ SV79 )
| ( SV79 = SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1536,plain,
! [SV576: $i,SV360: $i,SV80: $i] :
( ( ! [SY3451: $i] :
( ( ( kpair @ SV80 @ SV360 )
!= ( kpair @ SV576 @ SY3451 ) )
| ( SV360 = SY3451 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1246]) ).
thf(1537,plain,
! [SV577: $i,SV361: $i,SV81: $i] :
( ( ~ ( func @ SV81 @ SV361 @ SV577 )
| ! [SY3452: $i] :
( ~ ( func @ SV81 @ SV361 @ SY3452 )
| ~ ! [SY3453: $i] :
( ~ ( in @ SY3453 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3453 )
= ( ap @ SV81 @ SV361 @ SY3452 @ SY3453 ) ) )
| ! [SY3454: $i] :
( ~ ( in @ SY3454 @ SV81 )
| ! [SY3455: $i] :
( ~ ( in @ SY3455 @ SV361 )
| ~ ( in @ ( kpair @ SY3454 @ SY3455 ) @ SY3452 )
| ( in @ ( kpair @ SY3454 @ SY3455 ) @ SV577 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1247]) ).
thf(1538,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ( ~ ( in @ SV362 @ ( powerset @ SV82 ) )
| ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) )
| ~ ( ~ ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) )
| ( in @ SV362 @ ( powerset @ SV82 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1539,plain,
! [SV363: $i,SV83: $i] :
( ( ( SV83 != SV363 )
= $true )
| ( ( ! [SY3050: $i,SY3051: $i] :
( ( SY3050 != SY3051 )
| ~ ( ~ ( ~ ( in @ SY3050 @ SV83 )
| ( in @ SY3051 @ SV363 ) )
| ~ ( ~ ( in @ SY3051 @ SV363 )
| ( in @ SY3050 @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1540,plain,
! [SV364: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
!= ( setadjoin @ SV364 @ emptyset ) )
= $true )
| ( ( SV84 = SV364 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1541,plain,
! [SV85: $i,SV365: $i] :
( ( ( ~ ( in @ SV365 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ! [SY3052: $i] :
( ~ ( in @ SY3052 @ ( powerset @ SV85 ) )
| ! [SY3053: $o,SY3054: $i] :
( ~ ( in @ SY3054 @ SV85 )
| ~ ( in @ SY3054 @ ( binunion @ SV365 @ SY3052 ) )
| ~ ( ~ ( in @ SY3054 @ SV365 )
| SY3053 )
| ~ ( ~ ( in @ SY3054 @ SY3052 )
| SY3053 )
| SY3053 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1251]) ).
thf(1542,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ! [SY3456: $o] :
( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
| ~ ( ~ ( in @ SV578 @ SV86 )
| SY3456 )
| ~ ( ~ ( in @ SV578 @ SV366 )
| SY3456 )
| SY3456 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1252]) ).
thf(1543,plain,
! [SV367: $i,SV87: $i,SV579: $i] :
( ( ~ ( in @ SV579 @ SV87 )
| ~ ( in @ SV579 @ SV367 )
| ~ ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1253]) ).
thf(1544,plain,
! [SV368: $i,SV88: $i,SV580: $i] :
( ( ~ ( in @ SV580 @ ( cartprod @ SV88 @ SV368 ) )
| ( in @ ( ksnd @ SV580 ) @ SV368 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1254]) ).
thf(1545,plain,
! [SV369: $i,SV89: $i,SV581: $i] :
( ( ~ ( in @ SV581 @ SV89 )
| ! [SY3457: $i] :
( ~ ( in @ SY3457 @ SV369 )
| ( ( ksnd @ ( kpair @ SV581 @ SY3457 ) )
= SY3457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1255]) ).
thf(1546,plain,
! [SV370: $i,SV90: $i,SV582: $i] :
( ( ~ ( in @ SV582 @ ( funcSet @ SV90 @ SV370 ) )
| ( func @ SV90 @ SV370 @ SV582 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1256]) ).
thf(1547,plain,
! [SV371: $i,SV91: $i] :
( ( ( SV91 != SV371 )
= $true )
| ( ( subset @ SV91 @ SV371 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1548,plain,
! [SV372: $i,SV92: $i,SV583: $i] :
( ( ~ ( in @ SV583 @ SV92 )
| ! [SY3458: $i] :
( ~ ( in @ SY3458 @ SV372 )
| ( ( kpair @ SV583 @ SY3458 )
= ( kpair @ SV583 @ SY3458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1258]) ).
thf(1549,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ~ ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
| ! [SY3459: $o] :
( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SY3459 )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SY3459 )
| SY3459 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1259]) ).
thf(1550,plain,
! [SV374: $i,SV94: $i,SV585: $i] :
( ( ~ ( in @ SV585 @ SV94 )
| ~ ~ ( in @ SV585 @ SV374 )
| ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1260]) ).
thf(1551,plain,
! [SV95: $i > $o] :
( ( ( ~ ! [SY2388: $i] :
~ ( SV95 @ SY2388 ) )
= $false )
| ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1552,plain,
! [SV375: $i,SV96: $i] :
( ( ( SV96 != SV375 )
= $true )
| ( ( ! [SY3067: $i,SY3068: $i] :
( ( SY3067 != SY3068 )
| ( ( setadjoin @ SV96 @ SY3067 )
= ( setadjoin @ SV375 @ SY3068 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1262]) ).
thf(1553,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY3069: $i,SY3070: $i] :
( ( SY3069 != SY3070 )
| ~ ( ~ ( ~ ( SV97 @ SY3069 )
| ( SV376 @ SY3070 ) )
| ~ ( ~ ( SV376 @ SY3070 )
| ( SV97 @ SY3069 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1263]) ).
thf(1554,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3077: $i] :
( ~ ( in @ SY3077 @ SV98 )
| ! [SY3078: $i] :
( ~ ( in @ SY3078 @ SV98 )
| ~ ( SV377 @ SY3077 )
| ~ ( SV377 @ SY3078 )
| ( SY3077 = SY3078 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1264]) ).
thf(1555,plain,
! [SV99: $o,SV378: $i] :
( ( ( ~ ( in @ SV378 @ ( prop2set @ SV99 ) ) )
= $true )
| ( SV99 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1265]) ).
thf(1556,plain,
! [SV379: $i] :
( ( ( ~ ( in @ SV379 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1266]) ).
thf(1557,plain,
! [SV380: $i] :
( ( ( ~ ( in @ SV380 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1558,plain,
! [SV381: $i,SV100: $i,SV586: $i] :
( ( ~ ( in @ SV586 @ SV100 )
| ! [SY3460: $i] :
( ~ ( in @ SY3460 @ SV381 )
| ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SY3460 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1268]) ).
thf(1559,plain,
! [SV101: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ ( powerset @ SV101 ) ) )
= $true )
| ( ( ! [SY3083: $i] :
( ~ ( in @ SY3083 @ ( powerset @ SV101 ) )
| ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SY3083 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1269]) ).
thf(1560,plain,
! [SV102: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ! [SY3084: $i] :
( ~ ( in @ SY3084 @ ( powerset @ SV102 ) )
| ~ ( subset @ ( setminus @ SV102 @ SY3084 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SY3084 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1270]) ).
thf(1561,plain,
! [SV384: $i,SV103: $i,SV587: $i] :
( ( ~ ( in @ ( setadjoin @ SV587 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ ( setadjoin @ SV384 @ emptyset ) ) @ emptyset ) ) )
| ( SV103 = SV587 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1271]) ).
thf(1562,plain,
! [SV104: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ ( powerset @ SV104 ) ) )
= $true )
| ( ( ! [SY3086: $i] :
( ~ ( in @ SY3086 @ ( powerset @ SV104 ) )
| ! [SY3087: $i] :
( ~ ( in @ SY3087 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SY3086 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3087 ) @ ( binunion @ SY3086 @ SY3087 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1272]) ).
thf(1563,plain,
! [SV105: $i > $o] :
( ( ( ~ ! [SY2423: $i] :
~ ~ ( ~ ( SV105 @ SY2423 )
| ~ ! [SY2424: $i] :
( ~ ( SV105 @ SY2424 )
| ( SY2423 = SY2424 ) ) ) )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1273]) ).
thf(1564,plain,
! [SV386: $i > $o,SV106: $i] :
( ( ( ~ ~ ~ ! [SY3088: $i] :
~ ~ ( ~ ( in @ SY3088 @ SV106 )
| ~ ( SV386 @ SY3088 ) ) )
= $true )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1274]) ).
thf(1565,plain,
! [SV107: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( powerset @ SV107 ) ) )
= $true )
| ( ( ! [SY3090: $i] :
( ~ ( in @ SY3090 @ ( powerset @ SV107 ) )
| ! [SY3091: $i] :
( ~ ( in @ SY3091 @ SV107 )
| ~ ~ ( in @ SY3091 @ SV387 )
| ~ ( in @ SY3091 @ ( binintersect @ SV387 @ SY3090 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1275]) ).
thf(1566,plain,
! [SV388: $o,SV108: $i,SV588: $i] :
( ( ~ ( in @ SV588 @ SV108 )
| ! [SY3461: $i] :
( ~ ( in @ SY3461 @ SV108 )
| ( in @ ( if @ SV108 @ SV388 @ SV588 @ SY3461 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SY3461 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1276]) ).
thf(1567,plain,
! [SV108: $i,SV589: $i] :
( ( ~ ( in @ SV589 @ SV108 )
| ! [SY3462: $i] :
( ~ ( in @ SY3462 @ SV108 )
| ( in @ ( if @ SV108 @ $true @ SV589 @ SY3462 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SY3462 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1568,plain,
! [SV108: $i,SV590: $i] :
( ( ~ ( in @ SV590 @ SV108 )
| ! [SY3463: $i] :
( ~ ( in @ SY3463 @ SV108 )
| ( in @ ( if @ SV108 @ $false @ SV590 @ SY3463 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SY3463 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1278]) ).
thf(1569,plain,
! [SV109: $i,SV389: $i,SV591: $i] :
( ( ~ ( in @ SV591 @ SV389 )
| ( in @ SV591 @ ( binunion @ SV109 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1279]) ).
thf(1570,plain,
! [SV390: $i,SV110: $i] :
( ( ( ( binintersect @ SV110 @ SV390 )
!= SV390 )
= $true )
| ( ( subset @ SV390 @ SV110 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1280]) ).
thf(1571,plain,
! [SV111: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( powerset @ SV111 ) ) )
= $true )
| ( ( ! [SY3095: $i] :
( ~ ( in @ SY3095 @ ( powerset @ SV111 ) )
| ~ ! [SY3096: $i] :
( ~ ( in @ SY3096 @ SV111 )
| ~ ( in @ SY3096 @ SV391 )
| ( in @ SY3096 @ SY3095 ) )
| ~ ! [SY3097: $i] :
( ~ ( in @ SY3097 @ SV111 )
| ~ ( in @ SY3097 @ SY3095 )
| ( in @ SY3097 @ SV391 ) )
| ( SV391 = SY3095 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1572,plain,
! [SV112: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ! [SY3098: $i] :
( ~ ( in @ SY3098 @ ( powerset @ SV112 ) )
| ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV112 )
| ~ ~ ( in @ SY3099 @ SV392 )
| ~ ~ ( in @ SY3099 @ SY3098 )
| ~ ( in @ SY3099 @ ( binunion @ SV392 @ SY3098 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1282]) ).
thf(1573,plain,
! [SV393: $i,SV113: $i] :
( ( ( ~ ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV113 )
| ( in @ SY3100 @ SV393 ) ) )
= $true )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1283]) ).
thf(1574,plain,
! [SV394: $i,SV114: $i,SV592: $i] :
( ( ~ ~ ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
| ~ ~ ( in @ SV592 @ SV394 )
| ~ ( in @ SV592 @ SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1284]) ).
thf(1575,plain,
! [SV395: $i,SV115: $i] :
( ( ( ~ ( breln1 @ SV115 @ SV395 ) )
= $true )
| ( ( breln1 @ SV115 @ ( breln1invset @ SV115 @ SV395 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1285]) ).
thf(1576,plain,
! [SV116: $i] :
( ( ( in @ SV116 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV116 @ SV116 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1577,plain,
! [SV396: $o,SV117: $i,SV593: $i] :
( ( ~ ( in @ SV593 @ SV117 )
| ! [SY3464: $i] :
( ~ ( in @ SY3464 @ SV117 )
| ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3465: $i] :
( ~ ( ~ SV396
| ( SY3465 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3465 != SY3464 ) ) ) )
= ( setadjoin @ SY3464 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1287]) ).
thf(1578,plain,
! [SV117: $i,SV594: $i] :
( ( ~ ( in @ SV594 @ SV117 )
| ! [SY3466: $i] :
( ~ ( in @ SY3466 @ SV117 )
| ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3467: $i] :
( ~ ( ~ $true
| ( SY3467 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3467 != SY3466 ) ) ) )
= ( setadjoin @ SY3466 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1288]) ).
thf(1579,plain,
! [SV117: $i,SV595: $i] :
( ( ~ ( in @ SV595 @ SV117 )
| ! [SY3468: $i] :
( ~ ( in @ SY3468 @ SV117 )
| ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3469: $i] :
( ~ ( ~ $false
| ( SY3469 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3469 != SY3468 ) ) ) )
= ( setadjoin @ SY3468 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1289]) ).
thf(1580,plain,
! [SV118: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ ( powerset @ SV118 ) ) )
= $true )
| ( ( ! [SY3105: $i] :
( ~ ( in @ SY3105 @ ( powerset @ SV118 ) )
| ! [SY3106: $i] :
( ~ ( in @ SY3106 @ ( binintersect @ SV397 @ SY3105 ) )
| ( in @ SY3106 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1581,plain,
! [SV398: $i,SV119: $i,SV596: $i] :
( ( ~ ( in @ SV596 @ ( cartprod @ SV119 @ SV398 ) )
| ( iskpair @ SV596 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1291]) ).
thf(1582,plain,
! [SV399: $i,SV597: $i,SV120: $i] :
( ( ~ ( subset @ SV120 @ SV597 )
| ( subset @ SV120 @ ( setadjoin @ SV399 @ SV597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1292]) ).
thf(1583,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ~ ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV121 )
| ~ ( SV400 @ SY3109 ) ) )
= $true )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1293]) ).
thf(1584,plain,
! [SV122: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ ( powerset @ SV122 ) ) )
= $true )
| ( ( ! [SY3111: $i] :
( ~ ( in @ SY3111 @ ( powerset @ SV122 ) )
| ! [SY3112: $i] :
( ~ ( in @ SY3112 @ SV122 )
| ~ ( in @ SY3112 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SY3111 ) ) )
| ( in @ SY3112 @ ( setminus @ SV122 @ SV401 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1294]) ).
thf(1585,plain,
! [SV598: $i > $i > $o,SV402: $i,SV123: $i] :
( ( ! [SY3470: $i,SY3471: $i] :
( ~ ( in @ ( kpair @ SY3470 @ SY3471 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SY3472: $i,SY3473: $i] : ( SV598 @ SY3472 @ SY3473 ) ) )
| ( in @ SY3470 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1295]) ).
thf(1586,plain,
! [SV403: $i,SV124: $i,SV599: $i] :
( ( ~ ( in @ SV599 @ SV124 )
| ( in @ SV599 @ ( binunion @ SV124 @ SV403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1587,plain,
! [SV600: $i,SV404: $i,SV125: $i] :
( ( ~ ( func @ SV125 @ SV404 @ SV600 )
| ! [SY3474: $i] :
( ~ ( in @ SY3474 @ SV125 )
| ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SY3474 ) @ SV404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1588,plain,
! [SV601: $i,SV405: $i,SV126: $i] :
( ( ~ ( breln @ SV126 @ SV405 @ SV601 )
| ! [SY3475: $i > $o] :
( ~ ! [SY3476: $i] :
( ~ ( in @ SY3476 @ SV126 )
| ! [SY3477: $i] :
( ~ ( in @ SY3477 @ SV405 )
| ~ ( in @ ( kpair @ SY3476 @ SY3477 ) @ SV601 )
| ( SY3475 @ ( kpair @ SY3476 @ SY3477 ) ) ) )
| ! [SY3478: $i] :
( ~ ( in @ SY3478 @ SV601 )
| ( SY3475 @ SY3478 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1298]) ).
thf(1589,plain,
! [SV127: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ ( powerset @ SV127 ) ) )
= $true )
| ( ( ! [SY3126: $i] :
( ~ ( in @ SY3126 @ ( powerset @ SV127 ) )
| ! [SY3127: $i] :
( ~ ( in @ SY3127 @ SV127 )
| ~ ( in @ SY3127 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3127 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SY3126 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1299]) ).
thf(1590,plain,
! [SV407: $i,SV128: $i,SV602: $i] :
( ( ~ ~ ( in @ SV602 @ SV128 )
| ~ ( in @ SV602 @ SV407 )
| ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1300]) ).
thf(1591,plain,
! [SV129: $i > $o] :
( ( ( ~ ! [SY2490: $i] :
~ ~ ( ~ ( SV129 @ SY2490 )
| ~ ! [SY2491: $i] :
( ~ ( SV129 @ SY2491 )
| ( SY2490 = SY2491 ) ) ) )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1301]) ).
thf(1592,plain,
! [SV408: $i,SV130: $i,SV603: $i] :
( ( ~ ( in @ SV603 @ ( setadjoin @ SV130 @ SV408 ) )
| ( SV603 = SV130 )
| ( in @ SV603 @ SV408 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1302]) ).
thf(1593,plain,
! [SV131: $i] :
( ( ( iskpair @ SV131 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV131 )
@ ^ [SY2496: $i] : ( in @ ( setadjoin @ SY2496 @ emptyset ) @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1594,plain,
! [SV132: $i,SV409: $i] :
( ( ( ~ ( in @ SV409 @ ( powerset @ SV132 ) ) )
= $true )
| ( ( ! [SY3130: $i] :
( ~ ( in @ SY3130 @ ( powerset @ SV132 ) )
| ! [SY3131: $i] :
( ~ ( in @ SY3131 @ SV132 )
| ~ ( in @ SY3131 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SY3130 ) ) )
| ( in @ SY3131 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SY3130 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1304]) ).
thf(1595,plain,
! [SV133: $i,SV410: $i] :
( ( ( ~ ( subset @ SV410 @ SV133 ) )
= $true )
| ( ( ( binintersect @ SV133 @ SV410 )
= SV410 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1305]) ).
thf(1596,plain,
! [SV134: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ! [SY3132: $i] :
( ~ ( in @ SY3132 @ ( powerset @ SV134 ) )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SY3132 ) )
| ~ ( in @ SY3133 @ SV411 )
| ( in @ SY3133 @ SY3132 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1306]) ).
thf(1597,plain,
! [SV135: $i] :
( ( ( ! [SY2504: $i] :
~ ( in @ SY2504 @ SV135 ) )
= $false )
| ( ( SV135 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1307]) ).
thf(1598,plain,
! [SV412: $i,SV136: $i,SV604: $i] :
( ( ~ ( in @ SV604 @ ( binintersect @ SV136 @ SV412 ) )
| ( in @ SV604 @ SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1308]) ).
thf(1599,plain,
! [SV605: $i,SV413: $i,SV137: $i] :
( ( ~ ( func @ SV137 @ SV413 @ SV605 )
| ! [SY3479: $i] :
( ~ ( func @ SV137 @ SV413 @ SY3479 )
| ~ ! [SY3480: $i] :
( ~ ( in @ SY3480 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3480 )
= ( ap @ SV137 @ SV413 @ SY3479 @ SY3480 ) ) )
| ( SV605 = SY3479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1309]) ).
thf(1600,plain,
! [SV414: $o,SV138: $i,SV606: $i] :
( ( ~ ( in @ SV606 @ SV138 )
| ! [SY3481: $i] :
( ~ ( in @ SY3481 @ SV138 )
| ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3482: $i] :
( ~ ( ~ SV414
| ( SY3482 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3482 != SY3481 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1310]) ).
thf(1601,plain,
! [SV138: $i,SV607: $i] :
( ( ~ ( in @ SV607 @ SV138 )
| ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV138 )
| ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3484: $i] :
( ~ ( ~ $true
| ( SY3484 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3484 != SY3483 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1602,plain,
! [SV138: $i,SV608: $i] :
( ( ~ ( in @ SV608 @ SV138 )
| ! [SY3485: $i] :
( ~ ( in @ SY3485 @ SV138 )
| ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3486: $i] :
( ~ ( ~ $false
| ( SY3486 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3486 != SY3485 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1312]) ).
thf(1603,plain,
! [SV139: $i > $o] :
( ( ( ~ ! [SY2515: $i] :
~ ~ ( ~ ( SV139 @ SY2515 )
| ~ ! [SY2516: $i] :
( ~ ( SV139 @ SY2516 )
| ( SY2515 = SY2516 ) ) ) )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1313]) ).
thf(1604,plain,
! [SV415: $i > $o,SV140: $i,SV609: $i] :
( ( ~ ( in @ SV609 @ SV140 )
| ~ ( SV415 @ SV609 )
| ( in @ SV609
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1605,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY3143: $i,SY3144: $i] :
( ( SY3143 != SY3144 )
| ~ ( ~ ( ~ ( SV141 @ SY3143 )
| ( SV416 @ SY3144 ) )
| ~ ( ~ ( SV416 @ SY3144 )
| ( SV141 @ SY3143 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1315]) ).
thf(1606,plain,
! [SV417: $i,SV142: $i,SV610: $i] :
( ( ~ ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
| ~ ! [SY3488: $i] :
~ ~ ( ~ ( in @ SY3488 @ SV142 )
| ~ ~ ! [SY3489: $i] :
~ ~ ( ~ ( in @ SY3489 @ SV417 )
| ( SV610
!= ( kpair @ SY3488 @ SY3489 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1316]) ).
thf(1607,plain,
! [SV143: $i,SV418: $i] :
( ( ( ~ ( in @ SV418 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( ! [SY3156: $i] :
( ~ ( in @ SY3156 @ ( powerset @ SV143 ) )
| ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SY3156 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1317]) ).
thf(1608,plain,
! [SV419: $i,SV144: $i] :
( ( ( ~ ( breln1 @ SV144 @ SV419 ) )
= $true )
| ( ( ! [SY3157: $i > $o] :
( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV144 )
| ! [SY3159: $i] :
( ~ ( in @ SY3159 @ SV144 )
| ~ ( in @ ( kpair @ SY3158 @ SY3159 ) @ SV419 )
| ( SY3157 @ ( kpair @ SY3158 @ SY3159 ) ) ) )
| ! [SY3160: $i] :
( ~ ( in @ SY3160 @ SV419 )
| ( SY3157 @ SY3160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1318]) ).
thf(1609,plain,
! [SV145: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ ( powerset @ SV145 ) ) )
= $true )
| ( ( ! [SY3161: $i] :
( ~ ( in @ SY3161 @ ( powerset @ SV145 ) )
| ! [SY3162: $i] :
( ~ ( in @ SY3162 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3162 )
| ( subset @ ( binintersect @ SV420 @ SY3161 ) @ SY3162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1610,plain,
! [SV421: $i,SV146: $i] :
( ( ( ( binintersect @ SV146 @ SV421 )
!= SV146 )
= $true )
| ( ( subset @ SV146 @ SV421 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1320]) ).
thf(1611,plain,
! [SV422: $o,SV147: $i,SV611: $i] :
( ( ~ ( in @ SV611 @ SV147 )
| ! [SY3490: $i] :
( ~ ( in @ SY3490 @ SV147 )
| ~ ~ SV422
| ( in @ SY3490
@ ( dsetconstr @ SV147
@ ^ [SY3491: $i] :
( ~ ( ~ SV422
| ( SY3491 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3491 != SY3490 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1612,plain,
! [SV147: $i,SV612: $i] :
( ( ~ ( in @ SV612 @ SV147 )
| ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV147 )
| ~ ~ $true
| ( in @ SY3492
@ ( dsetconstr @ SV147
@ ^ [SY3493: $i] :
( ~ ( ~ $true
| ( SY3493 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3493 != SY3492 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1322]) ).
thf(1613,plain,
! [SV147: $i,SV613: $i] :
( ( ~ ( in @ SV613 @ SV147 )
| ! [SY3494: $i] :
( ~ ( in @ SY3494 @ SV147 )
| ~ ~ $false
| ( in @ SY3494
@ ( dsetconstr @ SV147
@ ^ [SY3495: $i] :
( ~ ( ~ $false
| ( SY3495 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3495 != SY3494 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1323]) ).
thf(1614,plain,
! [SV148: $i] :
( ( ( in @ SV148 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1615,plain,
! [SV423: $o,SV149: $i,SV614: $i] :
( ( ~ ( in @ SV614 @ SV149 )
| ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV149 )
| ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SY3496 )
= SY3496 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1325]) ).
thf(1616,plain,
! [SV149: $i,SV615: $i] :
( ( ~ ( in @ SV615 @ SV149 )
| ! [SY3497: $i] :
( ~ ( in @ SY3497 @ SV149 )
| ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SY3497 )
= SY3497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1326]) ).
thf(1617,plain,
! [SV149: $i,SV616: $i] :
( ( ~ ( in @ SV616 @ SV149 )
| ! [SY3498: $i] :
( ~ ( in @ SY3498 @ SV149 )
| ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SY3498 )
= SY3498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1618,plain,
! [SV424: $i,SV150: $i,SV617: $i] :
( ( ~ ( subset @ SV617 @ SV150 )
| ~ ( subset @ SV617 @ SV424 )
| ( subset @ SV617 @ ( binintersect @ SV150 @ SV424 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1328]) ).
thf(1619,plain,
! [SV151: $i,SV425: $i] :
( ( ( ~ ( in @ SV425 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ! [SY3169: $i] :
( ~ ( in @ SY3169 @ ( powerset @ SV151 ) )
| ~ ( subset @ SV425 @ ( setminus @ SV151 @ SY3169 ) )
| ! [SY3170: $i] :
( ~ ( in @ SY3170 @ SV151 )
| ~ ( in @ SY3170 @ SY3169 )
| ( in @ SY3170 @ ( setminus @ SV151 @ SV425 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1329]) ).
thf(1620,plain,
! [SV152: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ ( powerset @ SV152 ) ) )
= $true )
| ( ( ! [SY3171: $i] :
( ~ ( in @ SY3171 @ ( powerset @ SV152 ) )
| ! [SY3172: $i] :
( ~ ( in @ SY3172 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SY3171 )
| ~ ( subset @ SV426 @ SY3172 )
| ( subset @ SV426 @ ( binintersect @ SY3171 @ SY3172 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1621,plain,
! [SV153: $i] :
( ( ( iskpair @ SV153 )
= $false )
| ( ( singleton
@ ( dsetconstr @ ( setunion @ SV153 )
@ ^ [SY2563: $i] :
( SV153
= ( kpair @ ( kfst @ SV153 ) @ SY2563 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1622,plain,
! [SV154: $i,SV427: $i] :
( ( ( ~ ( in @ SV427 @ ( powerset @ SV154 ) ) )
= $true )
| ( ( ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( powerset @ SV154 ) )
| ! [SY3174: $i] :
( ~ ( in @ SY3174 @ ( powerset @ SV154 ) )
| ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV154 )
| ~ ( in @ SY3175 @ ( binintersect @ SV427 @ SY3173 ) )
| ( in @ SY3175 @ ( binunion @ SV427 @ SY3174 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1623,plain,
! [SV428: $i > $o,SV155: $i] :
( ( ( ~ ~ ! [SY3176: $i] :
~ ~ ( ~ ( in @ SY3176 @ SV155 )
| ~ ( SV428 @ SY3176 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1624,plain,
! [SV156: $i,SV429: $i] :
( ( ( ~ ( in @ SV429 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( ! [SY3178: $i] :
( ~ ( in @ SY3178 @ ( powerset @ SV156 ) )
| ! [SY3179: $i] :
( ~ ( in @ SY3179 @ SV156 )
| ~ ( in @ SY3179 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3179 @ ( binintersect @ SV429 @ SY3178 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1334]) ).
thf(1625,plain,
! [SV157: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ ( powerset @ SV157 ) ) )
= $true )
| ( ( in @ ( powerset @ SV430 ) @ ( powerset @ ( powerset @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1626,plain,
! [SV618: $i,SV431: $i,SV158: $i] :
( ( ~ ( subset @ SV158 @ SV431 )
| ~ ( subset @ SV431 @ SV618 )
| ( subset @ SV158 @ SV618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1336]) ).
thf(1627,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3181: $i] :
( ~ ( in @ SY3181 @ SV159 )
| ! [SY3182: $i] :
( ~ ( in @ SY3182 @ SV159 )
| ~ ( SV432 @ SY3181 )
| ~ ( SV432 @ SY3182 )
| ( SY3181 = SY3182 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1337]) ).
thf(1628,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ~ ( in @ SV619 @ SV160 )
| ~ ( ~ ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) )
| ~ ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1338]) ).
thf(1629,plain,
! [SV434: $i > $o,SV161: $i,SV620: $i] :
( ( ~ ( in @ SV620 @ SV161 )
| ~ ( SV434 @ SV620 )
| ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1339]) ).
thf(1630,plain,
! [SV621: $i,SV435: $i,SV162: $i] :
( ( ( ( setadjoin @ SV162 @ ( setadjoin @ SV435 @ emptyset ) )
!= ( setadjoin @ SV621 @ emptyset ) )
| ( SV162 = SV435 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1340]) ).
thf(1631,plain,
! [SV436: $i,SV163: $i,SV622: $i] :
( ( ! [SY3502: $i] :
( ~ ( in @ ( kpair @ SV622 @ SY3502 ) @ ( cartprod @ SV163 @ SV436 ) )
| ( in @ SY3502 @ SV436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1341]) ).
thf(1632,plain,
! [SV164: $o] :
( ( SV164 = $false )
| ( ( set2prop @ ( prop2set @ SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1633,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1634,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1344]) ).
thf(1635,plain,
! [SV437: $i,SV165: $i,SV623: $i] :
( ( ~ ( in @ SV623 @ SV165 )
| ! [SY3503: $i] :
( ~ ( in @ SY3503 @ SV437 )
| ( in @ ( kpair @ SV623 @ SY3503 ) @ ( cartprod @ SV165 @ SV437 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1345]) ).
thf(1636,plain,
! [SV166: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ ( powerset @ SV166 ) ) )
= $true )
| ( ( ! [SY3195: $i] :
( ~ ( in @ SY3195 @ ( powerset @ SV166 ) )
| ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SY3195 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1346]) ).
thf(1637,plain,
! [SV439: $i,SV167: $i,SV624: $i] :
( ( ~ ( in @ SV624 @ SV167 )
| ! [SY3504: $i] :
( ~ ( in @ SY3504 @ SV439 )
| ( ( kfst @ ( kpair @ SV624 @ SY3504 ) )
= SV624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1347]) ).
thf(1638,plain,
! [SV440: $i > $o,SV168: $i] :
( ( ( ~ ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) ) )
= $true )
| ( ( ~ ! [SY3199: $i] :
~ ~ ( ~ ( in @ SY3199 @ SV168 )
| ~ ( SV440 @ SY3199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1348]) ).
thf(1639,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
| ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ~ ( ~ ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1349]) ).
thf(1640,plain,
! [SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ! [SY3201: $i] :
( ~ ( in @ SY3201 @ SV442 )
| ~ ! [SY2609: $i] :
~ ~ ( ~ ( SV170 @ SY3201 @ SY2609 )
| ~ ! [SY2610: $i] :
( ~ ( SV170 @ SY3201 @ SY2610 )
| ( SY2609 = SY2610 ) ) ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1350]) ).
thf(1641,plain,
! [SV171: $i,SV626: $i,SV443: $i] :
( ( ~ ( in @ SV443 @ SV626 )
| ~ ( in @ SV626 @ SV171 )
| ( in @ SV443 @ ( setunion @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1351]) ).
thf(1642,plain,
! [SV444: $i,SV172: $i] :
( ( ( ~ ( subset @ SV172 @ SV444 ) )
= $true )
| ( ( in @ SV172 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1643,plain,
! [SV627: $i,SV445: $i,SV173: $i] :
( ( ~ ( breln @ SV173 @ SV445 @ SV627 )
| ! [SY3505: $i > $o] :
( ~ ! [SY3506: $i] :
( ~ ( in @ SY3506 @ SV173 )
| ! [SY3507: $i] :
( ~ ( in @ SY3507 @ SV445 )
| ~ ( in @ ( kpair @ SY3506 @ SY3507 ) @ SV627 )
| ( SY3505 @ ( kpair @ SY3506 @ SY3507 ) ) ) )
| ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV627 )
| ( SY3505 @ SY3508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1353]) ).
thf(1644,plain,
! [SV628: $i,SV446: $i,SV174: $i] :
( ( ! [SY3509: $i] :
( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV628 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV628 @ ( setadjoin @ SY3509 @ emptyset ) ) @ emptyset ) ) )
| ( SV174 = SV628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1354]) ).
thf(1645,plain,
! [SV447: $i,SV175: $i] :
( ( ( SV175 != SV447 )
= $true )
| ( ( ( powerset @ SV175 )
= ( powerset @ SV447 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1646,plain,
! [SV176: $i,SV448: $i] :
( ( ( ~ ( in @ SV448 @ SV176 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV448 @ emptyset ) @ SV176 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1647,plain,
! [SV449: $i,SV177: $i] :
( ( ( ~ ! [SY3216: $i] :
( ~ ( in @ SY3216 @ SV177 )
| ( in @ SY3216 @ SV449 ) ) )
= $true )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1648,plain,
! [SV178: $i,SV450: $i,SV629: $i] :
( ( ~ ( in @ SV629 @ SV450 )
| ( in @ SV629 @ ( setadjoin @ SV178 @ SV450 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1358]) ).
thf(1649,plain,
! [SV630: $i,SV451: $i,SV179: $i] :
( ( ! [SY3510: $i] :
( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SY3510 @ emptyset ) ) @ emptyset ) ) )
| ( SV630 != SY3510 )
| ( SV451 = SY3510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1359]) ).
thf(1650,plain,
! [SV452: $i,SV180: $i,SV631: $i] :
( ( ~ ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
| ! [SY3511: $i] :
( ~ ( in @ SY3511 @ SV180 )
| ! [SY3512: $i] :
( ~ ( in @ SY3512 @ SV452 )
| ~ ( in @ ( kpair @ SY3511 @ SY3512 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SY3511 )
= SY3512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1360]) ).
thf(1651,plain,
! [SV453: $i,SV181: $i,SV632: $i] :
( ( ~ ( in @ SV632 @ SV181 )
| ( in @ ( setadjoin @ SV632 @ emptyset ) @ ( powerset @ ( binunion @ SV181 @ SV453 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1361]) ).
thf(1652,plain,
! [SV182: $i] :
( ( ( singleton @ SV182 )
= $false )
| ( ( in @ ( setunion @ SV182 ) @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1653,plain,
! [SV183: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ ( powerset @ SV183 ) ) )
= $true )
| ( ( ! [SY3225: $i] :
( ~ ( in @ SY3225 @ ( powerset @ SV183 ) )
| ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SY3225 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1363]) ).
thf(1654,plain,
! [SV184: $i] :
( ( ( ! [SY2645: $i] :
~ ( in @ SY2645 @ SV184 ) )
= $false )
| ( ( SV184 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1655,plain,
! [SV455: $i,SV185: $i] :
( ( ( ~ ( breln1 @ SV185 @ SV455 ) )
= $true )
| ( ( ! [SY3226: $i] :
( ~ ( breln1 @ SV185 @ SY3226 )
| ~ ! [SY3227: $i] :
( ~ ( in @ SY3227 @ SV185 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SV185 )
| ~ ( in @ ( kpair @ SY3227 @ SY3228 ) @ SV455 )
| ( in @ ( kpair @ SY3227 @ SY3228 ) @ SY3226 ) ) )
| ( subset @ SV455 @ SY3226 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1365]) ).
thf(1656,plain,
! [SV456: $i,SV186: $i,SV633: $i] :
( ( ~ ( in @ SV633 @ SV186 )
| ~ ( in @ SV633 @ SV456 )
| ( in @ SV633 @ ( binintersect @ SV186 @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1366]) ).
thf(1657,plain,
! [SV187: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ ( powerset @ SV187 ) ) )
= $true )
| ( ( ! [SY3230: $i] :
( ~ ( in @ SY3230 @ ( powerset @ SV187 ) )
| ! [SY3231: $i] :
( ~ ( in @ SY3231 @ ( powerset @ SV187 ) )
| ! [SY3232: $i] :
( ~ ( in @ SY3232 @ SV187 )
| ~ ( in @ SY3232 @ ( binintersect @ SV457 @ SY3230 ) )
| ( in @ SY3232 @ ( binintersect @ ( binunion @ SV457 @ SY3231 ) @ ( binunion @ SY3230 @ SY3231 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1367]) ).
thf(1658,plain,
! [SV458: $i,SV188: $i] :
( ( ( ~ ( breln1 @ SV188 @ SV458 ) )
= $true )
| ( ( ! [SY3233: $i] :
( ~ ( in @ SY3233 @ SV188 )
| ! [SY3234: $i] :
( ~ ( in @ SY3234 @ SV188 )
| ~ ( in @ ( kpair @ SY3234 @ SY3233 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SY3233 @ SY3234 ) @ SV458 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1368]) ).
thf(1659,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( setunion @ SV189 ) ) )
= $true )
| ( ( ! [SY3235: $o] :
( ~ ! [SY3236: $i] :
( ~ ( in @ SV459 @ SY3236 )
| ~ ( in @ SY3236 @ SV189 )
| SY3235 )
| SY3235 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1369]) ).
thf(1660,plain,
! [SV190: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ ( powerset @ SV190 ) ) )
= $true )
| ( ( subset @ SV460 @ ( setminus @ SV190 @ ( setminus @ SV190 @ SV460 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1370]) ).
thf(1661,plain,
! [SV634: $i,SV461: $i,SV191: $i] :
( ( ~ ( func @ SV191 @ SV461 @ SV634 )
| ( ( lam @ SV191 @ SV461
@ ^ [SY3513: $i] : ( ap @ SV191 @ SV461 @ SV634 @ SY3513 ) )
= SV634 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1371]) ).
thf(1662,plain,
! [SV192: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( powerset @ SV192 ) ) )
= $true )
| ( ( ! [SY3239: $i] :
( ~ ( in @ SY3239 @ ( powerset @ SV192 ) )
| ! [SY3240: $i] :
( ~ ( in @ SY3240 @ SV192 )
| ~ ~ ( in @ SY3240 @ ( binunion @ SV462 @ SY3239 ) )
| ~ ( in @ SY3240 @ SV462 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1663,plain,
! [SV193: $i,SV463: $i] :
( ( ( ~ ( in @ SV463 @ ( powerset @ SV193 ) ) )
= $true )
| ( ( ! [SY3241: $i] :
( ~ ( in @ SY3241 @ ( powerset @ SV193 ) )
| ! [SY3242: $i] :
( ~ ( in @ SY3242 @ SV193 )
| ~ ( in @ SY3242 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SY3241 ) ) )
| ( in @ SY3242 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SY3241 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1664,plain,
! [SV194: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( powerset @ SV194 ) ) )
= $true )
| ( ( ! [SY3243: $i] :
( ~ ( in @ SY3243 @ ( powerset @ SV194 ) )
| ! [SY3244: $i] :
( ~ ( in @ SY3244 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SY3243 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3244 ) @ ( binunion @ SY3243 @ SY3244 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1665,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ~ ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
| ! [SY3514: $o] :
( ~ ( ( SV635 != SV195 )
| SY3514 )
| ~ ( ~ ( in @ SV635 @ SV465 )
| SY3514 )
| SY3514 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1666,plain,
! [SV466: $i,SV196: $i,SV636: $i] :
( ( ~ ( in @ SV636 @ ( cartprod @ SV196 @ SV466 ) )
| ( in @ ( kfst @ SV636 ) @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1376]) ).
thf(1667,plain,
! [SV467: $i,SV197: $i] :
( ( ( ~ ~ ~ ! [SY3248: $i] :
~ ~ ( ~ ( in @ SY3248 @ SV197 )
| ~ ( in @ SY3248 @ SV467 ) ) )
= $true )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1377]) ).
thf(1668,plain,
! [SV468: $i,SV198: $i] :
( ( ( ( setminus @ SV198 @ SV468 )
!= emptyset )
= $true )
| ( ( subset @ SV198 @ SV468 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1378]) ).
thf(1669,plain,
! [SV199: $i,SV469: $i] :
( ( ( ~ ( in @ SV469 @ ( powerset @ SV199 ) ) )
= $true )
| ( ( ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( powerset @ SV199 ) )
| ( in @ ( setminus @ SV469 @ SY3249 ) @ ( powerset @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1379]) ).
thf(1670,plain,
! [SV470: $i,SV637: $i > $i,SV200: $i] :
( ( ~ ! [SY3515: $i] :
( ~ ( in @ SY3515 @ SV200 )
| ( in @ ( SV637 @ SY3515 ) @ SV470 ) )
| ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1380]) ).
thf(1671,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ ( setunion @ SV201 ) ) )
= $true )
| ( ( ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ SV201 )
| ~ ( in @ SV471 @ SY3253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1381]) ).
thf(1672,plain,
! [SV472: $i,SV202: $i] :
( ( ( SV202 != SV472 )
= $true )
| ( ( ( setadjoin @ SV202 @ ( setadjoin @ SV472 @ emptyset ) )
= ( setadjoin @ SV202 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1382]) ).
thf(1673,plain,
! [SV203: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ ( powerset @ SV203 ) ) )
= $true )
| ( ( ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( powerset @ SV203 ) )
| ( in @ ( binintersect @ SV473 @ SY3254 ) @ ( powerset @ SV203 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1383]) ).
thf(1674,plain,
! [SV204: $i,SV474: $i] :
( ( ( ~ ( in @ SV474 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV204 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV204 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SY3255 ) @ ( binunion @ SY3256 @ SY3257 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SY3255 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3256 ) @ ( setminus @ SV204 @ SY3257 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1384]) ).
thf(1675,plain,
! [SV205: $i] :
( ( ( subset @ SV205 @ emptyset )
= $false )
| ( ( SV205 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1385]) ).
thf(1676,plain,
! [SV475: $i,SV206: $i,SV638: $i] :
( ( ~ ( in @ SV638 @ ( binunion @ SV206 @ SV475 ) )
| ( in @ SV638 @ SV206 )
| ( in @ SV638 @ SV475 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1386]) ).
thf(1677,plain,
! [SV207: $i > $o] :
( ( ( ~ ! [SY2700: $i] :
~ ~ ( ~ ( SV207 @ SY2700 )
| ~ ! [SY2701: $i] :
( ~ ( SV207 @ SY2701 )
| ( SY2700 = SY2701 ) ) ) )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1678,plain,
! [SV208: $i,SV476: $i] :
( ( ( ~ ( in @ SV476 @ ( breln1Set @ SV208 ) ) )
= $true )
| ( ( breln1 @ SV208 @ SV476 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1388]) ).
thf(1679,plain,
! [SV477: $i,SV209: $i] :
( ( ( ~ ( ( SV209 != SV477 ) ) )
= $true )
| ( ( ~ ( in @ SV477 @ ( setadjoin @ SV209 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1389]) ).
thf(1680,plain,
! [SV210: $i,SV478: $i] :
( ( ( ~ ( subset @ SV478 @ SV210 ) )
= $true )
| ( ( in @ SV478 @ ( powerset @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1681,plain,
! [SV479: $i,SV211: $i,SV639: $i] :
( ( ~ ( in @ SV639 @ SV211 )
| ! [SY3517: $i] :
( ~ ( in @ SY3517 @ SV479 )
| ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SY3517 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1391]) ).
thf(1682,plain,
! [SV480: $i,SV212: $i] :
( ( ( ~ ( breln1 @ SV212 @ SV480 ) )
= $true )
| ( ( ! [SY3261: $i] :
( ~ ( breln1 @ SV212 @ SY3261 )
| ( breln1 @ SV212 @ ( binunion @ SV480 @ SY3261 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1683,plain,
! [SV640: $i,SV481: $i,SV213: $i] :
( ( ~ ( func @ SV213 @ SV481 @ SV640 )
| ( in @ SV640 @ ( funcSet @ SV213 @ SV481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1393]) ).
thf(1684,plain,
! [SV482: $o,SV214: $i,SV641: $i] :
( ( ~ ( in @ SV641 @ SV214 )
| ! [SY3518: $i] :
( ~ ( in @ SY3518 @ SV214 )
| ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SY3518 )
= SV641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1685,plain,
! [SV214: $i,SV642: $i] :
( ( ~ ( in @ SV642 @ SV214 )
| ! [SY3519: $i] :
( ~ ( in @ SY3519 @ SV214 )
| ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SY3519 )
= SV642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1395]) ).
thf(1686,plain,
! [SV214: $i,SV643: $i] :
( ( ~ ( in @ SV643 @ SV214 )
| ! [SY3520: $i] :
( ~ ( in @ SY3520 @ SV214 )
| ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SY3520 )
= SV643 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1687,plain,
! [SV483: $i,SV215: $i] :
( ( ( ~ ( breln1 @ SV215 @ SV483 ) )
= $true )
| ( ( ! [SY3265: $i] :
( ~ ( breln1 @ SV215 @ SY3265 )
| ! [SY3266: $i] :
( ~ ( in @ SY3266 @ SV215 )
| ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV215 )
| ~ ( in @ ( kpair @ SY3266 @ SY3267 ) @ SV483 )
| ( in @ ( kpair @ SY3266 @ SY3267 ) @ ( binunion @ SV483 @ SY3265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1397]) ).
thf(1688,plain,
! [SV216: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( powerset @ SV216 ) ) )
= $true )
| ( ( ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( powerset @ SV216 ) )
| ~ ( subset @ SV484 @ ( setminus @ SV216 @ SY3268 ) )
| ( subset @ SY3268 @ ( setminus @ SV216 @ SV484 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1689,plain,
! [SV644: $i > $i > $o,SV485: $i,SV217: $i] :
( ( ! [SY3521: $i,SY3522: $i] :
( ~ ( in @ ( kpair @ SY3521 @ SY3522 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SY3523: $i,SY3524: $i] : ( SV644 @ SY3523 @ SY3524 ) ) )
| ( in @ SY3522 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1690,plain,
! [SV218: $i,SV486: $i] :
( ( ( ~ ( in @ SV486 @ ( powerset @ SV218 ) ) )
= $true )
| ( ( ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( powerset @ SV218 ) )
| ( ( setminus @ SV218 @ ( binunion @ SV486 @ SY3274 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SY3274 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1691,plain,
! [SV487: $i,SV219: $i,SV645: $i] :
( ( ~ ~ ( in @ SV645 @ SV219 )
| ~ ~ ( in @ SV645 @ SV487 )
| ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1401]) ).
thf(1692,plain,
! [SV220: $i,SV488: $i] :
( ( ( ~ ( in @ SV488 @ ( powerset @ SV220 ) ) )
= $true )
| ( ( ! [SY3276: $i] :
( ~ ( in @ SY3276 @ SV220 )
| ~ ( in @ SY3276 @ SV488 )
| ~ ( in @ SY3276 @ ( setminus @ SV220 @ SV488 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1402]) ).
thf(1693,plain,
! [SV489: $i > $o,SV221: $i] :
( ( ( ~ ~ ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV221 )
| ( SV489 @ SY3277 ) ) )
= $true )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1403]) ).
thf(1694,plain,
! [SV490: $i,SV222: $i] :
( ( ( SV222 != SV490 )
= $true )
| ( ( in @ SV222 @ ( setadjoin @ SV490 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1404]) ).
thf(1695,plain,
! [SV223: $i,SV491: $i] :
( ( ( ~ ( in @ SV491 @ ( powerset @ SV223 ) ) )
= $true )
| ( ( ! [SY3279: $i] :
( ~ ( in @ SY3279 @ ( powerset @ SV223 ) )
| ! [SY3280: $i] :
( ~ ( in @ SY3280 @ SV223 )
| ~ ( in @ SY3280 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SY3279 ) ) )
| ( in @ SY3280 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SY3279 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1405]) ).
thf(1696,plain,
! [SV224: $i,SV492: $i,SV646: $i] :
( ( ~ ( in @ SV646 @ SV492 )
| ~ ( in @ SV646 @ ( setminus @ SV224 @ SV492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1697,plain,
! [SV493: $i,SV225: $i,SV647: $i] :
( ( ~ ( in @ SV647 @ SV225 )
| ~ ~ ( in @ SV647 @ SV493 )
| ~ ( subset @ SV225 @ SV493 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1407]) ).
thf(1698,plain,
! [SV648: $i,SV494: $i,SV226: $i] :
( ( ~ ( breln @ SV226 @ SV494 @ SV648 )
| ! [SY3525: $i] :
( ~ ( breln @ SV226 @ SV494 @ SY3525 )
| ~ ! [SY3526: $i] :
( ~ ( in @ SY3526 @ SV226 )
| ! [SY3527: $i] :
( ~ ( in @ SY3527 @ SV494 )
| ~ ( in @ ( kpair @ SY3526 @ SY3527 ) @ SV648 )
| ( in @ ( kpair @ SY3526 @ SY3527 ) @ SY3525 ) ) )
| ( subset @ SV648 @ SY3525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1408]) ).
thf(1699,plain,
! [SV227: $i,SV495: $i] :
( ( ( ~ ( in @ SV495 @ ( powerset @ SV227 ) ) )
= $true )
| ( ( ! [SY3287: $i] :
( ~ ( in @ SY3287 @ ( powerset @ SV227 ) )
| ( in @ ( binunion @ SV495 @ SY3287 ) @ ( powerset @ SV227 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1700,plain,
! [SV649: $i,SV228: $i,SV496: $i] :
( ( ~ ( in @ SV496 @ ( powerset @ SV228 ) )
| ~ ( in @ SV649 @ SV496 )
| ( in @ SV649 @ SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1410]) ).
thf(1701,plain,
! [SV229: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ ( powerset @ SV229 ) ) )
= $true )
| ( ( subset @ SV497 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1702,plain,
! [SV498: $i,SV230: $i] :
( ( ( ~ ( subset @ SV230 @ SV498 ) )
= $true )
| ( ( ( binintersect @ SV230 @ SV498 )
= SV230 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1412]) ).
thf(1703,plain,
! [SV499: $i,SV231: $i,SV650: $i] :
( ( ~ ( in @ SV650 @ SV231 )
| ! [SY3528: $i] :
( ~ ( in @ SY3528 @ SV499 )
| ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SY3528 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1413]) ).
thf(1704,plain,
! [SV232: $i,SV500: $i] :
( ( ( ~ ( in @ SV500 @ ( powerset @ SV232 ) ) )
= $true )
| ( ( ! [SY3291: $i] :
( ~ ( in @ SY3291 @ ( powerset @ SV232 ) )
| ~ ! [SY3292: $i] :
( ~ ( in @ SY3292 @ SV232 )
| ~ ( in @ SY3292 @ SV500 )
| ( in @ SY3292 @ SY3291 ) )
| ( subset @ SV500 @ SY3291 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1414]) ).
thf(1705,plain,
! [SV233: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ ( powerset @ SV233 ) ) )
= $true )
| ( ( ! [SY3293: $i] :
( ~ ( in @ SY3293 @ ( powerset @ SV233 ) )
| ~ ! [SY3294: $i] :
( ~ ( in @ SY3294 @ SV233 )
| ~ ( in @ SY3294 @ SV501 )
| ( in @ SY3294 @ SY3293 ) )
| ( in @ SV501 @ ( powerset @ SY3293 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1415]) ).
thf(1706,plain,
! [SV502: $i,SV234: $i,SV651: $i] :
( ( ~ ( in @ SV651 @ ( setadjoin @ SV234 @ ( setadjoin @ SV502 @ emptyset ) ) )
| ( SV651 = SV234 )
| ( SV651 = SV502 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1416]) ).
thf(1707,plain,
! [SV235: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ ( powerset @ SV235 ) ) )
= $true )
| ( ( ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV235 )
| ~ ( in @ SY3296 @ SV503 )
| ( in @ SY3296 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1417]) ).
thf(1708,plain,
! [SV504: $i,SV236: $i] :
( ( ( ~ ~ ( subset @ SV236 @ SV504 ) )
= $true )
| ( ( SV236 != SV504 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1418]) ).
thf(1709,plain,
! [SV505: $o,SV237: $i,SV652: $i] :
( ( ~ ( in @ SV652 @ SV237 )
| ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV237 )
| ( in @ ( if @ SV237 @ SV505 @ SV652 @ SY3529 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1710,plain,
! [SV237: $i,SV653: $i] :
( ( ~ ( in @ SV653 @ SV237 )
| ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV237 )
| ( in @ ( if @ SV237 @ $true @ SV653 @ SY3530 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1711,plain,
! [SV237: $i,SV654: $i] :
( ( ~ ( in @ SV654 @ SV237 )
| ! [SY3531: $i] :
( ~ ( in @ SY3531 @ SV237 )
| ( in @ ( if @ SV237 @ $false @ SV654 @ SY3531 ) @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1421]) ).
thf(1712,plain,
! [SV238: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ ( powerset @ SV238 ) ) )
= $true )
| ( ( ! [SY3299: $i] :
( ~ ( in @ SY3299 @ ( powerset @ SV238 ) )
| ! [SY3300: $i] :
( ~ ( in @ SY3300 @ ( powerset @ SV238 ) )
| ! [SY3301: $i] :
( ~ ( in @ SY3301 @ SV238 )
| ~ ( in @ SY3301 @ ( binintersect @ SV506 @ SY3299 ) )
| ( in @ SY3301 @ ( binunion @ SY3299 @ SY3300 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1422]) ).
thf(1713,plain,
! [SV507: $i > $o,SV239: $i,SV655: $i] :
( ( ~ ( in @ SV655
@ ( dsetconstr @ SV239
@ ^ [SY3303: $i] : ( SV507 @ SY3303 ) ) )
| ( in @ SV655 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1423]) ).
thf(1714,plain,
! [SV508: $i,SV240: $i] :
( ( ( ~ ( breln1 @ SV240 @ SV508 ) )
= $true )
| ( ( ! [SY3304: $i] :
( ~ ( breln1 @ SV240 @ SY3304 )
| ! [SY3305: $i] :
( ~ ( in @ SY3305 @ SV240 )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3306 ) @ ( breln1compset @ SV240 @ SV508 @ SY3304 ) )
| ! [SY3307: $o] :
( ~ ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3308 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3308 @ SY3306 ) @ SY3304 )
| SY3307 )
| SY3307 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1424]) ).
thf(1715,plain,
! [SV509: $i,SV241: $i] :
( ( ( ~ ( breln1 @ SV241 @ SV509 ) )
= $true )
| ( ( ! [SY3309: $i > $o] :
( ~ ! [SY3310: $i] :
( ~ ( in @ SY3310 @ SV241 )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ SV241 )
| ~ ( in @ ( kpair @ SY3310 @ SY3311 ) @ SV509 )
| ( SY3309 @ ( kpair @ SY3310 @ SY3311 ) ) ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV509 )
| ( SY3309 @ SY3312 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1716,plain,
! [SV242: $i,SV510: $i] :
( ( ( ~ ( in @ SV510 @ ( powerset @ SV242 ) ) )
= $true )
| ( ( ! [SY3313: $i] :
( ~ ( in @ SY3313 @ ( powerset @ SV242 ) )
| ! [SY3314: $i] :
( ~ ( in @ SY3314 @ SV242 )
| ~ ( in @ SY3314 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SY3313 ) ) )
| ~ ( in @ SY3314 @ SV510 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1426]) ).
thf(1717,plain,
! [SV243: $i,SV511: $i] :
( ( ( ~ ( in @ SV511 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY3315: $i] :
( ~ ( in @ SY3315 @ ( powerset @ SV243 ) )
| ! [SY3316: $i] :
( ~ ( in @ SY3316 @ SV243 )
| ~ ( in @ SY3316 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SY3315 ) ) )
| ( in @ SY3316 @ ( setminus @ SV243 @ SY3315 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1427]) ).
thf(1718,plain,
! [SV512: $i,SV244: $i,SV656: $i] :
( ( ~ ( in @ SV656 @ ( funcSet @ SV244 @ SV512 ) )
| ( ( lam @ SV244 @ SV512
@ ^ [SY3533: $i] : ( ap @ SV244 @ SV512 @ SV656 @ SY3533 ) )
= SV656 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1428]) ).
thf(1719,plain,
! [SV245: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ ( powerset @ SV245 ) ) )
= $true )
| ( ( in @ ( setminus @ SV245 @ SV513 ) @ ( powerset @ SV245 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1429]) ).
thf(1720,plain,
! [SV514: $i,SV246: $i] :
( ( ( SV246 != SV514 )
= $true )
| ( ( ( setunion @ SV246 )
= ( setunion @ SV514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1721,plain,
! [SV515: $i,SV247: $i] :
( ( ( ~ ( subset @ SV247 @ SV515 ) )
= $true )
| ( ( ( setminus @ SV247 @ SV515 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1431]) ).
thf(1722,plain,
! [SV516: $i,SV248: $i] :
( ( ( SV248 != SV516 )
= $true )
| ( ( subset @ SV516 @ SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1432]) ).
thf(1723,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i] :
( ( ! [SY3534: $i] :
( ~ ( in @ SY3534 @ SV249 )
| ! [SY3535: $i] :
( ~ ( in @ SY3535 @ SV517 )
| ~ ( in @ ( kpair @ SY3534 @ SY3535 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SY3534 @ SY3535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1433]) ).
thf(1724,plain,
! [SV250: $i > $o] :
( ( ( ~ ! [SY2811: $i] :
~ ! [SY2812: $i] :
~ ( ~ ( ~ ( SV250 @ SY2812 )
| ( SY2812 = SY2811 ) )
| ~ ( ( SY2812 != SY2811 )
| ( SV250 @ SY2812 ) ) ) )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1725,plain,
! [SV658: $i,SV518: $i,SV251: $i] :
( ( ~ ( breln @ SV251 @ SV518 @ SV658 )
| ! [SY3538: $i] :
( ~ ( breln @ SV251 @ SV518 @ SY3538 )
| ~ ! [SY3539: $i] :
( ~ ( in @ SY3539 @ SV251 )
| ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV518 )
| ~ ( in @ ( kpair @ SY3539 @ SY3540 ) @ SV658 )
| ( in @ ( kpair @ SY3539 @ SY3540 ) @ SY3538 ) ) )
| ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV251 )
| ! [SY3542: $i] :
( ~ ( in @ SY3542 @ SV518 )
| ~ ( in @ ( kpair @ SY3541 @ SY3542 ) @ SY3538 )
| ( in @ ( kpair @ SY3541 @ SY3542 ) @ SV658 ) ) )
| ( SV658 = SY3538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1435]) ).
thf(1726,plain,
! [SV252: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ ( powerset @ SV252 ) ) )
= $true )
| ( ( ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV252 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SY3330 ) )
| ~ ( in @ SY3331 @ SY3330 )
| ~ ( in @ SY3331 @ SV519 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1727,plain,
! [SV253: $i > $o,SV520: $i] :
( ( ( ~ ( in @ SV520 @ emptyset ) )
= $true )
| ( ( SV253 @ SV520 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1728,plain,
! [SV254: $i] :
( ( ( ~ ! [SY2826: $i] :
~ ( in @ SY2826 @ SV254 ) )
= $false )
| ( ( SV254 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1729,plain,
! [SV521: $i,SV255: $i,SV659: $i] :
( ( ~ ( in @ SV659 @ ( setminus @ SV255 @ SV521 ) )
| ( in @ SV659 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1439]) ).
thf(1730,plain,
! [SV522: $i > $o,SV256: $i] :
( ( ( ~ ~ ~ ! [SY3333: $i] :
~ ~ ( ~ ( in @ SY3333 @ SV256 )
| ~ ( SV522 @ SY3333 ) ) )
= $true )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1440]) ).
thf(1731,plain,
! [SV257: $i,SV523: $i] :
( ( ( ~ ( in @ SV523 @ SV257 ) )
= $true )
| ( ( in @ SV523 @ ( powerset @ ( setunion @ SV257 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1732,plain,
! [SV524: $i,SV258: $i] :
( ( ( ~ ( breln1 @ SV258 @ SV524 ) )
= $true )
| ( ( ! [SY3335: $i] :
( ~ ( breln1 @ SV258 @ SY3335 )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV258 )
| ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV258 )
| ! [SY3338: $i] :
( ~ ( in @ SY3338 @ SV258 )
| ~ ( in @ ( kpair @ SY3336 @ SY3338 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3338 @ SY3337 ) @ SY3335 )
| ( in @ ( kpair @ SY3336 @ SY3337 ) @ ( breln1compset @ SV258 @ SV524 @ SY3335 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1733,plain,
! [SV525: $i,SV259: $i] :
( ( ( ~ ( breln1 @ SV259 @ SV525 ) )
= $true )
| ( ( ! [SY3339: $i] :
( ~ ( breln1 @ SV259 @ SY3339 )
| ~ ! [SY3340: $i] :
( ~ ( in @ SY3340 @ SV259 )
| ! [SY3341: $i] :
( ~ ( in @ SY3341 @ SV259 )
| ~ ( in @ ( kpair @ SY3340 @ SY3341 ) @ SV525 )
| ( in @ ( kpair @ SY3340 @ SY3341 ) @ SY3339 ) ) )
| ~ ! [SY3342: $i] :
( ~ ( in @ SY3342 @ SV259 )
| ! [SY3343: $i] :
( ~ ( in @ SY3343 @ SV259 )
| ~ ( in @ ( kpair @ SY3342 @ SY3343 ) @ SY3339 )
| ( in @ ( kpair @ SY3342 @ SY3343 ) @ SV525 ) ) )
| ( SV525 = SY3339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1443]) ).
thf(1734,plain,
! [SV526: $i > $o,SV260: $i,SV660: $i] :
( ( ~ ( in @ SV660
@ ( dsetconstr @ SV260
@ ^ [SY3345: $i] : ( SV526 @ SY3345 ) ) )
| ( SV526 @ SV660 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1444]) ).
thf(1735,plain,
! [SV527: $i,SV261: $i] :
( ( ( ~ ! [SY3346: $i] :
~ ( ~ ( ~ ( in @ SY3346 @ SV261 )
| ( in @ SY3346 @ SV527 ) )
| ~ ( ~ ( in @ SY3346 @ SV527 )
| ( in @ SY3346 @ SV261 ) ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1445]) ).
thf(1736,plain,
! [SV661: $i,SV528: $i,SV262: $i] :
( ( ~ ( func @ SV262 @ SV528 @ SV661 )
| ! [SY3544: $i] :
( ~ ( in @ SY3544 @ SV262 )
| ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3545: $i] : ( in @ ( kpair @ SY3544 @ SY3545 ) @ SV661 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1446]) ).
thf(1737,plain,
! [SV263: $i > $o] :
( ( ( ~ ! [SY2853: $i] :
~ ~ ( ~ ( SV263 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV263 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1738,plain,
! [SV264: $i,SV529: $i] :
( ( ( ~ ( in @ SV529 @ ( powerset @ SV264 ) ) )
= $true )
| ( ( ! [SY3350: $i] :
( ~ ( in @ SY3350 @ ( powerset @ SV264 ) )
| ! [SY3351: $i] :
( ~ ( in @ SY3351 @ SV264 )
| ~ ( subset @ SV529 @ SY3350 )
| ~ ~ ( in @ SY3351 @ SY3350 )
| ~ ( in @ SY3351 @ SV529 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1448]) ).
thf(1739,plain,
! [SV265: $i] :
( ( ( ~ ! [SY2860: $i] :
~ ( in @ SY2860 @ SV265 ) )
= $false )
| ( ( ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1740,plain,
! [SV530: $i,SV266: $i,SV662: $i] :
( ( ~ ~ ( in @ SV662 @ SV266 )
| ~ ( in @ SV662 @ ( setminus @ SV266 @ SV530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1450]) ).
thf(1741,plain,
! [SV663: $i,SV531: $i,SV267: $i] :
( ( ! [SY3546: $i] :
( ( ( kpair @ SV267 @ SV531 )
!= ( kpair @ SV663 @ SY3546 ) )
| ( SV267 = SV663 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1742,plain,
! [SV268: $i] :
( ( ( SV268 != emptyset )
= $false )
| ( ( ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1452]) ).
thf(1743,plain,
! [SV269: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ ( powerset @ SV269 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV269 @ ( setminus @ SV269 @ SV532 ) ) @ SV532 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1453]) ).
thf(1744,plain,
! [SV533: $i,SV270: $i] :
( ( ( ~ ( in @ SV270 @ ( setadjoin @ SV533 @ emptyset ) ) )
= $true )
| ( ( SV270 = SV533 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1454]) ).
thf(1745,plain,
! [SV271: $i] :
( ( ( iskpair @ SV271 )
= $false )
| ( ( ( kpair @ ( kfst @ SV271 ) @ ( ksnd @ SV271 ) )
= SV271 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1455]) ).
thf(1746,plain,
! [SV272: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ ( powerset @ SV272 ) ) )
= $true )
| ( ( ! [SY3355: $i] :
( ~ ( in @ SY3355 @ ( powerset @ SV272 ) )
| ~ ( subset @ SV534 @ SY3355 )
| ( subset @ ( setminus @ SV272 @ SY3355 ) @ ( setminus @ SV272 @ SV534 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1456]) ).
thf(1747,plain,
! [SV535: $i,SV273: $i,SV664: $i] :
( ( ~ ( in @ SV664 @ SV273 )
| ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV535 )
| ( in @ ( kpair @ SV664 @ SY3547 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1457]) ).
thf(1748,plain,
! [SV665: $i,SV536: $i,SV274: $i] :
( ( ~ ( func @ SV274 @ SV536 @ SV665 )
| ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SV274 )
| ( ( ap @ SV274 @ SV536 @ SV665 @ SY3548 )
= ( ap @ SV274 @ SV536 @ SV665 @ SY3548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1458]) ).
thf(1749,plain,
! [SV275: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ ( powerset @ SV275 ) ) )
= $true )
| ( ( ! [SY3360: $i] :
( ~ ( in @ SY3360 @ ( powerset @ SV275 ) )
| ! [SY3361: $i] :
( ~ ( in @ SY3361 @ SV275 )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SY3360 ) )
| ( in @ SY3361 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SY3360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1459]) ).
thf(1750,plain,
! [SV666: $i,SV538: $i,SV276: $i] :
( ( ~ ( func @ SV276 @ SV538 @ SV666 )
| ! [SY3549: $i] :
( ~ ( in @ SY3549 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3550: $i] : ( in @ ( kpair @ SY3549 @ SY3550 ) @ SV666 ) ) )
@ SV538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1460]) ).
thf(1751,plain,
! [SV539: $i,SV277: $i,SV667: $i] :
( ( ~ ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) )
| ! [SY3551: $i] :
( ~ ( in @ SY3551 @ SV277 )
| ( in @ ( kpair @ SY3551 @ ( ap @ SV277 @ SV539 @ SV667 @ SY3551 ) ) @ SV667 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1752,plain,
! [SV540: $i > $o,SV278: $i] :
( ( ( ~ ~ ! [SY3367: $i] :
~ ~ ( ~ ( in @ SY3367 @ SV278 )
| ~ ~ ( SV540 @ SY3367 ) ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1462]) ).
thf(1753,plain,
! [SV541: $i,SV279: $i] :
( ( ( ~ ( breln1 @ SV279 @ SV541 ) )
= $true )
| ( ( ! [SY3369: $i] :
( ~ ( in @ SY3369 @ SV279 )
| ! [SY3370: $i] :
( ~ ( in @ SY3370 @ SV279 )
| ~ ( in @ ( kpair @ SY3369 @ SY3370 ) @ SV541 )
| ( in @ ( kpair @ SY3370 @ SY3369 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1463]) ).
thf(1754,plain,
! [SV542: $i,SV668: $i > $i,SV280: $i] :
( ( ~ ! [SY3552: $i] :
( ~ ( in @ SY3552 @ SV280 )
| ( in @ ( SV668 @ SY3552 ) @ SV542 ) )
| ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1464]) ).
thf(1755,plain,
! [SV543: $i,SV281: $i,SV669: $i] :
( ( ! [SY3555: $i] :
( ~ ( in @ ( kpair @ SV669 @ SY3555 ) @ ( cartprod @ SV281 @ SV543 ) )
| ( in @ SV669 @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1465]) ).
thf(1756,plain,
! [SV544: $i,SV670: $i > $i,SV282: $i] :
( ( ~ ! [SY3556: $i] :
( ~ ( in @ SY3556 @ SV282 )
| ( in @ ( SV670 @ SY3556 ) @ SV544 ) )
| ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1466]) ).
thf(1757,plain,
! [SV283: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ ( powerset @ SV283 ) ) )
= $true )
| ( ( ! [SY3381: $i] :
( ~ ( in @ SY3381 @ ( powerset @ SV283 ) )
| ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SY3381 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1467]) ).
thf(1758,plain,
! [SV284: $i] :
( ( ( SV284 != emptyset )
= $false )
| ( ( ~ ! [SY2910: $i] :
~ ~ ( ~ ( in @ SY2910 @ SV284 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1468]) ).
thf(1759,plain,
! [SV546: $i,SV285: $i,SV671: $i] :
( ( ~ ( in @ SV671 @ SV285 )
| ~ ~ ( in @ SV671 @ SV546 )
| ( SV285 != SV546 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1469]) ).
thf(1760,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ~ ~ ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) )
| ~ ( in @ SV672 @ SV286 )
| ( in @ SV672 @ SV547 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1470]) ).
thf(1761,plain,
! [SV673: $i,SV548: $i,SV287: $i] :
( ( ~ ( func @ SV287 @ SV548 @ SV673 )
| ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV287 )
| ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SV548 )
| ~ ( in @ ( kpair @ SY3559 @ SY3560 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SY3559 )
= SY3560 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1471]) ).
thf(1762,plain,
! [SV549: $o,SV288: $i,SV674: $i] :
( ( ~ ( in @ SV674 @ SV288 )
| ! [SY3561: $i] :
( ~ ( in @ SY3561 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3562: $i] :
( ~ ( ~ SV549
| ( SY3562 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3562 != SY3561 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1472]) ).
thf(1763,plain,
! [SV288: $i,SV675: $i] :
( ( ~ ( in @ SV675 @ SV288 )
| ! [SY3563: $i] :
( ~ ( in @ SY3563 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3564: $i] :
( ~ ( ~ $true
| ( SY3564 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3564 != SY3563 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1473]) ).
thf(1764,plain,
! [SV288: $i,SV676: $i] :
( ( ~ ( in @ SV676 @ SV288 )
| ! [SY3565: $i] :
( ~ ( in @ SY3565 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3566: $i] :
( ~ ( ~ $false
| ( SY3566 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3566 != SY3565 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1474]) ).
thf(1765,plain,
! [SV550: $i,SV289: $i,SV677: $i] :
( ( ~ ( in @ SV677 @ ( cartprod @ SV289 @ SV550 ) )
| ( ( kpair @ ( kfst @ SV677 ) @ ( ksnd @ SV677 ) )
= SV677 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1475]) ).
thf(1766,plain,
! [SV551: $i,SV290: $i,SV678: $i] :
( ( ~ ( in @ SV678 @ ( setadjoin @ SV290 @ ( setadjoin @ SV551 @ emptyset ) ) )
| ( SV678 = SV290 )
| ( SV678 = SV551 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1476]) ).
thf(1767,plain,
! [SV291: $i > $o] :
( ( ( ~ ! [SY2927: $i] :
~ ~ ( ~ ( SV291 @ SY2927 )
| ~ ! [SY2928: $i] :
( ~ ( SV291 @ SY2928 )
| ( SY2927 = SY2928 ) ) ) )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1477]) ).
thf(1768,plain,
! [SV552: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ ( setadjoin @ SV552 @ emptyset ) ) )
= $true )
| ( ( in @ SV552 @ ( setadjoin @ SV292 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1478]) ).
thf(1769,plain,
! [SV553: $i,SV293: $i] :
( ( ( SV293 != SV553 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV293 @ ( setadjoin @ SV553 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1479]) ).
thf(1770,plain,
! [SV554: $i,SV294: $i,SV679: $i] :
( ( ~ ( in @ SV679 @ SV294 )
| ~ ~ ( in @ SV679 @ SV554 )
| ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1771,plain,
! [SV295: $i] :
( ( ( in @ SV295 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1481]) ).
thf(1772,plain,
! [SV555: $o,SV296: $i,SV680: $i] :
( ( ~ ( in @ SV680 @ SV296 )
| ! [SY3567: $i] :
( ~ ( in @ SY3567 @ SV296 )
| ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3568: $i] :
( ~ ( ~ SV555
| ( SY3568 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3568 != SY3567 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1482]) ).
thf(1773,plain,
! [SV296: $i,SV681: $i] :
( ( ~ ( in @ SV681 @ SV296 )
| ! [SY3569: $i] :
( ~ ( in @ SY3569 @ SV296 )
| ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3570: $i] :
( ~ ( ~ $true
| ( SY3570 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3570 != SY3569 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1483]) ).
thf(1774,plain,
! [SV296: $i,SV682: $i] :
( ( ~ ( in @ SV682 @ SV296 )
| ! [SY3571: $i] :
( ~ ( in @ SY3571 @ SV296 )
| ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3572: $i] :
( ~ ( ~ $false
| ( SY3572 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3572 != SY3571 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1484]) ).
thf(1775,plain,
! [SV35: $i,SV320: $i] :
( ( ( in @ SV320 @ ( powerset @ SV35 ) )
= $false )
| ( ( ! [SY2950: $i] :
( ~ ( in @ SY2950 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SY2950 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SY2950 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1488]) ).
thf(1776,plain,
! [SV321: $i,SV36: $i,SV559: $i] :
( ( ( ~ ( in @ SV559 @ ( setminus @ SV36 @ SV321 ) ) )
= $true )
| ( ( ~ ( in @ SV559 @ SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1489]) ).
thf(1777,plain,
! [SV37: $i,SV322: $i] :
( ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false )
| ( ( ! [SY2952: $i] :
( ~ ( in @ SY2952 @ ( powerset @ SV37 ) )
| ! [SY2953: $i] :
( ~ ( in @ SY2953 @ ( powerset @ SV37 ) )
| ! [SY2954: $i] :
( ~ ( in @ SY2954 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY2953 )
| ~ ( subset @ SY2952 @ SY2954 )
| ( subset @ ( binintersect @ SV322 @ SY2952 ) @ ( binintersect @ SY2953 @ SY2954 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1490]) ).
thf(1778,plain,
! [SV38: $i > $o] :
( ( ( ! [SY2204: $i] :
~ ~ ( ~ ( SV38 @ SY2204 )
| ~ ! [SY2205: $i] :
( ~ ( SV38 @ SY2205 )
| ( SY2204 = SY2205 ) ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1779,plain,
! [SV323: $i,SV39: $i] :
( ( ( subset @ SV39 @ SV323 )
= $false )
| ( ( subset @ ( powerset @ SV39 ) @ ( powerset @ SV323 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1780,plain,
! [SV324: $i,SV40: $i] :
( ( ( breln1 @ SV40 @ SV324 )
= $false )
| ( ( ! [SY2955: $i] :
( ~ ( breln1 @ SV40 @ SY2955 )
| ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SY2955 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1493]) ).
thf(1781,plain,
! [SV560: $i,SV325: $i,SV41: $i] :
( ( ( ~ ( subset @ SV41 @ SV325 ) )
= $true )
| ( ( ~ ~ ( in @ SV560 @ SV325 )
| ~ ( in @ SV560 @ SV41 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1494]) ).
thf(1782,plain,
! [SV326: $i,SV42: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV42 ) )
= $true )
| ( ( ! [SY3400: $i] :
( ~ ( in @ SY3400 @ SV326 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SY3400 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1495]) ).
thf(1783,plain,
! [SV327: $i,SV43: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ ( binintersect @ SV43 @ SV327 ) ) )
= $true )
| ( ( in @ SV562 @ SV327 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1784,plain,
! [SV328: $i,SV44: $i] :
( ( ( SV44 = SV328 )
= $false )
| ( ( ! [SY2960: $i > $o,SY2961: $i > $o] :
( ~ ! [SY2962: $i] :
( ~ ( in @ SY2962 @ SV44 )
| ! [SY2963: $i] :
( ~ ( in @ SY2963 @ SV328 )
| ( SY2962 != SY2963 )
| ~ ( ~ ( ~ ( SY2960 @ SY2962 )
| ( SY2961 @ SY2963 ) )
| ~ ( ~ ( SY2961 @ SY2963 )
| ( SY2960 @ SY2962 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SX4: $i] : ( SY2960 @ SX4 ) )
= ( dsetconstr @ SV328
@ ^ [SX4: $i] : ( SY2961 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1785,plain,
! [SV45: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
| ~ ! [SY3410: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY3410 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3410 ) )
| ~ ! [SY3413: $i] :
~ ~ ! [SY3414: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3413 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3414 @ SY3410 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3413 )
| ~ ( in @ SX5 @ SY3410 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3413 ) )
| ( in @ SY3414 @ SY3416 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1498]) ).
thf(1786,plain,
! [SV329: $i > $o,SV46: $i] :
( ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false )
| ( ( ! [SY2967: $i] :
( ~ ( in @ SY2967 @ SV46 )
| ! [SY2968: $i] :
( ~ ( in @ SY2968 @ SV46 )
| ~ ( SV329 @ SY2967 )
| ~ ( SV329 @ SY2968 )
| ( SY2967 = SY2968 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1787,plain,
! [SV48: $i,SV330: $i] :
( ( ( in @ SV330 @ SV48 )
= $false )
| ( ( in @ ( setadjoin @ SV330 @ emptyset ) @ ( powerset @ SV48 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1503]) ).
thf(1788,plain,
! [SV331: $i,SV563: $i > $i,SV49: $i] :
( ( ( ~ ! [SY3418: $i] :
( ~ ( in @ SY3418 @ SV49 )
| ( in @ ( SV563 @ SY3418 ) @ SV331 ) ) )
= $true )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1789,plain,
! [SV50: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV50 )
| ( ( setunion @ SV50 )
= SV683 ) )
= $true )
| ( ( singleton @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1505]) ).
thf(1790,plain,
! [SV332: $i,SV51: $i] :
( ( ( ! [SY2972: $i] :
( ~ ( in @ SY2972 @ SV51 )
| ( in @ SY2972 @ SV332 ) ) )
= $false )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1506]) ).
thf(1791,plain,
! [SV52: $i] :
( ( ( ~ ( in @ emptyset @ SV52 )
| ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1792,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ( ~ ( in @ SV333 @ ( setunion @ SV53 ) )
| ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1793,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ( ~ ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) )
| ( in @ SV333 @ ( setunion @ SV53 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1508]) ).
thf(1794,plain,
! [SV334: $i > $o,SV54: $i,SV564: $i] :
( ( ( ~ ( in @ SV564 @ SV54 ) )
= $true )
| ( ( ~ ( SV334 @ SV564 )
| ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1795,plain,
! [SV335: $i,SV565: $i > $i,SV55: $i] :
( ( ( ~ ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV55 )
| ( in @ ( SV565 @ SY3422 ) @ SV335 ) ) )
= $true )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1796,plain,
! [SV336: $i,SV56: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) ) )
= $true )
| ( ( ! [SY3425: $i] :
( ~ ( in @ SY3425 @ SV56 )
| ( ( ap @ SV56 @ SV336 @ SV566 @ SY3425 )
= ( ap @ SV56 @ SV336 @ SV566 @ SY3425 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1511]) ).
thf(1797,plain,
! [SV57: $i,SV337: $i] :
( ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false )
| ( ( ! [SY2984: $i] :
( ~ ( in @ SY2984 @ ( powerset @ SV57 ) )
| ! [SY2985: $i] :
( ~ ( in @ SY2985 @ SV57 )
| ~ ( in @ SY2985 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SY2984 ) ) )
| ( in @ SY2985 @ ( setminus @ SV57 @ SV337 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1512]) ).
thf(1798,plain,
! [SV684: $i,SV567: $i,SV338: $i,SV58: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV338 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV567 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV567 @ ( setadjoin @ SV684 @ emptyset ) ) @ emptyset ) ) )
| ( SV338 = SV684 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1799,plain,
! [SV59: $i,SV339: $i] :
( ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false )
| ( ( ! [SY2988: $i] :
( ~ ( in @ SY2988 @ SV59 )
| ~ ~ ( in @ SY2988 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SY2988 @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1800,plain,
! [SV60: $i,SV340: $i] :
( ( ( in @ SV340 @ ( powerset @ SV60 ) )
= $false )
| ( ( SV340
= ( setminus @ SV60 @ ( setminus @ SV60 @ SV340 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1801,plain,
! [SV341: $i,SV61: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) ) )
= $true )
| ( ( ! [SY3427: $i] :
( ~ ( in @ SY3427 @ ( funcSet @ SV61 @ SV341 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3428 )
= ( ap @ SV61 @ SV341 @ SY3427 @ SY3428 ) ) )
| ( SV568 = SY3427 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1516]) ).
thf(1802,plain,
! [SV62: $i,SV342: $i] :
( ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false )
| ( ( ! [SY2992: $i] :
( ~ ( in @ SY2992 @ ( powerset @ SV62 ) )
| ~ ( subset @ SV342 @ ( setminus @ SV62 @ SY2992 ) )
| ( subset @ SY2992 @ ( setminus @ SV62 @ SV342 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1803,plain,
! [SV63: $i,SV343: $i] :
( ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false )
| ( ( ! [SY2993: $i] :
( ~ ( in @ SY2993 @ ( powerset @ SV63 ) )
| ! [SY2994: $i] :
( ~ ( in @ SY2994 @ SV63 )
| ~ ~ ( in @ SY2994 @ ( binunion @ SV343 @ SY2993 ) )
| ~ ( in @ SY2994 @ SY2993 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1518]) ).
thf(1804,plain,
! [SV64: $i,SV344: $i] :
( ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false )
| ( ( ! [SY2995: $i] :
( ~ ( in @ SY2995 @ ( powerset @ SV64 ) )
| ! [SY2996: $i] :
( ~ ( in @ SY2996 @ ( powerset @ SV64 ) )
| ~ ( subset @ SY2995 @ SY2996 )
| ( subset @ ( binintersect @ SV344 @ SY2995 ) @ SY2996 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1805,plain,
! [SV65: $i,SV345: $i] :
( ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false )
| ( ( ! [SY2997: $i] :
( ~ ( in @ SY2997 @ ( powerset @ SV65 ) )
| ! [SY2998: $i] :
( ~ ( in @ SY2998 @ SV65 )
| ~ ~ ( in @ SY2998 @ SY2997 )
| ~ ( in @ SY2998 @ ( binintersect @ SV345 @ SY2997 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1520]) ).
thf(1806,plain,
! [SV66: $i,SV346: $i] :
( ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false )
| ( ( ! [SY2999: $i] :
( ~ ( in @ SY2999 @ SV66 )
| ~ ( in @ SY2999 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SY2999 @ SV346 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1807,plain,
! [SV67: $i,SV347: $i] :
( ( ( ! [SY3000: $i] :
( ~ ( in @ SY3000 @ SV347 )
| ( in @ SY3000 @ SV67 ) ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1808,plain,
! [SV348: $i,SV68: $i] :
( ( ( breln1 @ SV68 @ SV348 )
= $false )
| ( ( ! [SY3001: $i] :
( ~ ( breln1 @ SV68 @ SY3001 )
| ! [SY3002: $i] :
( ~ ( in @ SY3002 @ SV68 )
| ! [SY3003: $i] :
( ~ ( in @ SY3003 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3003 ) @ ( breln1compset @ SV68 @ SV348 @ SY3001 ) )
| ~ ! [SY3004: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3004 @ SV68 )
| ~ ( in @ ( kpair @ SY3002 @ SY3004 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3004 @ SY3003 ) @ SY3001 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1809,plain,
! [SV69: $i,SV349: $i] :
( ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false )
| ( ( ! [SY3005: $i] :
( ~ ( in @ SY3005 @ ( powerset @ SV69 ) )
| ! [SY3006: $i] :
( ~ ( in @ SY3006 @ SV69 )
| ~ ( in @ SY3006 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SY3005 ) ) )
| ( in @ SY3006 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SY3005 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1810,plain,
! [SV350: $i,SV569: $i > $i,SV70: $i] :
( ( ( ~ ! [SY3429: $i] :
( ~ ( in @ SY3429 @ SV70 )
| ( in @ ( SV569 @ SY3429 ) @ SV350 ) ) )
= $true )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1525]) ).
thf(1811,plain,
! [SV570: $i > $i > $o,SV351: $i,SV71: $i,SV685: $i] :
( ( ~ ( in @ SV685 @ SV71 )
| ! [SY3573: $i] :
( ~ ( in @ SY3573 @ SV351 )
| ~ ( SV570 @ SV685 @ SY3573 )
| ( in @ ( kpair @ SV685 @ SY3573 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1526]) ).
thf(1812,plain,
! [SV352: $i,SV72: $i,SV571: $i] :
( ( ( ~ ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) ) )
= $true )
| ( ( ! [SY3436: $i] :
( ~ ( in @ SY3436 @ SV72 )
| ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SY3436 ) @ SV352 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1527]) ).
thf(1813,plain,
! [SV572: $i > $i > $o,SV353: $i,SV73: $i,SV686: $i] :
( ( ! [SY3576: $i] :
( ~ ( in @ ( kpair @ SV686 @ SY3576 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SY3439: $i,SY3440: $i] : ( SV572 @ SY3439 @ SY3440 ) ) )
| ( SV572 @ SV686 @ SY3576 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1814,plain,
! [SV573: $i > $i > $o,SV354: $i,SV74: $i] :
( ( ( ~ ! [SY3441: $i] :
( ~ ( in @ SY3441 @ SV74 )
| ~ ! [SY3442: $i] :
~ ~ ( ~ ( in @ SY3442 @ SV354 )
| ~ ( SV573 @ SY3441 @ SY3442 ) ) ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1529]) ).
thf(1815,plain,
! [SV574: $i,SV355: $i,SV75: $i] :
( ( ( ~ ( func @ SV75 @ SV355 @ SV574 ) )
= $true )
| ( ( ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV75 )
| ( in @ ( kpair @ SY3447 @ ( ap @ SV75 @ SV355 @ SV574 @ SY3447 ) ) @ SV574 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1530]) ).
thf(1816,plain,
! [SV356: $i > $o,SV76: $i] :
( ( ( ~ ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV76 )
| ( SV356 @ SY3032 ) ) )
= $false )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1817,plain,
! [SV575: $i,SV357: $i,SV77: $i] :
( ( ( ~ ( subset @ SV77 @ SV357 ) )
= $true )
| ( ( ~ ( in @ SV575 @ SV77 )
| ( in @ SV575 @ SV357 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1532]) ).
thf(1818,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK3_SY3035 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1819,plain,
( ( ! [SY3448: $i] :
( ~ ( breln1 @ sK1_SX0 @ SY3448 )
| ! [SY3449: $i] :
( ~ ( in @ SY3449 @ sK1_SX0 )
| ! [SY3450: $i] :
( ~ ( in @ SY3450 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY3449 @ SY3450 ) @ SY3448 )
| ( in @ ( kpair @ SY3449 @ SY3450 ) @ ( binunion @ sK3_SY3035 @ SY3448 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1533]) ).
thf(1820,plain,
! [SV358: $i,SV78: $i] :
( ( ( SV78 = SV358 )
= $false )
| ( ( ! [SY3039: $i,SY3040: $i] :
( ( SY3039 != SY3040 )
| ~ ( in @ SY3039 @ SV78 )
| ( in @ SY3040 @ SV358 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1821,plain,
! [SV359: $i,SV79: $i] :
( ( ( subset @ SV79 @ SV359 )
= $false )
| ( ( ~ ( subset @ SV359 @ SV79 )
| ( SV79 = SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1822,plain,
! [SV687: $i,SV576: $i,SV360: $i,SV80: $i] :
( ( ( ( kpair @ SV80 @ SV360 )
!= ( kpair @ SV576 @ SV687 ) )
| ( SV360 = SV687 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1536]) ).
thf(1823,plain,
! [SV577: $i,SV361: $i,SV81: $i] :
( ( ( ~ ( func @ SV81 @ SV361 @ SV577 ) )
= $true )
| ( ( ! [SY3452: $i] :
( ~ ( func @ SV81 @ SV361 @ SY3452 )
| ~ ! [SY3453: $i] :
( ~ ( in @ SY3453 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3453 )
= ( ap @ SV81 @ SV361 @ SY3452 @ SY3453 ) ) )
| ! [SY3454: $i] :
( ~ ( in @ SY3454 @ SV81 )
| ! [SY3455: $i] :
( ~ ( in @ SY3455 @ SV361 )
| ~ ( in @ ( kpair @ SY3454 @ SY3455 ) @ SY3452 )
| ( in @ ( kpair @ SY3454 @ SY3455 ) @ SV577 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1824,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ( ~ ( in @ SV362 @ ( powerset @ SV82 ) )
| ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1825,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ( ~ ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) )
| ( in @ SV362 @ ( powerset @ SV82 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1538]) ).
thf(1826,plain,
! [SV363: $i,SV83: $i] :
( ( ( SV83 = SV363 )
= $false )
| ( ( ! [SY3050: $i,SY3051: $i] :
( ( SY3050 != SY3051 )
| ~ ( ~ ( ~ ( in @ SY3050 @ SV83 )
| ( in @ SY3051 @ SV363 ) )
| ~ ( ~ ( in @ SY3051 @ SV363 )
| ( in @ SY3050 @ SV83 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1539]) ).
thf(1827,plain,
! [SV364: $i,SV84: $i] :
( ( ( ( setadjoin @ SV84 @ emptyset )
= ( setadjoin @ SV364 @ emptyset ) )
= $false )
| ( ( SV84 = SV364 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1828,plain,
! [SV85: $i,SV365: $i] :
( ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false )
| ( ( ! [SY3052: $i] :
( ~ ( in @ SY3052 @ ( powerset @ SV85 ) )
| ! [SY3053: $o,SY3054: $i] :
( ~ ( in @ SY3054 @ SV85 )
| ~ ( in @ SY3054 @ ( binunion @ SV365 @ SY3052 ) )
| ~ ( ~ ( in @ SY3054 @ SV365 )
| SY3053 )
| ~ ( ~ ( in @ SY3054 @ SY3052 )
| SY3053 )
| SY3053 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1829,plain,
! [SV688: $o,SV366: $i,SV86: $i,SV578: $i] :
( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
| ~ ( ~ ( in @ SV578 @ SV86 )
| SV688 )
| ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1830,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
| ~ ( ~ ( in @ SV578 @ SV86 )
| $true )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1831,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
| ~ ( ~ ( in @ SV578 @ SV86 )
| $false )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1832,plain,
! [SV367: $i,SV87: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV87 ) )
= $true )
| ( ( ~ ( in @ SV579 @ SV367 )
| ~ ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1543]) ).
thf(1833,plain,
! [SV368: $i,SV88: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ ( cartprod @ SV88 @ SV368 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV580 ) @ SV368 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1544]) ).
thf(1834,plain,
! [SV369: $i,SV89: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ SV89 ) )
= $true )
| ( ( ! [SY3457: $i] :
( ~ ( in @ SY3457 @ SV369 )
| ( ( ksnd @ ( kpair @ SV581 @ SY3457 ) )
= SY3457 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1545]) ).
thf(1835,plain,
! [SV370: $i,SV90: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ ( funcSet @ SV90 @ SV370 ) ) )
= $true )
| ( ( func @ SV90 @ SV370 @ SV582 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1836,plain,
! [SV371: $i,SV91: $i] :
( ( ( SV91 = SV371 )
= $false )
| ( ( subset @ SV91 @ SV371 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1837,plain,
! [SV372: $i,SV92: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV92 ) )
= $true )
| ( ( ! [SY3458: $i] :
( ~ ( in @ SY3458 @ SV372 )
| ( ( kpair @ SV583 @ SY3458 )
= ( kpair @ SV583 @ SY3458 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1838,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) ) )
= $true )
| ( ( ! [SY3459: $o] :
( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SY3459 )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SY3459 )
| SY3459 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1839,plain,
! [SV374: $i,SV94: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV94 ) )
= $true )
| ( ( ~ ~ ( in @ SV585 @ SV374 )
| ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1550]) ).
thf(1840,plain,
! [SV95: $i > $o] :
( ( ( ! [SY2388: $i] :
~ ( SV95 @ SY2388 ) )
= $true )
| ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1841,plain,
! [SV375: $i,SV96: $i] :
( ( ( SV96 = SV375 )
= $false )
| ( ( ! [SY3067: $i,SY3068: $i] :
( ( SY3067 != SY3068 )
| ( ( setadjoin @ SV96 @ SY3067 )
= ( setadjoin @ SV375 @ SY3068 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1552]) ).
thf(1842,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY3069: $i,SY3070: $i] :
( ( SY3069 != SY3070 )
| ~ ( ~ ( ~ ( SV97 @ SY3069 )
| ( SV376 @ SY3070 ) )
| ~ ( ~ ( SV376 @ SY3070 )
| ( SV97 @ SY3069 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1843,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3077: $i] :
( ~ ( in @ SY3077 @ SV98 )
| ! [SY3078: $i] :
( ~ ( in @ SY3078 @ SV98 )
| ~ ( SV377 @ SY3077 )
| ~ ( SV377 @ SY3078 )
| ( SY3077 = SY3078 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1554]) ).
thf(1844,plain,
! [SV99: $o,SV378: $i] :
( ( ( in @ SV378 @ ( prop2set @ SV99 ) )
= $false )
| ( SV99 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1555]) ).
thf(1845,plain,
! [SV379: $i] :
( ( ( in @ SV379 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1556]) ).
thf(1846,plain,
! [SV380: $i] :
( ( ( in @ SV380 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1557]) ).
thf(1847,plain,
! [SV381: $i,SV100: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ SV100 ) )
= $true )
| ( ( ! [SY3460: $i] :
( ~ ( in @ SY3460 @ SV381 )
| ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SY3460 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1558]) ).
thf(1848,plain,
! [SV101: $i,SV382: $i] :
( ( ( in @ SV382 @ ( powerset @ SV101 ) )
= $false )
| ( ( ! [SY3083: $i] :
( ~ ( in @ SY3083 @ ( powerset @ SV101 ) )
| ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SY3083 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1559]) ).
thf(1849,plain,
! [SV102: $i,SV383: $i] :
( ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false )
| ( ( ! [SY3084: $i] :
( ~ ( in @ SY3084 @ ( powerset @ SV102 ) )
| ~ ( subset @ ( setminus @ SV102 @ SY3084 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SY3084 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1560]) ).
thf(1850,plain,
! [SV384: $i,SV103: $i,SV587: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV587 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ ( setadjoin @ SV384 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV103 = SV587 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1561]) ).
thf(1851,plain,
! [SV104: $i,SV385: $i] :
( ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false )
| ( ( ! [SY3086: $i] :
( ~ ( in @ SY3086 @ ( powerset @ SV104 ) )
| ! [SY3087: $i] :
( ~ ( in @ SY3087 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SY3086 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3087 ) @ ( binunion @ SY3086 @ SY3087 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1852,plain,
! [SV105: $i > $o] :
( ( ( ! [SY2423: $i] :
~ ~ ( ~ ( SV105 @ SY2423 )
| ~ ! [SY2424: $i] :
( ~ ( SV105 @ SY2424 )
| ( SY2423 = SY2424 ) ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1563]) ).
thf(1853,plain,
! [SV386: $i > $o,SV106: $i] :
( ( ( ~ ~ ! [SY3088: $i] :
~ ~ ( ~ ( in @ SY3088 @ SV106 )
| ~ ( SV386 @ SY3088 ) ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1854,plain,
! [SV107: $i,SV387: $i] :
( ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false )
| ( ( ! [SY3090: $i] :
( ~ ( in @ SY3090 @ ( powerset @ SV107 ) )
| ! [SY3091: $i] :
( ~ ( in @ SY3091 @ SV107 )
| ~ ~ ( in @ SY3091 @ SV387 )
| ~ ( in @ SY3091 @ ( binintersect @ SV387 @ SY3090 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1565]) ).
thf(1855,plain,
! [SV388: $o,SV108: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ SV108 ) )
= $true )
| ( ( ! [SY3461: $i] :
( ~ ( in @ SY3461 @ SV108 )
| ( in @ ( if @ SV108 @ SV388 @ SV588 @ SY3461 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SY3461 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1856,plain,
! [SV108: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV108 ) )
= $true )
| ( ( ! [SY3462: $i] :
( ~ ( in @ SY3462 @ SV108 )
| ( in @ ( if @ SV108 @ $true @ SV589 @ SY3462 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SY3462 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1857,plain,
! [SV108: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV108 ) )
= $true )
| ( ( ! [SY3463: $i] :
( ~ ( in @ SY3463 @ SV108 )
| ( in @ ( if @ SV108 @ $false @ SV590 @ SY3463 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SY3463 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1568]) ).
thf(1858,plain,
! [SV109: $i,SV389: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV389 ) )
= $true )
| ( ( in @ SV591 @ ( binunion @ SV109 @ SV389 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1859,plain,
! [SV390: $i,SV110: $i] :
( ( ( ( binintersect @ SV110 @ SV390 )
= SV390 )
= $false )
| ( ( subset @ SV390 @ SV110 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1860,plain,
! [SV111: $i,SV391: $i] :
( ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false )
| ( ( ! [SY3095: $i] :
( ~ ( in @ SY3095 @ ( powerset @ SV111 ) )
| ~ ! [SY3096: $i] :
( ~ ( in @ SY3096 @ SV111 )
| ~ ( in @ SY3096 @ SV391 )
| ( in @ SY3096 @ SY3095 ) )
| ~ ! [SY3097: $i] :
( ~ ( in @ SY3097 @ SV111 )
| ~ ( in @ SY3097 @ SY3095 )
| ( in @ SY3097 @ SV391 ) )
| ( SV391 = SY3095 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1861,plain,
! [SV112: $i,SV392: $i] :
( ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false )
| ( ( ! [SY3098: $i] :
( ~ ( in @ SY3098 @ ( powerset @ SV112 ) )
| ! [SY3099: $i] :
( ~ ( in @ SY3099 @ SV112 )
| ~ ~ ( in @ SY3099 @ SV392 )
| ~ ~ ( in @ SY3099 @ SY3098 )
| ~ ( in @ SY3099 @ ( binunion @ SV392 @ SY3098 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1862,plain,
! [SV393: $i,SV113: $i] :
( ( ( ! [SY3100: $i] :
( ~ ( in @ SY3100 @ SV113 )
| ( in @ SY3100 @ SV393 ) ) )
= $false )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1573]) ).
thf(1863,plain,
! [SV394: $i,SV114: $i,SV592: $i] :
( ( ( ~ ~ ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV592 @ SV394 )
| ~ ( in @ SV592 @ SV114 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1574]) ).
thf(1864,plain,
! [SV395: $i,SV115: $i] :
( ( ( breln1 @ SV115 @ SV395 )
= $false )
| ( ( breln1 @ SV115 @ ( breln1invset @ SV115 @ SV395 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1575]) ).
thf(1865,plain,
! [SV396: $o,SV117: $i,SV593: $i] :
( ( ( ~ ( in @ SV593 @ SV117 ) )
= $true )
| ( ( ! [SY3464: $i] :
( ~ ( in @ SY3464 @ SV117 )
| ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3465: $i] :
( ~ ( ~ SV396
| ( SY3465 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3465 != SY3464 ) ) ) )
= ( setadjoin @ SY3464 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1866,plain,
! [SV117: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV117 ) )
= $true )
| ( ( ! [SY3466: $i] :
( ~ ( in @ SY3466 @ SV117 )
| ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3467: $i] :
( ~ ( ~ $true
| ( SY3467 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3467 != SY3466 ) ) ) )
= ( setadjoin @ SY3466 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1578]) ).
thf(1867,plain,
! [SV117: $i,SV595: $i] :
( ( ( ~ ( in @ SV595 @ SV117 ) )
= $true )
| ( ( ! [SY3468: $i] :
( ~ ( in @ SY3468 @ SV117 )
| ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3469: $i] :
( ~ ( ~ $false
| ( SY3469 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3469 != SY3468 ) ) ) )
= ( setadjoin @ SY3468 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1579]) ).
thf(1868,plain,
! [SV118: $i,SV397: $i] :
( ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false )
| ( ( ! [SY3105: $i] :
( ~ ( in @ SY3105 @ ( powerset @ SV118 ) )
| ! [SY3106: $i] :
( ~ ( in @ SY3106 @ ( binintersect @ SV397 @ SY3105 ) )
| ( in @ SY3106 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1869,plain,
! [SV398: $i,SV119: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ ( cartprod @ SV119 @ SV398 ) ) )
= $true )
| ( ( iskpair @ SV596 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1581]) ).
thf(1870,plain,
! [SV399: $i,SV597: $i,SV120: $i] :
( ( ( ~ ( subset @ SV120 @ SV597 ) )
= $true )
| ( ( subset @ SV120 @ ( setadjoin @ SV399 @ SV597 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1582]) ).
thf(1871,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ! [SY3109: $i] :
( ~ ( in @ SY3109 @ SV121 )
| ~ ( SV400 @ SY3109 ) ) )
= $false )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1872,plain,
! [SV122: $i,SV401: $i] :
( ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false )
| ( ( ! [SY3111: $i] :
( ~ ( in @ SY3111 @ ( powerset @ SV122 ) )
| ! [SY3112: $i] :
( ~ ( in @ SY3112 @ SV122 )
| ~ ( in @ SY3112 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SY3111 ) ) )
| ( in @ SY3112 @ ( setminus @ SV122 @ SV401 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1873,plain,
! [SV598: $i > $i > $o,SV402: $i,SV123: $i,SV689: $i] :
( ( ! [SY3579: $i] :
( ~ ( in @ ( kpair @ SV689 @ SY3579 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SY3472: $i,SY3473: $i] : ( SV598 @ SY3472 @ SY3473 ) ) )
| ( in @ SV689 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1585]) ).
thf(1874,plain,
! [SV403: $i,SV124: $i,SV599: $i] :
( ( ( ~ ( in @ SV599 @ SV124 ) )
= $true )
| ( ( in @ SV599 @ ( binunion @ SV124 @ SV403 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1586]) ).
thf(1875,plain,
! [SV600: $i,SV404: $i,SV125: $i] :
( ( ( ~ ( func @ SV125 @ SV404 @ SV600 ) )
= $true )
| ( ( ! [SY3474: $i] :
( ~ ( in @ SY3474 @ SV125 )
| ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SY3474 ) @ SV404 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1876,plain,
! [SV601: $i,SV405: $i,SV126: $i] :
( ( ( ~ ( breln @ SV126 @ SV405 @ SV601 ) )
= $true )
| ( ( ! [SY3475: $i > $o] :
( ~ ! [SY3476: $i] :
( ~ ( in @ SY3476 @ SV126 )
| ! [SY3477: $i] :
( ~ ( in @ SY3477 @ SV405 )
| ~ ( in @ ( kpair @ SY3476 @ SY3477 ) @ SV601 )
| ( SY3475 @ ( kpair @ SY3476 @ SY3477 ) ) ) )
| ! [SY3478: $i] :
( ~ ( in @ SY3478 @ SV601 )
| ( SY3475 @ SY3478 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1877,plain,
! [SV127: $i,SV406: $i] :
( ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false )
| ( ( ! [SY3126: $i] :
( ~ ( in @ SY3126 @ ( powerset @ SV127 ) )
| ! [SY3127: $i] :
( ~ ( in @ SY3127 @ SV127 )
| ~ ( in @ SY3127 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3127 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SY3126 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1589]) ).
thf(1878,plain,
! [SV407: $i,SV128: $i,SV602: $i] :
( ( ( ~ ~ ( in @ SV602 @ SV128 ) )
= $true )
| ( ( ~ ( in @ SV602 @ SV407 )
| ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1590]) ).
thf(1879,plain,
! [SV129: $i > $o] :
( ( ( ! [SY2490: $i] :
~ ~ ( ~ ( SV129 @ SY2490 )
| ~ ! [SY2491: $i] :
( ~ ( SV129 @ SY2491 )
| ( SY2490 = SY2491 ) ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1591]) ).
thf(1880,plain,
! [SV408: $i,SV130: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ ( setadjoin @ SV130 @ SV408 ) ) )
= $true )
| ( ( ( SV603 = SV130 )
| ( in @ SV603 @ SV408 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1592]) ).
thf(1881,plain,
! [SV132: $i,SV409: $i] :
( ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false )
| ( ( ! [SY3130: $i] :
( ~ ( in @ SY3130 @ ( powerset @ SV132 ) )
| ! [SY3131: $i] :
( ~ ( in @ SY3131 @ SV132 )
| ~ ( in @ SY3131 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SY3130 ) ) )
| ( in @ SY3131 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SY3130 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1882,plain,
! [SV133: $i,SV410: $i] :
( ( ( subset @ SV410 @ SV133 )
= $false )
| ( ( ( binintersect @ SV133 @ SV410 )
= SV410 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1595]) ).
thf(1883,plain,
! [SV134: $i,SV411: $i] :
( ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false )
| ( ( ! [SY3132: $i] :
( ~ ( in @ SY3132 @ ( powerset @ SV134 ) )
| ! [SY3133: $i] :
( ~ ( in @ SY3133 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SY3132 ) )
| ~ ( in @ SY3133 @ SV411 )
| ( in @ SY3133 @ SY3132 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1596]) ).
thf(1884,plain,
! [SV135: $i] :
( ( ( ~ ( in @ ( sK4_SY2504 @ SV135 ) @ SV135 ) )
= $false )
| ( ( SV135 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1597]) ).
thf(1885,plain,
! [SV412: $i,SV136: $i,SV604: $i] :
( ( ( ~ ( in @ SV604 @ ( binintersect @ SV136 @ SV412 ) ) )
= $true )
| ( ( in @ SV604 @ SV136 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1886,plain,
! [SV605: $i,SV413: $i,SV137: $i] :
( ( ( ~ ( func @ SV137 @ SV413 @ SV605 ) )
= $true )
| ( ( ! [SY3479: $i] :
( ~ ( func @ SV137 @ SV413 @ SY3479 )
| ~ ! [SY3480: $i] :
( ~ ( in @ SY3480 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3480 )
= ( ap @ SV137 @ SV413 @ SY3479 @ SY3480 ) ) )
| ( SV605 = SY3479 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1599]) ).
thf(1887,plain,
! [SV414: $o,SV138: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV138 ) )
= $true )
| ( ( ! [SY3481: $i] :
( ~ ( in @ SY3481 @ SV138 )
| ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3482: $i] :
( ~ ( ~ SV414
| ( SY3482 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3482 != SY3481 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1888,plain,
! [SV138: $i,SV607: $i] :
( ( ( ~ ( in @ SV607 @ SV138 ) )
= $true )
| ( ( ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV138 )
| ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3484: $i] :
( ~ ( ~ $true
| ( SY3484 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3484 != SY3483 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1889,plain,
! [SV138: $i,SV608: $i] :
( ( ( ~ ( in @ SV608 @ SV138 ) )
= $true )
| ( ( ! [SY3485: $i] :
( ~ ( in @ SY3485 @ SV138 )
| ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3486: $i] :
( ~ ( ~ $false
| ( SY3486 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3486 != SY3485 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1602]) ).
thf(1890,plain,
! [SV139: $i > $o] :
( ( ( ! [SY2515: $i] :
~ ~ ( ~ ( SV139 @ SY2515 )
| ~ ! [SY2516: $i] :
( ~ ( SV139 @ SY2516 )
| ( SY2515 = SY2516 ) ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1603]) ).
thf(1891,plain,
! [SV415: $i > $o,SV140: $i,SV609: $i] :
( ( ( ~ ( in @ SV609 @ SV140 ) )
= $true )
| ( ( ~ ( SV415 @ SV609 )
| ( in @ SV609
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1604]) ).
thf(1892,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY3143: $i,SY3144: $i] :
( ( SY3143 != SY3144 )
| ~ ( ~ ( ~ ( SV141 @ SY3143 )
| ( SV416 @ SY3144 ) )
| ~ ( ~ ( SV416 @ SY3144 )
| ( SV141 @ SY3143 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1605]) ).
thf(1893,plain,
! [SV417: $i,SV142: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) ) )
= $true )
| ( ( ~ ! [SY3488: $i] :
~ ~ ( ~ ( in @ SY3488 @ SV142 )
| ~ ~ ! [SY3489: $i] :
~ ~ ( ~ ( in @ SY3489 @ SV417 )
| ( SV610
!= ( kpair @ SY3488 @ SY3489 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1894,plain,
! [SV143: $i,SV418: $i] :
( ( ( in @ SV418 @ ( powerset @ SV143 ) )
= $false )
| ( ( ! [SY3156: $i] :
( ~ ( in @ SY3156 @ ( powerset @ SV143 ) )
| ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SY3156 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1607]) ).
thf(1895,plain,
! [SV419: $i,SV144: $i] :
( ( ( breln1 @ SV144 @ SV419 )
= $false )
| ( ( ! [SY3157: $i > $o] :
( ~ ! [SY3158: $i] :
( ~ ( in @ SY3158 @ SV144 )
| ! [SY3159: $i] :
( ~ ( in @ SY3159 @ SV144 )
| ~ ( in @ ( kpair @ SY3158 @ SY3159 ) @ SV419 )
| ( SY3157 @ ( kpair @ SY3158 @ SY3159 ) ) ) )
| ! [SY3160: $i] :
( ~ ( in @ SY3160 @ SV419 )
| ( SY3157 @ SY3160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1896,plain,
! [SV145: $i,SV420: $i] :
( ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false )
| ( ( ! [SY3161: $i] :
( ~ ( in @ SY3161 @ ( powerset @ SV145 ) )
| ! [SY3162: $i] :
( ~ ( in @ SY3162 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3162 )
| ( subset @ ( binintersect @ SV420 @ SY3161 ) @ SY3162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1609]) ).
thf(1897,plain,
! [SV421: $i,SV146: $i] :
( ( ( ( binintersect @ SV146 @ SV421 )
= SV146 )
= $false )
| ( ( subset @ SV146 @ SV421 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1898,plain,
! [SV422: $o,SV147: $i,SV611: $i] :
( ( ( ~ ( in @ SV611 @ SV147 ) )
= $true )
| ( ( ! [SY3490: $i] :
( ~ ( in @ SY3490 @ SV147 )
| ~ ~ SV422
| ( in @ SY3490
@ ( dsetconstr @ SV147
@ ^ [SY3491: $i] :
( ~ ( ~ SV422
| ( SY3491 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3491 != SY3490 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1899,plain,
! [SV147: $i,SV612: $i] :
( ( ( ~ ( in @ SV612 @ SV147 ) )
= $true )
| ( ( ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV147 )
| ~ ~ $true
| ( in @ SY3492
@ ( dsetconstr @ SV147
@ ^ [SY3493: $i] :
( ~ ( ~ $true
| ( SY3493 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3493 != SY3492 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1612]) ).
thf(1900,plain,
! [SV147: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV147 ) )
= $true )
| ( ( ! [SY3494: $i] :
( ~ ( in @ SY3494 @ SV147 )
| ~ ~ $false
| ( in @ SY3494
@ ( dsetconstr @ SV147
@ ^ [SY3495: $i] :
( ~ ( ~ $false
| ( SY3495 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3495 != SY3494 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1901,plain,
! [SV423: $o,SV149: $i,SV614: $i] :
( ( ( ~ ( in @ SV614 @ SV149 ) )
= $true )
| ( ( ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV149 )
| ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SY3496 )
= SY3496 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1615]) ).
thf(1902,plain,
! [SV149: $i,SV615: $i] :
( ( ( ~ ( in @ SV615 @ SV149 ) )
= $true )
| ( ( ! [SY3497: $i] :
( ~ ( in @ SY3497 @ SV149 )
| ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SY3497 )
= SY3497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1616]) ).
thf(1903,plain,
! [SV149: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ SV149 ) )
= $true )
| ( ( ! [SY3498: $i] :
( ~ ( in @ SY3498 @ SV149 )
| ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SY3498 )
= SY3498 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1617]) ).
thf(1904,plain,
! [SV424: $i,SV150: $i,SV617: $i] :
( ( ( ~ ( subset @ SV617 @ SV150 ) )
= $true )
| ( ( ~ ( subset @ SV617 @ SV424 )
| ( subset @ SV617 @ ( binintersect @ SV150 @ SV424 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1618]) ).
thf(1905,plain,
! [SV151: $i,SV425: $i] :
( ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false )
| ( ( ! [SY3169: $i] :
( ~ ( in @ SY3169 @ ( powerset @ SV151 ) )
| ~ ( subset @ SV425 @ ( setminus @ SV151 @ SY3169 ) )
| ! [SY3170: $i] :
( ~ ( in @ SY3170 @ SV151 )
| ~ ( in @ SY3170 @ SY3169 )
| ( in @ SY3170 @ ( setminus @ SV151 @ SV425 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1906,plain,
! [SV152: $i,SV426: $i] :
( ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false )
| ( ( ! [SY3171: $i] :
( ~ ( in @ SY3171 @ ( powerset @ SV152 ) )
| ! [SY3172: $i] :
( ~ ( in @ SY3172 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SY3171 )
| ~ ( subset @ SV426 @ SY3172 )
| ( subset @ SV426 @ ( binintersect @ SY3171 @ SY3172 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1620]) ).
thf(1907,plain,
! [SV154: $i,SV427: $i] :
( ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false )
| ( ( ! [SY3173: $i] :
( ~ ( in @ SY3173 @ ( powerset @ SV154 ) )
| ! [SY3174: $i] :
( ~ ( in @ SY3174 @ ( powerset @ SV154 ) )
| ! [SY3175: $i] :
( ~ ( in @ SY3175 @ SV154 )
| ~ ( in @ SY3175 @ ( binintersect @ SV427 @ SY3173 ) )
| ( in @ SY3175 @ ( binunion @ SV427 @ SY3174 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1908,plain,
! [SV428: $i > $o,SV155: $i] :
( ( ( ~ ! [SY3176: $i] :
~ ~ ( ~ ( in @ SY3176 @ SV155 )
| ~ ( SV428 @ SY3176 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1909,plain,
! [SV156: $i,SV429: $i] :
( ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false )
| ( ( ! [SY3178: $i] :
( ~ ( in @ SY3178 @ ( powerset @ SV156 ) )
| ! [SY3179: $i] :
( ~ ( in @ SY3179 @ SV156 )
| ~ ( in @ SY3179 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3179 @ ( binintersect @ SV429 @ SY3178 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1624]) ).
thf(1910,plain,
! [SV157: $i,SV430: $i] :
( ( ( in @ SV430 @ ( powerset @ SV157 ) )
= $false )
| ( ( in @ ( powerset @ SV430 ) @ ( powerset @ ( powerset @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1625]) ).
thf(1911,plain,
! [SV618: $i,SV431: $i,SV158: $i] :
( ( ( ~ ( subset @ SV158 @ SV431 ) )
= $true )
| ( ( ~ ( subset @ SV431 @ SV618 )
| ( subset @ SV158 @ SV618 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1626]) ).
thf(1912,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3181: $i] :
( ~ ( in @ SY3181 @ SV159 )
| ! [SY3182: $i] :
( ~ ( in @ SY3182 @ SV159 )
| ~ ( SV432 @ SY3181 )
| ~ ( SV432 @ SY3182 )
| ( SY3181 = SY3182 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1627]) ).
thf(1913,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( ~ ( in @ SV619 @ SV160 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) )
| ~ ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1628]) ).
thf(1914,plain,
! [SV434: $i > $o,SV161: $i,SV620: $i] :
( ( ( ~ ( in @ SV620 @ SV161 ) )
= $true )
| ( ( ~ ( SV434 @ SV620 )
| ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1629]) ).
thf(1915,plain,
! [SV621: $i,SV435: $i,SV162: $i] :
( ( ( ( setadjoin @ SV162 @ ( setadjoin @ SV435 @ emptyset ) )
!= ( setadjoin @ SV621 @ emptyset ) )
= $true )
| ( ( SV162 = SV435 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1630]) ).
thf(1916,plain,
! [SV436: $i,SV163: $i,SV690: $i,SV622: $i] :
( ( ~ ( in @ ( kpair @ SV622 @ SV690 ) @ ( cartprod @ SV163 @ SV436 ) )
| ( in @ SV690 @ SV436 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1631]) ).
thf(1917,plain,
! [SV437: $i,SV165: $i,SV623: $i] :
( ( ( ~ ( in @ SV623 @ SV165 ) )
= $true )
| ( ( ! [SY3503: $i] :
( ~ ( in @ SY3503 @ SV437 )
| ( in @ ( kpair @ SV623 @ SY3503 ) @ ( cartprod @ SV165 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1918,plain,
! [SV166: $i,SV438: $i] :
( ( ( in @ SV438 @ ( powerset @ SV166 ) )
= $false )
| ( ( ! [SY3195: $i] :
( ~ ( in @ SY3195 @ ( powerset @ SV166 ) )
| ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SY3195 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1919,plain,
! [SV439: $i,SV167: $i,SV624: $i] :
( ( ( ~ ( in @ SV624 @ SV167 ) )
= $true )
| ( ( ! [SY3504: $i] :
( ~ ( in @ SY3504 @ SV439 )
| ( ( kfst @ ( kpair @ SV624 @ SY3504 ) )
= SV624 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1637]) ).
thf(1920,plain,
! [SV440: $i > $o,SV168: $i] :
( ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false )
| ( ( ~ ! [SY3199: $i] :
~ ~ ( ~ ( in @ SY3199 @ SV168 )
| ~ ( SV440 @ SY3199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1921,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
| ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ~ ( ~ ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1922,plain,
! [SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3201: $i] :
( ~ ( in @ SY3201 @ SV442 )
| ~ ! [SY2609: $i] :
~ ~ ( ~ ( SV170 @ SY3201 @ SY2609 )
| ~ ! [SY2610: $i] :
( ~ ( SV170 @ SY3201 @ SY2610 )
| ( SY2609 = SY2610 ) ) ) ) )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1640]) ).
thf(1923,plain,
! [SV171: $i,SV626: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ SV626 ) )
= $true )
| ( ( ~ ( in @ SV626 @ SV171 )
| ( in @ SV443 @ ( setunion @ SV171 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1641]) ).
thf(1924,plain,
! [SV444: $i,SV172: $i] :
( ( ( subset @ SV172 @ SV444 )
= $false )
| ( ( in @ SV172 @ ( powerset @ SV444 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1925,plain,
! [SV627: $i,SV445: $i,SV173: $i] :
( ( ( ~ ( breln @ SV173 @ SV445 @ SV627 ) )
= $true )
| ( ( ! [SY3505: $i > $o] :
( ~ ! [SY3506: $i] :
( ~ ( in @ SY3506 @ SV173 )
| ! [SY3507: $i] :
( ~ ( in @ SY3507 @ SV445 )
| ~ ( in @ ( kpair @ SY3506 @ SY3507 ) @ SV627 )
| ( SY3505 @ ( kpair @ SY3506 @ SY3507 ) ) ) )
| ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV627 )
| ( SY3505 @ SY3508 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1643]) ).
thf(1926,plain,
! [SV691: $i,SV628: $i,SV446: $i,SV174: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV628 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV628 @ ( setadjoin @ SV691 @ emptyset ) ) @ emptyset ) ) )
| ( SV174 = SV628 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1644]) ).
thf(1927,plain,
! [SV447: $i,SV175: $i] :
( ( ( SV175 = SV447 )
= $false )
| ( ( ( powerset @ SV175 )
= ( powerset @ SV447 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1928,plain,
! [SV176: $i,SV448: $i] :
( ( ( in @ SV448 @ SV176 )
= $false )
| ( ( subset @ ( setadjoin @ SV448 @ emptyset ) @ SV176 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1929,plain,
! [SV449: $i,SV177: $i] :
( ( ( ! [SY3216: $i] :
( ~ ( in @ SY3216 @ SV177 )
| ( in @ SY3216 @ SV449 ) ) )
= $false )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1930,plain,
! [SV178: $i,SV450: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV450 ) )
= $true )
| ( ( in @ SV629 @ ( setadjoin @ SV178 @ SV450 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1648]) ).
thf(1931,plain,
! [SV692: $i,SV630: $i,SV451: $i,SV179: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SV692 @ emptyset ) ) @ emptyset ) ) )
| ( SV630 != SV692 )
| ( SV451 = SV692 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1649]) ).
thf(1932,plain,
! [SV452: $i,SV180: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) ) )
= $true )
| ( ( ! [SY3511: $i] :
( ~ ( in @ SY3511 @ SV180 )
| ! [SY3512: $i] :
( ~ ( in @ SY3512 @ SV452 )
| ~ ( in @ ( kpair @ SY3511 @ SY3512 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SY3511 )
= SY3512 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1933,plain,
! [SV453: $i,SV181: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV181 ) )
= $true )
| ( ( in @ ( setadjoin @ SV632 @ emptyset ) @ ( powerset @ ( binunion @ SV181 @ SV453 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1934,plain,
! [SV183: $i,SV454: $i] :
( ( ( in @ SV454 @ ( powerset @ SV183 ) )
= $false )
| ( ( ! [SY3225: $i] :
( ~ ( in @ SY3225 @ ( powerset @ SV183 ) )
| ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SY3225 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1653]) ).
thf(1935,plain,
! [SV184: $i] :
( ( ( ~ ( in @ ( sK5_SY2645 @ SV184 ) @ SV184 ) )
= $false )
| ( ( SV184 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1654]) ).
thf(1936,plain,
! [SV455: $i,SV185: $i] :
( ( ( breln1 @ SV185 @ SV455 )
= $false )
| ( ( ! [SY3226: $i] :
( ~ ( breln1 @ SV185 @ SY3226 )
| ~ ! [SY3227: $i] :
( ~ ( in @ SY3227 @ SV185 )
| ! [SY3228: $i] :
( ~ ( in @ SY3228 @ SV185 )
| ~ ( in @ ( kpair @ SY3227 @ SY3228 ) @ SV455 )
| ( in @ ( kpair @ SY3227 @ SY3228 ) @ SY3226 ) ) )
| ( subset @ SV455 @ SY3226 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1655]) ).
thf(1937,plain,
! [SV456: $i,SV186: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV186 ) )
= $true )
| ( ( ~ ( in @ SV633 @ SV456 )
| ( in @ SV633 @ ( binintersect @ SV186 @ SV456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1656]) ).
thf(1938,plain,
! [SV187: $i,SV457: $i] :
( ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false )
| ( ( ! [SY3230: $i] :
( ~ ( in @ SY3230 @ ( powerset @ SV187 ) )
| ! [SY3231: $i] :
( ~ ( in @ SY3231 @ ( powerset @ SV187 ) )
| ! [SY3232: $i] :
( ~ ( in @ SY3232 @ SV187 )
| ~ ( in @ SY3232 @ ( binintersect @ SV457 @ SY3230 ) )
| ( in @ SY3232 @ ( binintersect @ ( binunion @ SV457 @ SY3231 ) @ ( binunion @ SY3230 @ SY3231 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1657]) ).
thf(1939,plain,
! [SV458: $i,SV188: $i] :
( ( ( breln1 @ SV188 @ SV458 )
= $false )
| ( ( ! [SY3233: $i] :
( ~ ( in @ SY3233 @ SV188 )
| ! [SY3234: $i] :
( ~ ( in @ SY3234 @ SV188 )
| ~ ( in @ ( kpair @ SY3234 @ SY3233 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SY3233 @ SY3234 ) @ SV458 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1658]) ).
thf(1940,plain,
! [SV189: $i,SV459: $i] :
( ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false )
| ( ( ! [SY3235: $o] :
( ~ ! [SY3236: $i] :
( ~ ( in @ SV459 @ SY3236 )
| ~ ( in @ SY3236 @ SV189 )
| SY3235 )
| SY3235 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1941,plain,
! [SV190: $i,SV460: $i] :
( ( ( in @ SV460 @ ( powerset @ SV190 ) )
= $false )
| ( ( subset @ SV460 @ ( setminus @ SV190 @ ( setminus @ SV190 @ SV460 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1660]) ).
thf(1942,plain,
! [SV634: $i,SV461: $i,SV191: $i] :
( ( ( ~ ( func @ SV191 @ SV461 @ SV634 ) )
= $true )
| ( ( ( lam @ SV191 @ SV461
@ ^ [SY3513: $i] : ( ap @ SV191 @ SV461 @ SV634 @ SY3513 ) )
= SV634 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1943,plain,
! [SV192: $i,SV462: $i] :
( ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false )
| ( ( ! [SY3239: $i] :
( ~ ( in @ SY3239 @ ( powerset @ SV192 ) )
| ! [SY3240: $i] :
( ~ ( in @ SY3240 @ SV192 )
| ~ ~ ( in @ SY3240 @ ( binunion @ SV462 @ SY3239 ) )
| ~ ( in @ SY3240 @ SV462 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1944,plain,
! [SV193: $i,SV463: $i] :
( ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false )
| ( ( ! [SY3241: $i] :
( ~ ( in @ SY3241 @ ( powerset @ SV193 ) )
| ! [SY3242: $i] :
( ~ ( in @ SY3242 @ SV193 )
| ~ ( in @ SY3242 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SY3241 ) ) )
| ( in @ SY3242 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SY3241 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1945,plain,
! [SV194: $i,SV464: $i] :
( ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false )
| ( ( ! [SY3243: $i] :
( ~ ( in @ SY3243 @ ( powerset @ SV194 ) )
| ! [SY3244: $i] :
( ~ ( in @ SY3244 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SY3243 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3244 ) @ ( binunion @ SY3243 @ SY3244 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1664]) ).
thf(1946,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) ) )
= $true )
| ( ( ! [SY3514: $o] :
( ~ ( ( SV635 != SV195 )
| SY3514 )
| ~ ( ~ ( in @ SV635 @ SV465 )
| SY3514 )
| SY3514 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1947,plain,
! [SV466: $i,SV196: $i,SV636: $i] :
( ( ( ~ ( in @ SV636 @ ( cartprod @ SV196 @ SV466 ) ) )
= $true )
| ( ( in @ ( kfst @ SV636 ) @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1666]) ).
thf(1948,plain,
! [SV467: $i,SV197: $i] :
( ( ( ~ ~ ! [SY3248: $i] :
~ ~ ( ~ ( in @ SY3248 @ SV197 )
| ~ ( in @ SY3248 @ SV467 ) ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1667]) ).
thf(1949,plain,
! [SV468: $i,SV198: $i] :
( ( ( ( setminus @ SV198 @ SV468 )
= emptyset )
= $false )
| ( ( subset @ SV198 @ SV468 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1668]) ).
thf(1950,plain,
! [SV199: $i,SV469: $i] :
( ( ( in @ SV469 @ ( powerset @ SV199 ) )
= $false )
| ( ( ! [SY3249: $i] :
( ~ ( in @ SY3249 @ ( powerset @ SV199 ) )
| ( in @ ( setminus @ SV469 @ SY3249 ) @ ( powerset @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1669]) ).
thf(1951,plain,
! [SV470: $i,SV637: $i > $i,SV200: $i] :
( ( ( ~ ! [SY3515: $i] :
( ~ ( in @ SY3515 @ SV200 )
| ( in @ ( SV637 @ SY3515 ) @ SV470 ) ) )
= $true )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1952,plain,
! [SV201: $i,SV471: $i] :
( ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false )
| ( ( ~ ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ SV201 )
| ~ ( in @ SV471 @ SY3253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1953,plain,
! [SV472: $i,SV202: $i] :
( ( ( SV202 = SV472 )
= $false )
| ( ( ( setadjoin @ SV202 @ ( setadjoin @ SV472 @ emptyset ) )
= ( setadjoin @ SV202 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1672]) ).
thf(1954,plain,
! [SV203: $i,SV473: $i] :
( ( ( in @ SV473 @ ( powerset @ SV203 ) )
= $false )
| ( ( ! [SY3254: $i] :
( ~ ( in @ SY3254 @ ( powerset @ SV203 ) )
| ( in @ ( binintersect @ SV473 @ SY3254 ) @ ( powerset @ SV203 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1673]) ).
thf(1955,plain,
! [SV204: $i,SV474: $i] :
( ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false )
| ( ( ! [SY3255: $i] :
( ~ ( in @ SY3255 @ ( powerset @ SV204 ) )
| ! [SY3256: $i] :
( ~ ( in @ SY3256 @ ( powerset @ SV204 ) )
| ! [SY3257: $i] :
( ~ ( in @ SY3257 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SY3255 ) @ ( binunion @ SY3256 @ SY3257 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SY3255 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3256 ) @ ( setminus @ SV204 @ SY3257 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1674]) ).
thf(1956,plain,
! [SV475: $i,SV206: $i,SV638: $i] :
( ( ( ~ ( in @ SV638 @ ( binunion @ SV206 @ SV475 ) ) )
= $true )
| ( ( ( in @ SV638 @ SV206 )
| ( in @ SV638 @ SV475 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1676]) ).
thf(1957,plain,
! [SV207: $i > $o] :
( ( ( ! [SY2700: $i] :
~ ~ ( ~ ( SV207 @ SY2700 )
| ~ ! [SY2701: $i] :
( ~ ( SV207 @ SY2701 )
| ( SY2700 = SY2701 ) ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1958,plain,
! [SV208: $i,SV476: $i] :
( ( ( in @ SV476 @ ( breln1Set @ SV208 ) )
= $false )
| ( ( breln1 @ SV208 @ SV476 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1959,plain,
! [SV477: $i,SV209: $i] :
( ( ( SV209 != SV477 )
= $false )
| ( ( ~ ( in @ SV477 @ ( setadjoin @ SV209 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1960,plain,
! [SV210: $i,SV478: $i] :
( ( ( subset @ SV478 @ SV210 )
= $false )
| ( ( in @ SV478 @ ( powerset @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1961,plain,
! [SV479: $i,SV211: $i,SV639: $i] :
( ( ( ~ ( in @ SV639 @ SV211 ) )
= $true )
| ( ( ! [SY3517: $i] :
( ~ ( in @ SY3517 @ SV479 )
| ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SY3517 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1962,plain,
! [SV480: $i,SV212: $i] :
( ( ( breln1 @ SV212 @ SV480 )
= $false )
| ( ( ! [SY3261: $i] :
( ~ ( breln1 @ SV212 @ SY3261 )
| ( breln1 @ SV212 @ ( binunion @ SV480 @ SY3261 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1682]) ).
thf(1963,plain,
! [SV640: $i,SV481: $i,SV213: $i] :
( ( ( ~ ( func @ SV213 @ SV481 @ SV640 ) )
= $true )
| ( ( in @ SV640 @ ( funcSet @ SV213 @ SV481 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1964,plain,
! [SV482: $o,SV214: $i,SV641: $i] :
( ( ( ~ ( in @ SV641 @ SV214 ) )
= $true )
| ( ( ! [SY3518: $i] :
( ~ ( in @ SY3518 @ SV214 )
| ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SY3518 )
= SV641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1965,plain,
! [SV214: $i,SV642: $i] :
( ( ( ~ ( in @ SV642 @ SV214 ) )
= $true )
| ( ( ! [SY3519: $i] :
( ~ ( in @ SY3519 @ SV214 )
| ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SY3519 )
= SV642 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1966,plain,
! [SV214: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ SV214 ) )
= $true )
| ( ( ! [SY3520: $i] :
( ~ ( in @ SY3520 @ SV214 )
| ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SY3520 )
= SV643 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1686]) ).
thf(1967,plain,
! [SV483: $i,SV215: $i] :
( ( ( breln1 @ SV215 @ SV483 )
= $false )
| ( ( ! [SY3265: $i] :
( ~ ( breln1 @ SV215 @ SY3265 )
| ! [SY3266: $i] :
( ~ ( in @ SY3266 @ SV215 )
| ! [SY3267: $i] :
( ~ ( in @ SY3267 @ SV215 )
| ~ ( in @ ( kpair @ SY3266 @ SY3267 ) @ SV483 )
| ( in @ ( kpair @ SY3266 @ SY3267 ) @ ( binunion @ SV483 @ SY3265 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1687]) ).
thf(1968,plain,
! [SV216: $i,SV484: $i] :
( ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false )
| ( ( ! [SY3268: $i] :
( ~ ( in @ SY3268 @ ( powerset @ SV216 ) )
| ~ ( subset @ SV484 @ ( setminus @ SV216 @ SY3268 ) )
| ( subset @ SY3268 @ ( setminus @ SV216 @ SV484 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1688]) ).
thf(1969,plain,
! [SV644: $i > $i > $o,SV485: $i,SV217: $i,SV693: $i] :
( ( ! [SY3582: $i] :
( ~ ( in @ ( kpair @ SV693 @ SY3582 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SY3523: $i,SY3524: $i] : ( SV644 @ SY3523 @ SY3524 ) ) )
| ( in @ SY3582 @ SV485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1689]) ).
thf(1970,plain,
! [SV218: $i,SV486: $i] :
( ( ( in @ SV486 @ ( powerset @ SV218 ) )
= $false )
| ( ( ! [SY3274: $i] :
( ~ ( in @ SY3274 @ ( powerset @ SV218 ) )
| ( ( setminus @ SV218 @ ( binunion @ SV486 @ SY3274 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SY3274 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1971,plain,
! [SV487: $i,SV219: $i,SV645: $i] :
( ( ( ~ ~ ( in @ SV645 @ SV219 ) )
= $true )
| ( ( ~ ~ ( in @ SV645 @ SV487 )
| ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1691]) ).
thf(1972,plain,
! [SV220: $i,SV488: $i] :
( ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false )
| ( ( ! [SY3276: $i] :
( ~ ( in @ SY3276 @ SV220 )
| ~ ( in @ SY3276 @ SV488 )
| ~ ( in @ SY3276 @ ( setminus @ SV220 @ SV488 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1692]) ).
thf(1973,plain,
! [SV489: $i > $o,SV221: $i] :
( ( ( ~ ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV221 )
| ( SV489 @ SY3277 ) ) )
= $false )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1693]) ).
thf(1974,plain,
! [SV490: $i,SV222: $i] :
( ( ( SV222 = SV490 )
= $false )
| ( ( in @ SV222 @ ( setadjoin @ SV490 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1694]) ).
thf(1975,plain,
! [SV223: $i,SV491: $i] :
( ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false )
| ( ( ! [SY3279: $i] :
( ~ ( in @ SY3279 @ ( powerset @ SV223 ) )
| ! [SY3280: $i] :
( ~ ( in @ SY3280 @ SV223 )
| ~ ( in @ SY3280 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SY3279 ) ) )
| ( in @ SY3280 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SY3279 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1976,plain,
! [SV224: $i,SV492: $i,SV646: $i] :
( ( ( ~ ( in @ SV646 @ SV492 ) )
= $true )
| ( ( ~ ( in @ SV646 @ ( setminus @ SV224 @ SV492 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1977,plain,
! [SV493: $i,SV225: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV225 ) )
= $true )
| ( ( ~ ~ ( in @ SV647 @ SV493 )
| ~ ( subset @ SV225 @ SV493 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1978,plain,
! [SV648: $i,SV494: $i,SV226: $i] :
( ( ( ~ ( breln @ SV226 @ SV494 @ SV648 ) )
= $true )
| ( ( ! [SY3525: $i] :
( ~ ( breln @ SV226 @ SV494 @ SY3525 )
| ~ ! [SY3526: $i] :
( ~ ( in @ SY3526 @ SV226 )
| ! [SY3527: $i] :
( ~ ( in @ SY3527 @ SV494 )
| ~ ( in @ ( kpair @ SY3526 @ SY3527 ) @ SV648 )
| ( in @ ( kpair @ SY3526 @ SY3527 ) @ SY3525 ) ) )
| ( subset @ SV648 @ SY3525 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1979,plain,
! [SV227: $i,SV495: $i] :
( ( ( in @ SV495 @ ( powerset @ SV227 ) )
= $false )
| ( ( ! [SY3287: $i] :
( ~ ( in @ SY3287 @ ( powerset @ SV227 ) )
| ( in @ ( binunion @ SV495 @ SY3287 ) @ ( powerset @ SV227 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1980,plain,
! [SV649: $i,SV228: $i,SV496: $i] :
( ( ( ~ ( in @ SV496 @ ( powerset @ SV228 ) ) )
= $true )
| ( ( ~ ( in @ SV649 @ SV496 )
| ( in @ SV649 @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1700]) ).
thf(1981,plain,
! [SV229: $i,SV497: $i] :
( ( ( in @ SV497 @ ( powerset @ SV229 ) )
= $false )
| ( ( subset @ SV497 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1701]) ).
thf(1982,plain,
! [SV498: $i,SV230: $i] :
( ( ( subset @ SV230 @ SV498 )
= $false )
| ( ( ( binintersect @ SV230 @ SV498 )
= SV230 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1702]) ).
thf(1983,plain,
! [SV499: $i,SV231: $i,SV650: $i] :
( ( ( ~ ( in @ SV650 @ SV231 ) )
= $true )
| ( ( ! [SY3528: $i] :
( ~ ( in @ SY3528 @ SV499 )
| ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SY3528 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1703]) ).
thf(1984,plain,
! [SV232: $i,SV500: $i] :
( ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false )
| ( ( ! [SY3291: $i] :
( ~ ( in @ SY3291 @ ( powerset @ SV232 ) )
| ~ ! [SY3292: $i] :
( ~ ( in @ SY3292 @ SV232 )
| ~ ( in @ SY3292 @ SV500 )
| ( in @ SY3292 @ SY3291 ) )
| ( subset @ SV500 @ SY3291 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1704]) ).
thf(1985,plain,
! [SV233: $i,SV501: $i] :
( ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false )
| ( ( ! [SY3293: $i] :
( ~ ( in @ SY3293 @ ( powerset @ SV233 ) )
| ~ ! [SY3294: $i] :
( ~ ( in @ SY3294 @ SV233 )
| ~ ( in @ SY3294 @ SV501 )
| ( in @ SY3294 @ SY3293 ) )
| ( in @ SV501 @ ( powerset @ SY3293 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1986,plain,
! [SV502: $i,SV234: $i,SV651: $i] :
( ( ( ~ ( in @ SV651 @ ( setadjoin @ SV234 @ ( setadjoin @ SV502 @ emptyset ) ) ) )
= $true )
| ( ( ( SV651 = SV234 )
| ( SV651 = SV502 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1706]) ).
thf(1987,plain,
! [SV235: $i,SV503: $i] :
( ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false )
| ( ( ! [SY3296: $i] :
( ~ ( in @ SY3296 @ SV235 )
| ~ ( in @ SY3296 @ SV503 )
| ( in @ SY3296 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1988,plain,
! [SV504: $i,SV236: $i] :
( ( ( ~ ( subset @ SV236 @ SV504 ) )
= $false )
| ( ( SV236 != SV504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1708]) ).
thf(1989,plain,
! [SV505: $o,SV237: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ SV237 ) )
= $true )
| ( ( ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV237 )
| ( in @ ( if @ SV237 @ SV505 @ SV652 @ SY3529 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1709]) ).
thf(1990,plain,
! [SV237: $i,SV653: $i] :
( ( ( ~ ( in @ SV653 @ SV237 ) )
= $true )
| ( ( ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV237 )
| ( in @ ( if @ SV237 @ $true @ SV653 @ SY3530 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1991,plain,
! [SV237: $i,SV654: $i] :
( ( ( ~ ( in @ SV654 @ SV237 ) )
= $true )
| ( ( ! [SY3531: $i] :
( ~ ( in @ SY3531 @ SV237 )
| ( in @ ( if @ SV237 @ $false @ SV654 @ SY3531 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1711]) ).
thf(1992,plain,
! [SV238: $i,SV506: $i] :
( ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false )
| ( ( ! [SY3299: $i] :
( ~ ( in @ SY3299 @ ( powerset @ SV238 ) )
| ! [SY3300: $i] :
( ~ ( in @ SY3300 @ ( powerset @ SV238 ) )
| ! [SY3301: $i] :
( ~ ( in @ SY3301 @ SV238 )
| ~ ( in @ SY3301 @ ( binintersect @ SV506 @ SY3299 ) )
| ( in @ SY3301 @ ( binunion @ SY3299 @ SY3300 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1993,plain,
! [SV507: $i > $o,SV239: $i,SV655: $i] :
( ( ( ~ ( in @ SV655
@ ( dsetconstr @ SV239
@ ^ [SY3303: $i] : ( SV507 @ SY3303 ) ) ) )
= $true )
| ( ( in @ SV655 @ SV239 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1713]) ).
thf(1994,plain,
! [SV508: $i,SV240: $i] :
( ( ( breln1 @ SV240 @ SV508 )
= $false )
| ( ( ! [SY3304: $i] :
( ~ ( breln1 @ SV240 @ SY3304 )
| ! [SY3305: $i] :
( ~ ( in @ SY3305 @ SV240 )
| ! [SY3306: $i] :
( ~ ( in @ SY3306 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3306 ) @ ( breln1compset @ SV240 @ SV508 @ SY3304 ) )
| ! [SY3307: $o] :
( ~ ! [SY3308: $i] :
( ~ ( in @ SY3308 @ SV240 )
| ~ ( in @ ( kpair @ SY3305 @ SY3308 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3308 @ SY3306 ) @ SY3304 )
| SY3307 )
| SY3307 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1995,plain,
! [SV509: $i,SV241: $i] :
( ( ( breln1 @ SV241 @ SV509 )
= $false )
| ( ( ! [SY3309: $i > $o] :
( ~ ! [SY3310: $i] :
( ~ ( in @ SY3310 @ SV241 )
| ! [SY3311: $i] :
( ~ ( in @ SY3311 @ SV241 )
| ~ ( in @ ( kpair @ SY3310 @ SY3311 ) @ SV509 )
| ( SY3309 @ ( kpair @ SY3310 @ SY3311 ) ) ) )
| ! [SY3312: $i] :
( ~ ( in @ SY3312 @ SV509 )
| ( SY3309 @ SY3312 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1996,plain,
! [SV242: $i,SV510: $i] :
( ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false )
| ( ( ! [SY3313: $i] :
( ~ ( in @ SY3313 @ ( powerset @ SV242 ) )
| ! [SY3314: $i] :
( ~ ( in @ SY3314 @ SV242 )
| ~ ( in @ SY3314 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SY3313 ) ) )
| ~ ( in @ SY3314 @ SV510 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1997,plain,
! [SV243: $i,SV511: $i] :
( ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY3315: $i] :
( ~ ( in @ SY3315 @ ( powerset @ SV243 ) )
| ! [SY3316: $i] :
( ~ ( in @ SY3316 @ SV243 )
| ~ ( in @ SY3316 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SY3315 ) ) )
| ( in @ SY3316 @ ( setminus @ SV243 @ SY3315 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1717]) ).
thf(1998,plain,
! [SV512: $i,SV244: $i,SV656: $i] :
( ( ( ~ ( in @ SV656 @ ( funcSet @ SV244 @ SV512 ) ) )
= $true )
| ( ( ( lam @ SV244 @ SV512
@ ^ [SY3533: $i] : ( ap @ SV244 @ SV512 @ SV656 @ SY3533 ) )
= SV656 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1718]) ).
thf(1999,plain,
! [SV245: $i,SV513: $i] :
( ( ( in @ SV513 @ ( powerset @ SV245 ) )
= $false )
| ( ( in @ ( setminus @ SV245 @ SV513 ) @ ( powerset @ SV245 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1719]) ).
thf(2000,plain,
! [SV514: $i,SV246: $i] :
( ( ( SV246 = SV514 )
= $false )
| ( ( ( setunion @ SV246 )
= ( setunion @ SV514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1720]) ).
thf(2001,plain,
! [SV515: $i,SV247: $i] :
( ( ( subset @ SV247 @ SV515 )
= $false )
| ( ( ( setminus @ SV247 @ SV515 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1721]) ).
thf(2002,plain,
! [SV516: $i,SV248: $i] :
( ( ( SV248 = SV516 )
= $false )
| ( ( subset @ SV516 @ SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1722]) ).
thf(2003,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i,SV694: $i] :
( ( ~ ( in @ SV694 @ SV249 )
| ! [SY3585: $i] :
( ~ ( in @ SY3585 @ SV517 )
| ~ ( in @ ( kpair @ SV694 @ SY3585 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SY3585 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1723]) ).
thf(2004,plain,
! [SV250: $i > $o] :
( ( ( ! [SY2811: $i] :
~ ! [SY2812: $i] :
~ ( ~ ( ~ ( SV250 @ SY2812 )
| ( SY2812 = SY2811 ) )
| ~ ( ( SY2812 != SY2811 )
| ( SV250 @ SY2812 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1724]) ).
thf(2005,plain,
! [SV658: $i,SV518: $i,SV251: $i] :
( ( ( ~ ( breln @ SV251 @ SV518 @ SV658 ) )
= $true )
| ( ( ! [SY3538: $i] :
( ~ ( breln @ SV251 @ SV518 @ SY3538 )
| ~ ! [SY3539: $i] :
( ~ ( in @ SY3539 @ SV251 )
| ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV518 )
| ~ ( in @ ( kpair @ SY3539 @ SY3540 ) @ SV658 )
| ( in @ ( kpair @ SY3539 @ SY3540 ) @ SY3538 ) ) )
| ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV251 )
| ! [SY3542: $i] :
( ~ ( in @ SY3542 @ SV518 )
| ~ ( in @ ( kpair @ SY3541 @ SY3542 ) @ SY3538 )
| ( in @ ( kpair @ SY3541 @ SY3542 ) @ SV658 ) ) )
| ( SV658 = SY3538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(2006,plain,
! [SV252: $i,SV519: $i] :
( ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false )
| ( ( ! [SY3330: $i] :
( ~ ( in @ SY3330 @ ( powerset @ SV252 ) )
| ! [SY3331: $i] :
( ~ ( in @ SY3331 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SY3330 ) )
| ~ ( in @ SY3331 @ SY3330 )
| ~ ( in @ SY3331 @ SV519 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1726]) ).
thf(2007,plain,
! [SV253: $i > $o,SV520: $i] :
( ( ( in @ SV520 @ emptyset )
= $false )
| ( ( SV253 @ SV520 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1727]) ).
thf(2008,plain,
! [SV254: $i] :
( ( ( ! [SY2826: $i] :
~ ( in @ SY2826 @ SV254 ) )
= $true )
| ( ( SV254 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1728]) ).
thf(2009,plain,
! [SV521: $i,SV255: $i,SV659: $i] :
( ( ( ~ ( in @ SV659 @ ( setminus @ SV255 @ SV521 ) ) )
= $true )
| ( ( in @ SV659 @ SV255 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1729]) ).
thf(2010,plain,
! [SV522: $i > $o,SV256: $i] :
( ( ( ~ ~ ! [SY3333: $i] :
~ ~ ( ~ ( in @ SY3333 @ SV256 )
| ~ ( SV522 @ SY3333 ) ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(2011,plain,
! [SV257: $i,SV523: $i] :
( ( ( in @ SV523 @ SV257 )
= $false )
| ( ( in @ SV523 @ ( powerset @ ( setunion @ SV257 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(2012,plain,
! [SV524: $i,SV258: $i] :
( ( ( breln1 @ SV258 @ SV524 )
= $false )
| ( ( ! [SY3335: $i] :
( ~ ( breln1 @ SV258 @ SY3335 )
| ! [SY3336: $i] :
( ~ ( in @ SY3336 @ SV258 )
| ! [SY3337: $i] :
( ~ ( in @ SY3337 @ SV258 )
| ! [SY3338: $i] :
( ~ ( in @ SY3338 @ SV258 )
| ~ ( in @ ( kpair @ SY3336 @ SY3338 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3338 @ SY3337 ) @ SY3335 )
| ( in @ ( kpair @ SY3336 @ SY3337 ) @ ( breln1compset @ SV258 @ SV524 @ SY3335 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1732]) ).
thf(2013,plain,
! [SV525: $i,SV259: $i] :
( ( ( breln1 @ SV259 @ SV525 )
= $false )
| ( ( ! [SY3339: $i] :
( ~ ( breln1 @ SV259 @ SY3339 )
| ~ ! [SY3340: $i] :
( ~ ( in @ SY3340 @ SV259 )
| ! [SY3341: $i] :
( ~ ( in @ SY3341 @ SV259 )
| ~ ( in @ ( kpair @ SY3340 @ SY3341 ) @ SV525 )
| ( in @ ( kpair @ SY3340 @ SY3341 ) @ SY3339 ) ) )
| ~ ! [SY3342: $i] :
( ~ ( in @ SY3342 @ SV259 )
| ! [SY3343: $i] :
( ~ ( in @ SY3343 @ SV259 )
| ~ ( in @ ( kpair @ SY3342 @ SY3343 ) @ SY3339 )
| ( in @ ( kpair @ SY3342 @ SY3343 ) @ SV525 ) ) )
| ( SV525 = SY3339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(2014,plain,
! [SV526: $i > $o,SV260: $i,SV660: $i] :
( ( ( ~ ( in @ SV660
@ ( dsetconstr @ SV260
@ ^ [SY3345: $i] : ( SV526 @ SY3345 ) ) ) )
= $true )
| ( ( SV526 @ SV660 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1734]) ).
thf(2015,plain,
! [SV527: $i,SV261: $i] :
( ( ( ! [SY3346: $i] :
~ ( ~ ( ~ ( in @ SY3346 @ SV261 )
| ( in @ SY3346 @ SV527 ) )
| ~ ( ~ ( in @ SY3346 @ SV527 )
| ( in @ SY3346 @ SV261 ) ) ) )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(2016,plain,
! [SV661: $i,SV528: $i,SV262: $i] :
( ( ( ~ ( func @ SV262 @ SV528 @ SV661 ) )
= $true )
| ( ( ! [SY3544: $i] :
( ~ ( in @ SY3544 @ SV262 )
| ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3545: $i] : ( in @ ( kpair @ SY3544 @ SY3545 ) @ SV661 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1736]) ).
thf(2017,plain,
! [SV263: $i > $o] :
( ( ( ! [SY2853: $i] :
~ ~ ( ~ ( SV263 @ SY2853 )
| ~ ! [SY2854: $i] :
( ~ ( SV263 @ SY2854 )
| ( SY2853 = SY2854 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(2018,plain,
! [SV264: $i,SV529: $i] :
( ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false )
| ( ( ! [SY3350: $i] :
( ~ ( in @ SY3350 @ ( powerset @ SV264 ) )
| ! [SY3351: $i] :
( ~ ( in @ SY3351 @ SV264 )
| ~ ( subset @ SV529 @ SY3350 )
| ~ ~ ( in @ SY3351 @ SY3350 )
| ~ ( in @ SY3351 @ SV529 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1738]) ).
thf(2019,plain,
! [SV265: $i] :
( ( ( ! [SY2860: $i] :
~ ( in @ SY2860 @ SV265 ) )
= $true )
| ( ( ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(2020,plain,
! [SV530: $i,SV266: $i,SV662: $i] :
( ( ( ~ ~ ( in @ SV662 @ SV266 ) )
= $true )
| ( ( ~ ( in @ SV662 @ ( setminus @ SV266 @ SV530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1740]) ).
thf(2021,plain,
! [SV695: $i,SV663: $i,SV531: $i,SV267: $i] :
( ( ( ( kpair @ SV267 @ SV531 )
!= ( kpair @ SV663 @ SV695 ) )
| ( SV267 = SV663 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2022,plain,
! [SV268: $i] :
( ( ( SV268 = emptyset )
= $true )
| ( ( ~ ! [SY2868: $i] :
~ ( in @ SY2868 @ SV268 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(2023,plain,
! [SV269: $i,SV532: $i] :
( ( ( in @ SV532 @ ( powerset @ SV269 ) )
= $false )
| ( ( subset @ ( setminus @ SV269 @ ( setminus @ SV269 @ SV532 ) ) @ SV532 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(2024,plain,
! [SV533: $i,SV270: $i] :
( ( ( in @ SV270 @ ( setadjoin @ SV533 @ emptyset ) )
= $false )
| ( ( SV270 = SV533 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(2025,plain,
! [SV272: $i,SV534: $i] :
( ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false )
| ( ( ! [SY3355: $i] :
( ~ ( in @ SY3355 @ ( powerset @ SV272 ) )
| ~ ( subset @ SV534 @ SY3355 )
| ( subset @ ( setminus @ SV272 @ SY3355 ) @ ( setminus @ SV272 @ SV534 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(2026,plain,
! [SV535: $i,SV273: $i,SV664: $i] :
( ( ( ~ ( in @ SV664 @ SV273 ) )
= $true )
| ( ( ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV535 )
| ( in @ ( kpair @ SV664 @ SY3547 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1747]) ).
thf(2027,plain,
! [SV665: $i,SV536: $i,SV274: $i] :
( ( ( ~ ( func @ SV274 @ SV536 @ SV665 ) )
= $true )
| ( ( ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SV274 )
| ( ( ap @ SV274 @ SV536 @ SV665 @ SY3548 )
= ( ap @ SV274 @ SV536 @ SV665 @ SY3548 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(2028,plain,
! [SV275: $i,SV537: $i] :
( ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false )
| ( ( ! [SY3360: $i] :
( ~ ( in @ SY3360 @ ( powerset @ SV275 ) )
| ! [SY3361: $i] :
( ~ ( in @ SY3361 @ SV275 )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3361 @ ( setminus @ SV275 @ SY3360 ) )
| ( in @ SY3361 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SY3360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1749]) ).
thf(2029,plain,
! [SV666: $i,SV538: $i,SV276: $i] :
( ( ( ~ ( func @ SV276 @ SV538 @ SV666 ) )
= $true )
| ( ( ! [SY3549: $i] :
( ~ ( in @ SY3549 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3550: $i] : ( in @ ( kpair @ SY3549 @ SY3550 ) @ SV666 ) ) )
@ SV538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1750]) ).
thf(2030,plain,
! [SV539: $i,SV277: $i,SV667: $i] :
( ( ( ~ ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) ) )
= $true )
| ( ( ! [SY3551: $i] :
( ~ ( in @ SY3551 @ SV277 )
| ( in @ ( kpair @ SY3551 @ ( ap @ SV277 @ SV539 @ SV667 @ SY3551 ) ) @ SV667 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1751]) ).
thf(2031,plain,
! [SV540: $i > $o,SV278: $i] :
( ( ( ~ ! [SY3367: $i] :
~ ~ ( ~ ( in @ SY3367 @ SV278 )
| ~ ~ ( SV540 @ SY3367 ) ) )
= $false )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1752]) ).
thf(2032,plain,
! [SV541: $i,SV279: $i] :
( ( ( breln1 @ SV279 @ SV541 )
= $false )
| ( ( ! [SY3369: $i] :
( ~ ( in @ SY3369 @ SV279 )
| ! [SY3370: $i] :
( ~ ( in @ SY3370 @ SV279 )
| ~ ( in @ ( kpair @ SY3369 @ SY3370 ) @ SV541 )
| ( in @ ( kpair @ SY3370 @ SY3369 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(2033,plain,
! [SV542: $i,SV668: $i > $i,SV280: $i] :
( ( ( ~ ! [SY3552: $i] :
( ~ ( in @ SY3552 @ SV280 )
| ( in @ ( SV668 @ SY3552 ) @ SV542 ) ) )
= $true )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1754]) ).
thf(2034,plain,
! [SV543: $i,SV281: $i,SV696: $i,SV669: $i] :
( ( ~ ( in @ ( kpair @ SV669 @ SV696 ) @ ( cartprod @ SV281 @ SV543 ) )
| ( in @ SV669 @ SV281 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1755]) ).
thf(2035,plain,
! [SV544: $i,SV670: $i > $i,SV282: $i] :
( ( ( ~ ! [SY3556: $i] :
( ~ ( in @ SY3556 @ SV282 )
| ( in @ ( SV670 @ SY3556 ) @ SV544 ) ) )
= $true )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1756]) ).
thf(2036,plain,
! [SV283: $i,SV545: $i] :
( ( ( in @ SV545 @ ( powerset @ SV283 ) )
= $false )
| ( ( ! [SY3381: $i] :
( ~ ( in @ SY3381 @ ( powerset @ SV283 ) )
| ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SY3381 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(2037,plain,
! [SV284: $i] :
( ( ( SV284 = emptyset )
= $true )
| ( ( ~ ! [SY2910: $i] :
~ ~ ( ~ ( in @ SY2910 @ SV284 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1758]) ).
thf(2038,plain,
! [SV546: $i,SV285: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV285 ) )
= $true )
| ( ( ~ ~ ( in @ SV671 @ SV546 )
| ( SV285 != SV546 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(2039,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ( ~ ~ ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) ) )
= $true )
| ( ( ~ ( in @ SV672 @ SV286 )
| ( in @ SV672 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(2040,plain,
! [SV673: $i,SV548: $i,SV287: $i] :
( ( ( ~ ( func @ SV287 @ SV548 @ SV673 ) )
= $true )
| ( ( ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV287 )
| ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SV548 )
| ~ ( in @ ( kpair @ SY3559 @ SY3560 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SY3559 )
= SY3560 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1761]) ).
thf(2041,plain,
! [SV549: $o,SV288: $i,SV674: $i] :
( ( ( ~ ( in @ SV674 @ SV288 ) )
= $true )
| ( ( ! [SY3561: $i] :
( ~ ( in @ SY3561 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3562: $i] :
( ~ ( ~ SV549
| ( SY3562 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3562 != SY3561 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1762]) ).
thf(2042,plain,
! [SV288: $i,SV675: $i] :
( ( ( ~ ( in @ SV675 @ SV288 ) )
= $true )
| ( ( ! [SY3563: $i] :
( ~ ( in @ SY3563 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3564: $i] :
( ~ ( ~ $true
| ( SY3564 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3564 != SY3563 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1763]) ).
thf(2043,plain,
! [SV288: $i,SV676: $i] :
( ( ( ~ ( in @ SV676 @ SV288 ) )
= $true )
| ( ( ! [SY3565: $i] :
( ~ ( in @ SY3565 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3566: $i] :
( ~ ( ~ $false
| ( SY3566 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3566 != SY3565 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1764]) ).
thf(2044,plain,
! [SV550: $i,SV289: $i,SV677: $i] :
( ( ( ~ ( in @ SV677 @ ( cartprod @ SV289 @ SV550 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV677 ) @ ( ksnd @ SV677 ) )
= SV677 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1765]) ).
thf(2045,plain,
! [SV551: $i,SV290: $i,SV678: $i] :
( ( ( ~ ( in @ SV678 @ ( setadjoin @ SV290 @ ( setadjoin @ SV551 @ emptyset ) ) ) )
= $true )
| ( ( ( SV678 = SV290 )
| ( SV678 = SV551 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(2046,plain,
! [SV291: $i > $o] :
( ( ( ! [SY2927: $i] :
~ ~ ( ~ ( SV291 @ SY2927 )
| ~ ! [SY2928: $i] :
( ~ ( SV291 @ SY2928 )
| ( SY2927 = SY2928 ) ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1767]) ).
thf(2047,plain,
! [SV552: $i,SV292: $i] :
( ( ( in @ SV292 @ ( setadjoin @ SV552 @ emptyset ) )
= $false )
| ( ( in @ SV552 @ ( setadjoin @ SV292 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(2048,plain,
! [SV553: $i,SV293: $i] :
( ( ( SV293 = SV553 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV293 @ ( setadjoin @ SV553 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV293 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(2049,plain,
! [SV554: $i,SV294: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV294 ) )
= $true )
| ( ( ~ ~ ( in @ SV679 @ SV554 )
| ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1770]) ).
thf(2050,plain,
! [SV295: $i,SV697: $o] :
( ( SV697 = $true )
| ( ( in @ SV295 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1771]) ).
thf(2051,plain,
! [SV295: $i] :
( ( $true = $true )
| ( ( in @ SV295 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1771]) ).
thf(2052,plain,
! [SV295: $i] :
( ( $false = $true )
| ( ( in @ SV295 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1771]) ).
thf(2053,plain,
! [SV555: $o,SV296: $i,SV680: $i] :
( ( ( ~ ( in @ SV680 @ SV296 ) )
= $true )
| ( ( ! [SY3567: $i] :
( ~ ( in @ SY3567 @ SV296 )
| ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3568: $i] :
( ~ ( ~ SV555
| ( SY3568 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3568 != SY3567 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1772]) ).
thf(2054,plain,
! [SV296: $i,SV681: $i] :
( ( ( ~ ( in @ SV681 @ SV296 ) )
= $true )
| ( ( ! [SY3569: $i] :
( ~ ( in @ SY3569 @ SV296 )
| ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3570: $i] :
( ~ ( ~ $true
| ( SY3570 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3570 != SY3569 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1773]) ).
thf(2055,plain,
! [SV296: $i,SV682: $i] :
( ( ( ~ ( in @ SV682 @ SV296 ) )
= $true )
| ( ( ! [SY3571: $i] :
( ~ ( in @ SY3571 @ SV296 )
| ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3572: $i] :
( ~ ( ~ $false
| ( SY3572 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3572 != SY3571 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1774]) ).
thf(2056,plain,
! [SV320: $i,SV35: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( powerset @ SV35 ) )
| ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SV698 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SV698 ) ) ) )
= $true )
| ( ( in @ SV320 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1775]) ).
thf(2057,plain,
! [SV321: $i,SV36: $i,SV559: $i] :
( ( ( in @ SV559 @ ( setminus @ SV36 @ SV321 ) )
= $false )
| ( ( ~ ( in @ SV559 @ SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1776]) ).
thf(2058,plain,
! [SV322: $i,SV37: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ ( powerset @ SV37 ) )
| ! [SY3588: $i] :
( ~ ( in @ SY3588 @ ( powerset @ SV37 ) )
| ! [SY3589: $i] :
( ~ ( in @ SY3589 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY3588 )
| ~ ( subset @ SV699 @ SY3589 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SY3588 @ SY3589 ) ) ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2059,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ~ ( ~ ( SV38 @ SV700 )
| ~ ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(2060,plain,
! [SV324: $i,SV701: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV701 )
| ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SV701 ) ) )
= $true )
| ( ( breln1 @ SV40 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1780]) ).
thf(2061,plain,
! [SV560: $i,SV325: $i,SV41: $i] :
( ( ( subset @ SV41 @ SV325 )
= $false )
| ( ( ~ ~ ( in @ SV560 @ SV325 )
| ~ ( in @ SV560 @ SV41 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(2062,plain,
! [SV326: $i,SV42: $i,SV561: $i] :
( ( ( in @ SV561 @ SV42 )
= $false )
| ( ( ! [SY3400: $i] :
( ~ ( in @ SY3400 @ SV326 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SY3400 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(2063,plain,
! [SV327: $i,SV43: $i,SV562: $i] :
( ( ( in @ SV562 @ ( binintersect @ SV43 @ SV327 ) )
= $false )
| ( ( in @ SV562 @ SV327 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(2064,plain,
! [SV702: $i > $o,SV328: $i,SV44: $i] :
( ( ( ! [SY3591: $i > $o] :
( ~ ! [SY3592: $i] :
( ~ ( in @ SY3592 @ SV44 )
| ! [SY3593: $i] :
( ~ ( in @ SY3593 @ SV328 )
| ( SY3592 != SY3593 )
| ~ ( ~ ( ~ ( SV702 @ SY3592 )
| ( SY3591 @ SY3593 ) )
| ~ ( ~ ( SY3591 @ SY3593 )
| ( SV702 @ SY3592 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SX4: $i] : ( SY3591 @ SX4 ) ) ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(2065,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
| ~ ! [SY3410: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY3410 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3410 ) )
| ~ ! [SY3413: $i] :
~ ~ ! [SY3414: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3413 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3414 @ SY3410 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3413 )
| ~ ( in @ SX5 @ SY3410 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3413 ) )
| ( in @ SY3414 @ SY3416 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1785]) ).
thf(2066,plain,
! [SV329: $i > $o,SV46: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV46 )
| ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV46 )
| ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SY3596 )
| ( SV703 = SY3596 ) ) )
= $true )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2067,plain,
! [SV331: $i,SV563: $i > $i,SV49: $i] :
( ( ( ! [SY3418: $i] :
( ~ ( in @ SY3418 @ SV49 )
| ( in @ ( SV563 @ SY3418 ) @ SV331 ) ) )
= $false )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(2068,plain,
! [SV50: $i,SV683: $i] :
( ( ( ~ ( in @ SV683 @ SV50 ) )
= $true )
| ( ( ( setunion @ SV50 )
= SV683 )
= $true )
| ( ( singleton @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1789]) ).
thf(2069,plain,
! [SV51: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK6_SY2972 @ SV332 @ SV51 ) @ SV51 )
| ( in @ ( sK6_SY2972 @ SV332 @ SV51 ) @ SV332 ) )
= $false )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1790]) ).
thf(2070,plain,
! [SV52: $i] :
( ( ( ~ ( in @ emptyset @ SV52 ) )
= $true )
| ( ( ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1791]) ).
thf(2071,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ( in @ SV333 @ ( setunion @ SV53 ) )
| ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(2072,plain,
! [SV53: $i,SV333: $i] :
( ( ~ ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) )
| ( in @ SV333 @ ( setunion @ SV53 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1793]) ).
thf(2073,plain,
! [SV334: $i > $o,SV54: $i,SV564: $i] :
( ( ( in @ SV564 @ SV54 )
= $false )
| ( ( ~ ( SV334 @ SV564 )
| ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1794]) ).
thf(2074,plain,
! [SV335: $i,SV565: $i > $i,SV55: $i] :
( ( ( ! [SY3422: $i] :
( ~ ( in @ SY3422 @ SV55 )
| ( in @ ( SV565 @ SY3422 ) @ SV335 ) ) )
= $false )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1795]) ).
thf(2075,plain,
! [SV336: $i,SV56: $i,SV566: $i] :
( ( ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) )
= $false )
| ( ( ! [SY3425: $i] :
( ~ ( in @ SY3425 @ SV56 )
| ( ( ap @ SV56 @ SV336 @ SV566 @ SY3425 )
= ( ap @ SV56 @ SV336 @ SV566 @ SY3425 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(2076,plain,
! [SV337: $i,SV57: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ ( powerset @ SV57 ) )
| ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV57 )
| ~ ( in @ SY3597 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SY3597 @ ( setminus @ SV57 @ SV337 ) ) ) )
= $true )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2077,plain,
! [SV684: $i,SV567: $i,SV338: $i,SV58: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV338 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV567 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV567 @ ( setadjoin @ SV684 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV338 = SV684 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1798]) ).
thf(2078,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ SV59 )
| ~ ~ ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SV705 @ SV339 ) )
= $true )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2079,plain,
! [SV341: $i,SV61: $i,SV568: $i] :
( ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( ! [SY3427: $i] :
( ~ ( in @ SY3427 @ ( funcSet @ SV61 @ SV341 ) )
| ~ ! [SY3428: $i] :
( ~ ( in @ SY3428 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3428 )
= ( ap @ SV61 @ SV341 @ SY3427 @ SY3428 ) ) )
| ( SV568 = SY3427 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(2080,plain,
! [SV342: $i,SV62: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ ( powerset @ SV62 ) )
| ~ ( subset @ SV342 @ ( setminus @ SV62 @ SV706 ) )
| ( subset @ SV706 @ ( setminus @ SV62 @ SV342 ) ) )
= $true )
| ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2081,plain,
! [SV343: $i,SV63: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ ( powerset @ SV63 ) )
| ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV63 )
| ~ ~ ( in @ SY3598 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SY3598 @ SV707 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1803]) ).
thf(2082,plain,
! [SV344: $i,SV64: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ ( powerset @ SV64 ) )
| ! [SY3599: $i] :
( ~ ( in @ SY3599 @ ( powerset @ SV64 ) )
| ~ ( subset @ SV708 @ SY3599 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SY3599 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1804]) ).
thf(2083,plain,
! [SV345: $i,SV65: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ ( powerset @ SV65 ) )
| ! [SY3600: $i] :
( ~ ( in @ SY3600 @ SV65 )
| ~ ~ ( in @ SY3600 @ SV709 )
| ~ ( in @ SY3600 @ ( binintersect @ SV345 @ SV709 ) ) ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1805]) ).
thf(2084,plain,
! [SV346: $i,SV66: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV66 )
| ~ ( in @ SV710 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SV710 @ SV346 ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1806]) ).
thf(2085,plain,
! [SV347: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK7_SY3000 @ SV67 @ SV347 ) @ SV347 )
| ( in @ ( sK7_SY3000 @ SV67 @ SV347 ) @ SV67 ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1807]) ).
thf(2086,plain,
! [SV348: $i,SV711: $i,SV68: $i] :
( ( ( ~ ( breln1 @ SV68 @ SV711 )
| ! [SY3601: $i] :
( ~ ( in @ SY3601 @ SV68 )
| ! [SY3602: $i] :
( ~ ( in @ SY3602 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3602 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3603: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3603 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3603 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3603 @ SY3602 ) @ SV711 ) ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1808]) ).
thf(2087,plain,
! [SV349: $i,SV69: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( powerset @ SV69 ) )
| ! [SY3604: $i] :
( ~ ( in @ SY3604 @ SV69 )
| ~ ( in @ SY3604 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SY3604 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2088,plain,
! [SV350: $i,SV569: $i > $i,SV70: $i] :
( ( ( ! [SY3429: $i] :
( ~ ( in @ SY3429 @ SV70 )
| ( in @ ( SV569 @ SY3429 ) @ SV350 ) ) )
= $false )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(2089,plain,
! [SV570: $i > $i > $o,SV351: $i,SV71: $i,SV685: $i] :
( ( ( ~ ( in @ SV685 @ SV71 ) )
= $true )
| ( ( ! [SY3573: $i] :
( ~ ( in @ SY3573 @ SV351 )
| ~ ( SV570 @ SV685 @ SY3573 )
| ( in @ ( kpair @ SV685 @ SY3573 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1811]) ).
thf(2090,plain,
! [SV352: $i,SV72: $i,SV571: $i] :
( ( ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) )
= $false )
| ( ( ! [SY3436: $i] :
( ~ ( in @ SY3436 @ SV72 )
| ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SY3436 ) @ SV352 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(2091,plain,
! [SV572: $i > $i > $o,SV353: $i,SV73: $i,SV713: $i,SV686: $i] :
( ( ~ ( in @ ( kpair @ SV686 @ SV713 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SY3439: $i,SY3440: $i] : ( SV572 @ SY3439 @ SY3440 ) ) )
| ( SV572 @ SV686 @ SV713 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2092,plain,
! [SV573: $i > $i > $o,SV354: $i,SV74: $i] :
( ( ( ! [SY3441: $i] :
( ~ ( in @ SY3441 @ SV74 )
| ~ ! [SY3442: $i] :
~ ~ ( ~ ( in @ SY3442 @ SV354 )
| ~ ( SV573 @ SY3441 @ SY3442 ) ) ) )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(2093,plain,
! [SV574: $i,SV355: $i,SV75: $i] :
( ( ( func @ SV75 @ SV355 @ SV574 )
= $false )
| ( ( ! [SY3447: $i] :
( ~ ( in @ SY3447 @ SV75 )
| ( in @ ( kpair @ SY3447 @ ( ap @ SV75 @ SV355 @ SV574 @ SY3447 ) ) @ SV574 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(2094,plain,
! [SV356: $i > $o,SV76: $i] :
( ( ( ! [SY3032: $i] :
( ~ ( in @ SY3032 @ SV76 )
| ( SV356 @ SY3032 ) ) )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(2095,plain,
! [SV575: $i,SV357: $i,SV77: $i] :
( ( ( subset @ SV77 @ SV357 )
= $false )
| ( ( ~ ( in @ SV575 @ SV77 )
| ( in @ SV575 @ SV357 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(2096,plain,
( ( breln1 @ sK1_SX0 @ sK3_SY3035 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1818]) ).
thf(2097,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK8_SY3448 )
| ! [SY3607: $i] :
( ~ ( in @ SY3607 @ sK1_SX0 )
| ! [SY3608: $i] :
( ~ ( in @ SY3608 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY3607 @ SY3608 ) @ sK8_SY3448 )
| ( in @ ( kpair @ SY3607 @ SY3608 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[1819]) ).
thf(2098,plain,
! [SV358: $i,SV78: $i,SV714: $i] :
( ( ( ! [SY3609: $i] :
( ( SV714 != SY3609 )
| ~ ( in @ SV714 @ SV78 )
| ( in @ SY3609 @ SV358 ) ) )
= $true )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1820]) ).
thf(2099,plain,
! [SV79: $i,SV359: $i] :
( ( ( ~ ( subset @ SV359 @ SV79 ) )
= $true )
| ( ( SV79 = SV359 )
= $true )
| ( ( subset @ SV79 @ SV359 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(2100,plain,
! [SV687: $i,SV576: $i,SV360: $i,SV80: $i] :
( ( ( ( kpair @ SV80 @ SV360 )
!= ( kpair @ SV576 @ SV687 ) )
= $true )
| ( ( SV360 = SV687 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1822]) ).
thf(2101,plain,
! [SV577: $i,SV361: $i,SV81: $i] :
( ( ( func @ SV81 @ SV361 @ SV577 )
= $false )
| ( ( ! [SY3452: $i] :
( ~ ( func @ SV81 @ SV361 @ SY3452 )
| ~ ! [SY3453: $i] :
( ~ ( in @ SY3453 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3453 )
= ( ap @ SV81 @ SV361 @ SY3452 @ SY3453 ) ) )
| ! [SY3454: $i] :
( ~ ( in @ SY3454 @ SV81 )
| ! [SY3455: $i] :
( ~ ( in @ SY3455 @ SV361 )
| ~ ( in @ ( kpair @ SY3454 @ SY3455 ) @ SY3452 )
| ( in @ ( kpair @ SY3454 @ SY3455 ) @ SV577 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(2102,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ( in @ SV362 @ ( powerset @ SV82 ) )
| ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1824]) ).
thf(2103,plain,
! [SV82: $i,SV362: $i] :
( ( ~ ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) )
| ( in @ SV362 @ ( powerset @ SV82 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1825]) ).
thf(2104,plain,
! [SV363: $i,SV83: $i,SV715: $i] :
( ( ( ! [SY3610: $i] :
( ( SV715 != SY3610 )
| ~ ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SY3610 @ SV363 ) )
| ~ ( ~ ( in @ SY3610 @ SV363 )
| ( in @ SV715 @ SV83 ) ) ) ) )
= $true )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1826]) ).
thf(2105,plain,
! [SV365: $i,SV85: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ ( powerset @ SV85 ) )
| ! [SY3611: $o,SY3612: $i] :
( ~ ( in @ SY3612 @ SV85 )
| ~ ( in @ SY3612 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SY3612 @ SV365 )
| SY3611 )
| ~ ( ~ ( in @ SY3612 @ SV716 )
| SY3611 )
| SY3611 ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1828]) ).
thf(2106,plain,
! [SV688: $o,SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| SV688 )
| ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1829]) ).
thf(2107,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $true )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1830]) ).
thf(2108,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $false )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(2109,plain,
! [SV367: $i,SV87: $i,SV579: $i] :
( ( ( in @ SV579 @ SV87 )
= $false )
| ( ( ~ ( in @ SV579 @ SV367 )
| ~ ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(2110,plain,
! [SV368: $i,SV88: $i,SV580: $i] :
( ( ( in @ SV580 @ ( cartprod @ SV88 @ SV368 ) )
= $false )
| ( ( in @ ( ksnd @ SV580 ) @ SV368 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(2111,plain,
! [SV369: $i,SV89: $i,SV581: $i] :
( ( ( in @ SV581 @ SV89 )
= $false )
| ( ( ! [SY3457: $i] :
( ~ ( in @ SY3457 @ SV369 )
| ( ( ksnd @ ( kpair @ SV581 @ SY3457 ) )
= SY3457 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1834]) ).
thf(2112,plain,
! [SV370: $i,SV90: $i,SV582: $i] :
( ( ( in @ SV582 @ ( funcSet @ SV90 @ SV370 ) )
= $false )
| ( ( func @ SV90 @ SV370 @ SV582 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1835]) ).
thf(2113,plain,
! [SV372: $i,SV92: $i,SV583: $i] :
( ( ( in @ SV583 @ SV92 )
= $false )
| ( ( ! [SY3458: $i] :
( ~ ( in @ SY3458 @ SV372 )
| ( ( kpair @ SV583 @ SY3458 )
= ( kpair @ SV583 @ SY3458 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(2114,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false )
| ( ( ! [SY3459: $o] :
( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SY3459 )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SY3459 )
| SY3459 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2115,plain,
! [SV374: $i,SV94: $i,SV585: $i] :
( ( ( in @ SV585 @ SV94 )
= $false )
| ( ( ~ ~ ( in @ SV585 @ SV374 )
| ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1839]) ).
thf(2116,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV717 ) )
= $true )
| ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2117,plain,
! [SV375: $i,SV96: $i,SV718: $i] :
( ( ( ! [SY3613: $i] :
( ( SV718 != SY3613 )
| ( ( setadjoin @ SV96 @ SV718 )
= ( setadjoin @ SV375 @ SY3613 ) ) ) )
= $true )
| ( ( SV96 = SV375 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2118,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3614: $i] :
( ( ( sK9_SY3069 @ SV376 @ SV97 )
!= SY3614 )
| ~ ( ~ ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ SY3614 ) )
| ~ ( ~ ( SV376 @ SY3614 )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1842]) ).
thf(2119,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
| ! [SY3615: $i] :
( ~ ( in @ SY3615 @ SV98 )
| ~ ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
| ~ ( SV377 @ SY3615 )
| ( ( sK10_SY3077 @ SV377 @ SV98 )
= SY3615 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1843]) ).
thf(2120,plain,
! [SV381: $i,SV100: $i,SV586: $i] :
( ( ( in @ SV586 @ SV100 )
= $false )
| ( ( ! [SY3460: $i] :
( ~ ( in @ SY3460 @ SV381 )
| ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SY3460 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(2121,plain,
! [SV382: $i,SV101: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ ( powerset @ SV101 ) )
| ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SV719 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) ) )
= $true )
| ( ( in @ SV382 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1848]) ).
thf(2122,plain,
! [SV383: $i,SV102: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( powerset @ SV102 ) )
| ~ ( subset @ ( setminus @ SV102 @ SV720 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SV720 ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1849]) ).
thf(2123,plain,
! [SV384: $i,SV103: $i,SV587: $i] :
( ( ( in @ ( setadjoin @ SV587 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV103 @ ( setadjoin @ SV384 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV103 = SV587 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1850]) ).
thf(2124,plain,
! [SV385: $i,SV104: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ ( powerset @ SV104 ) )
| ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3616 ) @ ( binunion @ SV721 @ SY3616 ) ) ) ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2125,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ~ ( ~ ( SV105 @ SV722 )
| ~ ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1852]) ).
thf(2126,plain,
! [SV386: $i > $o,SV106: $i] :
( ( ( ~ ! [SY3088: $i] :
~ ~ ( ~ ( in @ SY3088 @ SV106 )
| ~ ( SV386 @ SY3088 ) ) )
= $true )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1853]) ).
thf(2127,plain,
! [SV387: $i,SV107: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ ( powerset @ SV107 ) )
| ! [SY3618: $i] :
( ~ ( in @ SY3618 @ SV107 )
| ~ ~ ( in @ SY3618 @ SV387 )
| ~ ( in @ SY3618 @ ( binintersect @ SV387 @ SV723 ) ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1854]) ).
thf(2128,plain,
! [SV388: $o,SV108: $i,SV588: $i] :
( ( ( in @ SV588 @ SV108 )
= $false )
| ( ( ! [SY3461: $i] :
( ~ ( in @ SY3461 @ SV108 )
| ( in @ ( if @ SV108 @ SV388 @ SV588 @ SY3461 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SY3461 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1855]) ).
thf(2129,plain,
! [SV108: $i,SV589: $i] :
( ( ( in @ SV589 @ SV108 )
= $false )
| ( ( ! [SY3462: $i] :
( ~ ( in @ SY3462 @ SV108 )
| ( in @ ( if @ SV108 @ $true @ SV589 @ SY3462 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SY3462 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(2130,plain,
! [SV108: $i,SV590: $i] :
( ( ( in @ SV590 @ SV108 )
= $false )
| ( ( ! [SY3463: $i] :
( ~ ( in @ SY3463 @ SV108 )
| ( in @ ( if @ SV108 @ $false @ SV590 @ SY3463 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SY3463 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(2131,plain,
! [SV109: $i,SV389: $i,SV591: $i] :
( ( ( in @ SV591 @ SV389 )
= $false )
| ( ( in @ SV591 @ ( binunion @ SV109 @ SV389 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1858]) ).
thf(2132,plain,
! [SV391: $i,SV111: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( powerset @ SV111 ) )
| ~ ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV111 )
| ~ ( in @ SY3619 @ SV391 )
| ( in @ SY3619 @ SV724 ) )
| ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2133,plain,
! [SV392: $i,SV112: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ ( powerset @ SV112 ) )
| ! [SY3621: $i] :
( ~ ( in @ SY3621 @ SV112 )
| ~ ~ ( in @ SY3621 @ SV392 )
| ~ ~ ( in @ SY3621 @ SV725 )
| ~ ( in @ SY3621 @ ( binunion @ SV392 @ SV725 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2134,plain,
! [SV113: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK11_SY3100 @ SV393 @ SV113 ) @ SV113 )
| ( in @ ( sK11_SY3100 @ SV393 @ SV113 ) @ SV393 ) )
= $false )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1862]) ).
thf(2135,plain,
! [SV394: $i,SV114: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV592 @ SV394 )
| ~ ( in @ SV592 @ SV114 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1863]) ).
thf(2136,plain,
! [SV396: $o,SV117: $i,SV593: $i] :
( ( ( in @ SV593 @ SV117 )
= $false )
| ( ( ! [SY3464: $i] :
( ~ ( in @ SY3464 @ SV117 )
| ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3465: $i] :
( ~ ( ~ SV396
| ( SY3465 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3465 != SY3464 ) ) ) )
= ( setadjoin @ SY3464 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2137,plain,
! [SV117: $i,SV594: $i] :
( ( ( in @ SV594 @ SV117 )
= $false )
| ( ( ! [SY3466: $i] :
( ~ ( in @ SY3466 @ SV117 )
| ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3467: $i] :
( ~ ( ~ $true
| ( SY3467 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3467 != SY3466 ) ) ) )
= ( setadjoin @ SY3466 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(2138,plain,
! [SV117: $i,SV595: $i] :
( ( ( in @ SV595 @ SV117 )
= $false )
| ( ( ! [SY3468: $i] :
( ~ ( in @ SY3468 @ SV117 )
| ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3469: $i] :
( ~ ( ~ $false
| ( SY3469 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3469 != SY3468 ) ) ) )
= ( setadjoin @ SY3468 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(2139,plain,
! [SV397: $i,SV118: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ ( powerset @ SV118 ) )
| ! [SY3622: $i] :
( ~ ( in @ SY3622 @ ( binintersect @ SV397 @ SV726 ) )
| ( in @ SY3622 @ SV118 ) ) )
= $true )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2140,plain,
! [SV398: $i,SV119: $i,SV596: $i] :
( ( ( in @ SV596 @ ( cartprod @ SV119 @ SV398 ) )
= $false )
| ( ( iskpair @ SV596 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(2141,plain,
! [SV399: $i,SV597: $i,SV120: $i] :
( ( ( subset @ SV120 @ SV597 )
= $false )
| ( ( subset @ SV120 @ ( setadjoin @ SV399 @ SV597 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(2142,plain,
! [SV121: $i,SV400: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
| ~ ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1871]) ).
thf(2143,plain,
! [SV401: $i,SV122: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ ( powerset @ SV122 ) )
| ! [SY3623: $i] :
( ~ ( in @ SY3623 @ SV122 )
| ~ ( in @ SY3623 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SY3623 @ ( setminus @ SV122 @ SV401 ) ) ) )
= $true )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2144,plain,
! [SV598: $i > $i > $o,SV402: $i,SV123: $i,SV728: $i,SV689: $i] :
( ( ~ ( in @ ( kpair @ SV689 @ SV728 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SY3472: $i,SY3473: $i] : ( SV598 @ SY3472 @ SY3473 ) ) )
| ( in @ SV689 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2145,plain,
! [SV403: $i,SV124: $i,SV599: $i] :
( ( ( in @ SV599 @ SV124 )
= $false )
| ( ( in @ SV599 @ ( binunion @ SV124 @ SV403 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1874]) ).
thf(2146,plain,
! [SV600: $i,SV404: $i,SV125: $i] :
( ( ( func @ SV125 @ SV404 @ SV600 )
= $false )
| ( ( ! [SY3474: $i] :
( ~ ( in @ SY3474 @ SV125 )
| ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SY3474 ) @ SV404 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1875]) ).
thf(2147,plain,
! [SV601: $i,SV405: $i,SV126: $i] :
( ( ( breln @ SV126 @ SV405 @ SV601 )
= $false )
| ( ( ! [SY3475: $i > $o] :
( ~ ! [SY3476: $i] :
( ~ ( in @ SY3476 @ SV126 )
| ! [SY3477: $i] :
( ~ ( in @ SY3477 @ SV405 )
| ~ ( in @ ( kpair @ SY3476 @ SY3477 ) @ SV601 )
| ( SY3475 @ ( kpair @ SY3476 @ SY3477 ) ) ) )
| ! [SY3478: $i] :
( ~ ( in @ SY3478 @ SV601 )
| ( SY3475 @ SY3478 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1876]) ).
thf(2148,plain,
! [SV406: $i,SV127: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ ( powerset @ SV127 ) )
| ! [SY3626: $i] :
( ~ ( in @ SY3626 @ SV127 )
| ~ ( in @ SY3626 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3626 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) ) )
= $true )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2149,plain,
! [SV407: $i,SV128: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV128 ) )
= $false )
| ( ( ~ ( in @ SV602 @ SV407 )
| ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(2150,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ~ ( ~ ( SV129 @ SV730 )
| ~ ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2151,plain,
! [SV408: $i,SV130: $i,SV603: $i] :
( ( ( in @ SV603 @ ( setadjoin @ SV130 @ SV408 ) )
= $false )
| ( ( ( SV603 = SV130 )
| ( in @ SV603 @ SV408 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1880]) ).
thf(2152,plain,
! [SV409: $i,SV132: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( powerset @ SV132 ) )
| ! [SY3628: $i] :
( ~ ( in @ SY3628 @ SV132 )
| ~ ( in @ SY3628 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SY3628 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) ) )
= $true )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2153,plain,
! [SV411: $i,SV134: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ ( powerset @ SV134 ) )
| ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SY3629 @ SV411 )
| ( in @ SY3629 @ SV732 ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2154,plain,
! [SV135: $i] :
( ( ( in @ ( sK4_SY2504 @ SV135 ) @ SV135 )
= $true )
| ( ( SV135 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1884]) ).
thf(2155,plain,
! [SV412: $i,SV136: $i,SV604: $i] :
( ( ( in @ SV604 @ ( binintersect @ SV136 @ SV412 ) )
= $false )
| ( ( in @ SV604 @ SV136 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(2156,plain,
! [SV605: $i,SV413: $i,SV137: $i] :
( ( ( func @ SV137 @ SV413 @ SV605 )
= $false )
| ( ( ! [SY3479: $i] :
( ~ ( func @ SV137 @ SV413 @ SY3479 )
| ~ ! [SY3480: $i] :
( ~ ( in @ SY3480 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3480 )
= ( ap @ SV137 @ SV413 @ SY3479 @ SY3480 ) ) )
| ( SV605 = SY3479 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1886]) ).
thf(2157,plain,
! [SV414: $o,SV138: $i,SV606: $i] :
( ( ( in @ SV606 @ SV138 )
= $false )
| ( ( ! [SY3481: $i] :
( ~ ( in @ SY3481 @ SV138 )
| ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3482: $i] :
( ~ ( ~ SV414
| ( SY3482 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3482 != SY3481 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(2158,plain,
! [SV138: $i,SV607: $i] :
( ( ( in @ SV607 @ SV138 )
= $false )
| ( ( ! [SY3483: $i] :
( ~ ( in @ SY3483 @ SV138 )
| ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3484: $i] :
( ~ ( ~ $true
| ( SY3484 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3484 != SY3483 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1888]) ).
thf(2159,plain,
! [SV138: $i,SV608: $i] :
( ( ( in @ SV608 @ SV138 )
= $false )
| ( ( ! [SY3485: $i] :
( ~ ( in @ SY3485 @ SV138 )
| ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3486: $i] :
( ~ ( ~ $false
| ( SY3486 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3486 != SY3485 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(2160,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ~ ( ~ ( SV139 @ SV733 )
| ~ ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2161,plain,
! [SV415: $i > $o,SV140: $i,SV609: $i] :
( ( ( in @ SV609 @ SV140 )
= $false )
| ( ( ~ ( SV415 @ SV609 )
| ( in @ SV609
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1891]) ).
thf(2162,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3631: $i] :
( ( ( sK13_SY3143 @ SV416 @ SV141 )
!= SY3631 )
| ~ ( ~ ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ SY3631 ) )
| ~ ( ~ ( SV416 @ SY3631 )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1892]) ).
thf(2163,plain,
! [SV417: $i,SV142: $i,SV610: $i] :
( ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false )
| ( ( ~ ! [SY3488: $i] :
~ ~ ( ~ ( in @ SY3488 @ SV142 )
| ~ ~ ! [SY3489: $i] :
~ ~ ( ~ ( in @ SY3489 @ SV417 )
| ( SV610
!= ( kpair @ SY3488 @ SY3489 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2164,plain,
! [SV418: $i,SV143: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ ( powerset @ SV143 ) )
| ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SV734 ) ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2165,plain,
! [SV735: $i > $o,SV419: $i,SV144: $i] :
( ( ( ~ ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV144 )
| ! [SY3633: $i] :
( ~ ( in @ SY3633 @ SV144 )
| ~ ( in @ ( kpair @ SY3632 @ SY3633 ) @ SV419 )
| ( SV735 @ ( kpair @ SY3632 @ SY3633 ) ) ) )
| ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2166,plain,
! [SV420: $i,SV145: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ ( powerset @ SV145 ) )
| ! [SY3635: $i] :
( ~ ( in @ SY3635 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3635 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SY3635 ) ) )
= $true )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2167,plain,
! [SV422: $o,SV147: $i,SV611: $i] :
( ( ( in @ SV611 @ SV147 )
= $false )
| ( ( ! [SY3490: $i] :
( ~ ( in @ SY3490 @ SV147 )
| ~ ~ SV422
| ( in @ SY3490
@ ( dsetconstr @ SV147
@ ^ [SY3491: $i] :
( ~ ( ~ SV422
| ( SY3491 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3491 != SY3490 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1898]) ).
thf(2168,plain,
! [SV147: $i,SV612: $i] :
( ( ( in @ SV612 @ SV147 )
= $false )
| ( ( ! [SY3492: $i] :
( ~ ( in @ SY3492 @ SV147 )
| ~ ~ $true
| ( in @ SY3492
@ ( dsetconstr @ SV147
@ ^ [SY3493: $i] :
( ~ ( ~ $true
| ( SY3493 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3493 != SY3492 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1899]) ).
thf(2169,plain,
! [SV147: $i,SV613: $i] :
( ( ( in @ SV613 @ SV147 )
= $false )
| ( ( ! [SY3494: $i] :
( ~ ( in @ SY3494 @ SV147 )
| ~ ~ $false
| ( in @ SY3494
@ ( dsetconstr @ SV147
@ ^ [SY3495: $i] :
( ~ ( ~ $false
| ( SY3495 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3495 != SY3494 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(2170,plain,
! [SV423: $o,SV149: $i,SV614: $i] :
( ( ( in @ SV614 @ SV149 )
= $false )
| ( ( ! [SY3496: $i] :
( ~ ( in @ SY3496 @ SV149 )
| ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SY3496 )
= SY3496 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2171,plain,
! [SV149: $i,SV615: $i] :
( ( ( in @ SV615 @ SV149 )
= $false )
| ( ( ! [SY3497: $i] :
( ~ ( in @ SY3497 @ SV149 )
| ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SY3497 )
= SY3497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1902]) ).
thf(2172,plain,
! [SV149: $i,SV616: $i] :
( ( ( in @ SV616 @ SV149 )
= $false )
| ( ( ! [SY3498: $i] :
( ~ ( in @ SY3498 @ SV149 )
| ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SY3498 )
= SY3498 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1903]) ).
thf(2173,plain,
! [SV424: $i,SV150: $i,SV617: $i] :
( ( ( subset @ SV617 @ SV150 )
= $false )
| ( ( ~ ( subset @ SV617 @ SV424 )
| ( subset @ SV617 @ ( binintersect @ SV150 @ SV424 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2174,plain,
! [SV425: $i,SV151: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( powerset @ SV151 ) )
| ~ ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
| ! [SY3636: $i] :
( ~ ( in @ SY3636 @ SV151 )
| ~ ( in @ SY3636 @ SV737 )
| ( in @ SY3636 @ ( setminus @ SV151 @ SV425 ) ) ) )
= $true )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2175,plain,
! [SV426: $i,SV152: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ ( powerset @ SV152 ) )
| ! [SY3637: $i] :
( ~ ( in @ SY3637 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SY3637 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SY3637 ) ) ) )
= $true )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2176,plain,
! [SV427: $i,SV154: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( powerset @ SV154 ) )
| ! [SY3638: $i] :
( ~ ( in @ SY3638 @ ( powerset @ SV154 ) )
| ! [SY3639: $i] :
( ~ ( in @ SY3639 @ SV154 )
| ~ ( in @ SY3639 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3639 @ ( binunion @ SV427 @ SY3638 ) ) ) ) )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2177,plain,
! [SV428: $i > $o,SV155: $i] :
( ( ( ! [SY3176: $i] :
~ ~ ( ~ ( in @ SY3176 @ SV155 )
| ~ ( SV428 @ SY3176 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1908]) ).
thf(2178,plain,
! [SV429: $i,SV156: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ ( powerset @ SV156 ) )
| ! [SY3640: $i] :
( ~ ( in @ SY3640 @ SV156 )
| ~ ( in @ SY3640 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3640 @ ( binintersect @ SV429 @ SV740 ) ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2179,plain,
! [SV618: $i,SV431: $i,SV158: $i] :
( ( ( subset @ SV158 @ SV431 )
= $false )
| ( ( ~ ( subset @ SV431 @ SV618 )
| ( subset @ SV158 @ SV618 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1911]) ).
thf(2180,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
| ! [SY3641: $i] :
( ~ ( in @ SY3641 @ SV159 )
| ~ ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
| ~ ( SV432 @ SY3641 )
| ( ( sK14_SY3181 @ SV432 @ SV159 )
= SY3641 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1912]) ).
thf(2181,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( in @ SV619 @ SV160 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) )
| ~ ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1913]) ).
thf(2182,plain,
! [SV434: $i > $o,SV161: $i,SV620: $i] :
( ( ( in @ SV620 @ SV161 )
= $false )
| ( ( ~ ( SV434 @ SV620 )
| ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2183,plain,
! [SV621: $i,SV435: $i,SV162: $i] :
( ( ( ( setadjoin @ SV162 @ ( setadjoin @ SV435 @ emptyset ) )
= ( setadjoin @ SV621 @ emptyset ) )
= $false )
| ( ( SV162 = SV435 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1915]) ).
thf(2184,plain,
! [SV436: $i,SV163: $i,SV690: $i,SV622: $i] :
( ( ( ~ ( in @ ( kpair @ SV622 @ SV690 ) @ ( cartprod @ SV163 @ SV436 ) ) )
= $true )
| ( ( in @ SV690 @ SV436 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1916]) ).
thf(2185,plain,
! [SV437: $i,SV165: $i,SV623: $i] :
( ( ( in @ SV623 @ SV165 )
= $false )
| ( ( ! [SY3503: $i] :
( ~ ( in @ SY3503 @ SV437 )
| ( in @ ( kpair @ SV623 @ SY3503 ) @ ( cartprod @ SV165 @ SV437 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2186,plain,
! [SV438: $i,SV166: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( powerset @ SV166 ) )
| ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SV741 ) ) ) ) )
= $true )
| ( ( in @ SV438 @ ( powerset @ SV166 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2187,plain,
! [SV439: $i,SV167: $i,SV624: $i] :
( ( ( in @ SV624 @ SV167 )
= $false )
| ( ( ! [SY3504: $i] :
( ~ ( in @ SY3504 @ SV439 )
| ( ( kfst @ ( kpair @ SV624 @ SY3504 ) )
= SV624 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2188,plain,
! [SV440: $i > $o,SV168: $i] :
( ( ( ! [SY3199: $i] :
~ ~ ( ~ ( in @ SY3199 @ SV168 )
| ~ ( SV440 @ SY3199 ) ) )
= $false )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2189,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( ~ ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
| ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2190,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( ~ ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2191,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
| ~ ! [SY3642: $i] :
~ ~ ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3642 )
| ~ ! [SY3643: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3643 )
| ( SY3642 = SY3643 ) ) ) )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1922]) ).
thf(2192,plain,
! [SV171: $i,SV626: $i,SV443: $i] :
( ( ( in @ SV443 @ SV626 )
= $false )
| ( ( ~ ( in @ SV626 @ SV171 )
| ( in @ SV443 @ ( setunion @ SV171 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1923]) ).
thf(2193,plain,
! [SV627: $i,SV445: $i,SV173: $i] :
( ( ( breln @ SV173 @ SV445 @ SV627 )
= $false )
| ( ( ! [SY3505: $i > $o] :
( ~ ! [SY3506: $i] :
( ~ ( in @ SY3506 @ SV173 )
| ! [SY3507: $i] :
( ~ ( in @ SY3507 @ SV445 )
| ~ ( in @ ( kpair @ SY3506 @ SY3507 ) @ SV627 )
| ( SY3505 @ ( kpair @ SY3506 @ SY3507 ) ) ) )
| ! [SY3508: $i] :
( ~ ( in @ SY3508 @ SV627 )
| ( SY3505 @ SY3508 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1925]) ).
thf(2194,plain,
! [SV691: $i,SV628: $i,SV446: $i,SV174: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV628 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV628 @ ( setadjoin @ SV691 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV174 = SV628 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1926]) ).
thf(2195,plain,
! [SV177: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
| ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 ) )
= $false )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1929]) ).
thf(2196,plain,
! [SV178: $i,SV450: $i,SV629: $i] :
( ( ( in @ SV629 @ SV450 )
= $false )
| ( ( in @ SV629 @ ( setadjoin @ SV178 @ SV450 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1930]) ).
thf(2197,plain,
! [SV692: $i,SV630: $i,SV451: $i,SV179: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SV692 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV630 != SV692 )
| ( SV451 = SV692 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2198,plain,
! [SV452: $i,SV180: $i,SV631: $i] :
( ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false )
| ( ( ! [SY3511: $i] :
( ~ ( in @ SY3511 @ SV180 )
| ! [SY3512: $i] :
( ~ ( in @ SY3512 @ SV452 )
| ~ ( in @ ( kpair @ SY3511 @ SY3512 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SY3511 )
= SY3512 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1932]) ).
thf(2199,plain,
! [SV453: $i,SV181: $i,SV632: $i] :
( ( ( in @ SV632 @ SV181 )
= $false )
| ( ( in @ ( setadjoin @ SV632 @ emptyset ) @ ( powerset @ ( binunion @ SV181 @ SV453 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1933]) ).
thf(2200,plain,
! [SV454: $i,SV183: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ ( powerset @ SV183 ) )
| ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SV742 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV183 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2201,plain,
! [SV184: $i] :
( ( ( in @ ( sK5_SY2645 @ SV184 ) @ SV184 )
= $true )
| ( ( SV184 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1935]) ).
thf(2202,plain,
! [SV455: $i,SV743: $i,SV185: $i] :
( ( ( ~ ( breln1 @ SV185 @ SV743 )
| ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SV185 )
| ! [SY3645: $i] :
( ~ ( in @ SY3645 @ SV185 )
| ~ ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV455 )
| ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV743 ) ) )
| ( subset @ SV455 @ SV743 ) )
= $true )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2203,plain,
! [SV456: $i,SV186: $i,SV633: $i] :
( ( ( in @ SV633 @ SV186 )
= $false )
| ( ( ~ ( in @ SV633 @ SV456 )
| ( in @ SV633 @ ( binintersect @ SV186 @ SV456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1937]) ).
thf(2204,plain,
! [SV457: $i,SV187: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ ( powerset @ SV187 ) )
| ! [SY3646: $i] :
( ~ ( in @ SY3646 @ ( powerset @ SV187 ) )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV187 )
| ~ ( in @ SY3647 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3647 @ ( binintersect @ ( binunion @ SV457 @ SY3646 ) @ ( binunion @ SV744 @ SY3646 ) ) ) ) ) )
= $true )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2205,plain,
! [SV458: $i,SV188: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV188 )
| ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV188 )
| ~ ( in @ ( kpair @ SY3648 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SY3648 ) @ SV458 ) ) )
= $true )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2206,plain,
! [SV746: $o,SV189: $i,SV459: $i] :
( ( ( ~ ! [SY3649: $i] :
( ~ ( in @ SV459 @ SY3649 )
| ~ ( in @ SY3649 @ SV189 )
| SV746 )
| SV746 )
= $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1940]) ).
thf(2207,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $true )
| $true )
= $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1940]) ).
thf(2208,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $false )
| $false )
= $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1940]) ).
thf(2209,plain,
! [SV634: $i,SV461: $i,SV191: $i] :
( ( ( func @ SV191 @ SV461 @ SV634 )
= $false )
| ( ( ( lam @ SV191 @ SV461
@ ^ [SY3513: $i] : ( ap @ SV191 @ SV461 @ SV634 @ SY3513 ) )
= SV634 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2210,plain,
! [SV462: $i,SV192: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ ( powerset @ SV192 ) )
| ! [SY3650: $i] :
( ~ ( in @ SY3650 @ SV192 )
| ~ ~ ( in @ SY3650 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SY3650 @ SV462 ) ) )
= $true )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2211,plain,
! [SV463: $i,SV193: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV193 ) )
| ! [SY3651: $i] :
( ~ ( in @ SY3651 @ SV193 )
| ~ ( in @ SY3651 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SY3651 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2212,plain,
! [SV464: $i,SV194: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( powerset @ SV194 ) )
| ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3652 ) @ ( binunion @ SV749 @ SY3652 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2213,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false )
| ( ( ! [SY3514: $o] :
( ~ ( ( SV635 != SV195 )
| SY3514 )
| ~ ( ~ ( in @ SV635 @ SV465 )
| SY3514 )
| SY3514 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1946]) ).
thf(2214,plain,
! [SV466: $i,SV196: $i,SV636: $i] :
( ( ( in @ SV636 @ ( cartprod @ SV196 @ SV466 ) )
= $false )
| ( ( in @ ( kfst @ SV636 ) @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2215,plain,
! [SV467: $i,SV197: $i] :
( ( ( ~ ! [SY3248: $i] :
~ ~ ( ~ ( in @ SY3248 @ SV197 )
| ~ ( in @ SY3248 @ SV467 ) ) )
= $true )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1948]) ).
thf(2216,plain,
! [SV469: $i,SV199: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ ( powerset @ SV199 ) )
| ( in @ ( setminus @ SV469 @ SV750 ) @ ( powerset @ SV199 ) ) )
= $true )
| ( ( in @ SV469 @ ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2217,plain,
! [SV470: $i,SV637: $i > $i,SV200: $i] :
( ( ( ! [SY3515: $i] :
( ~ ( in @ SY3515 @ SV200 )
| ( in @ ( SV637 @ SY3515 ) @ SV470 ) ) )
= $false )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1951]) ).
thf(2218,plain,
! [SV471: $i,SV201: $i] :
( ( ( ! [SY3253: $i] :
~ ~ ( ~ ( in @ SY3253 @ SV201 )
| ~ ( in @ SV471 @ SY3253 ) ) )
= $false )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1952]) ).
thf(2219,plain,
! [SV473: $i,SV203: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( powerset @ SV203 ) )
| ( in @ ( binintersect @ SV473 @ SV751 ) @ ( powerset @ SV203 ) ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV203 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2220,plain,
! [SV474: $i,SV204: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV204 ) )
| ! [SY3653: $i] :
( ~ ( in @ SY3653 @ ( powerset @ SV204 ) )
| ! [SY3654: $i] :
( ~ ( in @ SY3654 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SY3653 @ SY3654 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3653 ) @ ( setminus @ SV204 @ SY3654 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2221,plain,
! [SV475: $i,SV206: $i,SV638: $i] :
( ( ( in @ SV638 @ ( binunion @ SV206 @ SV475 ) )
= $false )
| ( ( ( in @ SV638 @ SV206 )
| ( in @ SV638 @ SV475 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2222,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ~ ( ~ ( SV207 @ SV753 )
| ~ ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2223,plain,
! [SV477: $i,SV209: $i] :
( ( ( SV209 = SV477 )
= $true )
| ( ( ~ ( in @ SV477 @ ( setadjoin @ SV209 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2224,plain,
! [SV479: $i,SV211: $i,SV639: $i] :
( ( ( in @ SV639 @ SV211 )
= $false )
| ( ( ! [SY3517: $i] :
( ~ ( in @ SY3517 @ SV479 )
| ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SY3517 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2225,plain,
! [SV480: $i,SV754: $i,SV212: $i] :
( ( ( ~ ( breln1 @ SV212 @ SV754 )
| ( breln1 @ SV212 @ ( binunion @ SV480 @ SV754 ) ) )
= $true )
| ( ( breln1 @ SV212 @ SV480 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2226,plain,
! [SV640: $i,SV481: $i,SV213: $i] :
( ( ( func @ SV213 @ SV481 @ SV640 )
= $false )
| ( ( in @ SV640 @ ( funcSet @ SV213 @ SV481 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2227,plain,
! [SV482: $o,SV214: $i,SV641: $i] :
( ( ( in @ SV641 @ SV214 )
= $false )
| ( ( ! [SY3518: $i] :
( ~ ( in @ SY3518 @ SV214 )
| ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SY3518 )
= SV641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2228,plain,
! [SV214: $i,SV642: $i] :
( ( ( in @ SV642 @ SV214 )
= $false )
| ( ( ! [SY3519: $i] :
( ~ ( in @ SY3519 @ SV214 )
| ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SY3519 )
= SV642 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1965]) ).
thf(2229,plain,
! [SV214: $i,SV643: $i] :
( ( ( in @ SV643 @ SV214 )
= $false )
| ( ( ! [SY3520: $i] :
( ~ ( in @ SY3520 @ SV214 )
| ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SY3520 )
= SV643 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2230,plain,
! [SV483: $i,SV755: $i,SV215: $i] :
( ( ( ~ ( breln1 @ SV215 @ SV755 )
| ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV215 )
| ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV215 )
| ~ ( in @ ( kpair @ SY3656 @ SY3657 ) @ SV483 )
| ( in @ ( kpair @ SY3656 @ SY3657 ) @ ( binunion @ SV483 @ SV755 ) ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2231,plain,
! [SV484: $i,SV216: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ ( powerset @ SV216 ) )
| ~ ( subset @ SV484 @ ( setminus @ SV216 @ SV756 ) )
| ( subset @ SV756 @ ( setminus @ SV216 @ SV484 ) ) )
= $true )
| ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2232,plain,
! [SV644: $i > $i > $o,SV485: $i,SV217: $i,SV757: $i,SV693: $i] :
( ( ~ ( in @ ( kpair @ SV693 @ SV757 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SY3523: $i,SY3524: $i] : ( SV644 @ SY3523 @ SY3524 ) ) )
| ( in @ SV757 @ SV485 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2233,plain,
! [SV486: $i,SV218: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ ( powerset @ SV218 ) )
| ( ( setminus @ SV218 @ ( binunion @ SV486 @ SV758 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SV758 ) ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV218 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2234,plain,
! [SV487: $i,SV219: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV219 ) )
= $false )
| ( ( ~ ~ ( in @ SV645 @ SV487 )
| ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1971]) ).
thf(2235,plain,
! [SV488: $i,SV220: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV220 )
| ~ ( in @ SV759 @ SV488 )
| ~ ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) ) )
= $true )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2236,plain,
! [SV489: $i > $o,SV221: $i] :
( ( ( ! [SY3277: $i] :
( ~ ( in @ SY3277 @ SV221 )
| ( SV489 @ SY3277 ) ) )
= $true )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1973]) ).
thf(2237,plain,
! [SV491: $i,SV223: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ ( powerset @ SV223 ) )
| ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV223 )
| ~ ( in @ SY3660 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SY3660 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2238,plain,
! [SV224: $i,SV492: $i,SV646: $i] :
( ( ( in @ SV646 @ SV492 )
= $false )
| ( ( ~ ( in @ SV646 @ ( setminus @ SV224 @ SV492 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1976]) ).
thf(2239,plain,
! [SV493: $i,SV225: $i,SV647: $i] :
( ( ( in @ SV647 @ SV225 )
= $false )
| ( ( ~ ~ ( in @ SV647 @ SV493 )
| ~ ( subset @ SV225 @ SV493 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2240,plain,
! [SV648: $i,SV494: $i,SV226: $i] :
( ( ( breln @ SV226 @ SV494 @ SV648 )
= $false )
| ( ( ! [SY3525: $i] :
( ~ ( breln @ SV226 @ SV494 @ SY3525 )
| ~ ! [SY3526: $i] :
( ~ ( in @ SY3526 @ SV226 )
| ! [SY3527: $i] :
( ~ ( in @ SY3527 @ SV494 )
| ~ ( in @ ( kpair @ SY3526 @ SY3527 ) @ SV648 )
| ( in @ ( kpair @ SY3526 @ SY3527 ) @ SY3525 ) ) )
| ( subset @ SV648 @ SY3525 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1978]) ).
thf(2241,plain,
! [SV495: $i,SV227: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( powerset @ SV227 ) )
| ( in @ ( binunion @ SV495 @ SV761 ) @ ( powerset @ SV227 ) ) )
= $true )
| ( ( in @ SV495 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2242,plain,
! [SV649: $i,SV228: $i,SV496: $i] :
( ( ( in @ SV496 @ ( powerset @ SV228 ) )
= $false )
| ( ( ~ ( in @ SV649 @ SV496 )
| ( in @ SV649 @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2243,plain,
! [SV499: $i,SV231: $i,SV650: $i] :
( ( ( in @ SV650 @ SV231 )
= $false )
| ( ( ! [SY3528: $i] :
( ~ ( in @ SY3528 @ SV499 )
| ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SY3528 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2244,plain,
! [SV500: $i,SV232: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV232 ) )
| ~ ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV232 )
| ~ ( in @ SY3661 @ SV500 )
| ( in @ SY3661 @ SV762 ) )
| ( subset @ SV500 @ SV762 ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2245,plain,
! [SV501: $i,SV233: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV233 ) )
| ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV233 )
| ~ ( in @ SY3662 @ SV501 )
| ( in @ SY3662 @ SV763 ) )
| ( in @ SV501 @ ( powerset @ SV763 ) ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2246,plain,
! [SV502: $i,SV234: $i,SV651: $i] :
( ( ( in @ SV651 @ ( setadjoin @ SV234 @ ( setadjoin @ SV502 @ emptyset ) ) )
= $false )
| ( ( ( SV651 = SV234 )
| ( SV651 = SV502 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1986]) ).
thf(2247,plain,
! [SV503: $i,SV235: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV235 )
| ~ ( in @ SV764 @ SV503 )
| ( in @ SV764 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) )
= $true )
| ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2248,plain,
! [SV504: $i,SV236: $i] :
( ( ( subset @ SV236 @ SV504 )
= $true )
| ( ( SV236 != SV504 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1988]) ).
thf(2249,plain,
! [SV505: $o,SV237: $i,SV652: $i] :
( ( ( in @ SV652 @ SV237 )
= $false )
| ( ( ! [SY3529: $i] :
( ~ ( in @ SY3529 @ SV237 )
| ( in @ ( if @ SV237 @ SV505 @ SV652 @ SY3529 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2250,plain,
! [SV237: $i,SV653: $i] :
( ( ( in @ SV653 @ SV237 )
= $false )
| ( ( ! [SY3530: $i] :
( ~ ( in @ SY3530 @ SV237 )
| ( in @ ( if @ SV237 @ $true @ SV653 @ SY3530 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2251,plain,
! [SV237: $i,SV654: $i] :
( ( ( in @ SV654 @ SV237 )
= $false )
| ( ( ! [SY3531: $i] :
( ~ ( in @ SY3531 @ SV237 )
| ( in @ ( if @ SV237 @ $false @ SV654 @ SY3531 ) @ SV237 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1991]) ).
thf(2252,plain,
! [SV506: $i,SV238: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ ( powerset @ SV238 ) )
| ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( powerset @ SV238 ) )
| ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV238 )
| ~ ( in @ SY3664 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3664 @ ( binunion @ SV765 @ SY3663 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2253,plain,
! [SV507: $i > $o,SV239: $i,SV655: $i] :
( ( ( in @ SV655
@ ( dsetconstr @ SV239
@ ^ [SY3303: $i] : ( SV507 @ SY3303 ) ) )
= $false )
| ( ( in @ SV655 @ SV239 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1993]) ).
thf(2254,plain,
! [SV508: $i,SV766: $i,SV240: $i] :
( ( ( ~ ( breln1 @ SV240 @ SV766 )
| ! [SY3665: $i] :
( ~ ( in @ SY3665 @ SV240 )
| ! [SY3666: $i] :
( ~ ( in @ SY3666 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3666 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3667: $o] :
( ~ ! [SY3668: $i] :
( ~ ( in @ SY3668 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3668 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3668 @ SY3666 ) @ SV766 )
| SY3667 )
| SY3667 ) ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2255,plain,
! [SV767: $i > $o,SV509: $i,SV241: $i] :
( ( ( ~ ! [SY3669: $i] :
( ~ ( in @ SY3669 @ SV241 )
| ! [SY3670: $i] :
( ~ ( in @ SY3670 @ SV241 )
| ~ ( in @ ( kpair @ SY3669 @ SY3670 ) @ SV509 )
| ( SV767 @ ( kpair @ SY3669 @ SY3670 ) ) ) )
| ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2256,plain,
! [SV510: $i,SV242: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( powerset @ SV242 ) )
| ! [SY3672: $i] :
( ~ ( in @ SY3672 @ SV242 )
| ~ ( in @ SY3672 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SY3672 @ SV510 ) ) )
= $true )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2257,plain,
! [SV511: $i,SV243: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ ( powerset @ SV243 ) )
| ! [SY3673: $i] :
( ~ ( in @ SY3673 @ SV243 )
| ~ ( in @ SY3673 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SY3673 @ ( setminus @ SV243 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2258,plain,
! [SV512: $i,SV244: $i,SV656: $i] :
( ( ( in @ SV656 @ ( funcSet @ SV244 @ SV512 ) )
= $false )
| ( ( ( lam @ SV244 @ SV512
@ ^ [SY3533: $i] : ( ap @ SV244 @ SV512 @ SV656 @ SY3533 ) )
= SV656 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2259,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i,SV694: $i] :
( ( ( ~ ( in @ SV694 @ SV249 ) )
= $true )
| ( ( ! [SY3585: $i] :
( ~ ( in @ SY3585 @ SV517 )
| ~ ( in @ ( kpair @ SV694 @ SY3585 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SY3585 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2003]) ).
thf(2260,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ! [SY3674: $i] :
~ ( ~ ( ~ ( SV250 @ SY3674 )
| ( SY3674 = SV770 ) )
| ~ ( ( SY3674 != SV770 )
| ( SV250 @ SY3674 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2261,plain,
! [SV658: $i,SV518: $i,SV251: $i] :
( ( ( breln @ SV251 @ SV518 @ SV658 )
= $false )
| ( ( ! [SY3538: $i] :
( ~ ( breln @ SV251 @ SV518 @ SY3538 )
| ~ ! [SY3539: $i] :
( ~ ( in @ SY3539 @ SV251 )
| ! [SY3540: $i] :
( ~ ( in @ SY3540 @ SV518 )
| ~ ( in @ ( kpair @ SY3539 @ SY3540 ) @ SV658 )
| ( in @ ( kpair @ SY3539 @ SY3540 ) @ SY3538 ) ) )
| ~ ! [SY3541: $i] :
( ~ ( in @ SY3541 @ SV251 )
| ! [SY3542: $i] :
( ~ ( in @ SY3542 @ SV518 )
| ~ ( in @ ( kpair @ SY3541 @ SY3542 ) @ SY3538 )
| ( in @ ( kpair @ SY3541 @ SY3542 ) @ SV658 ) ) )
| ( SV658 = SY3538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2005]) ).
thf(2262,plain,
! [SV519: $i,SV252: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( powerset @ SV252 ) )
| ! [SY3675: $i] :
( ~ ( in @ SY3675 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SY3675 @ SV771 )
| ~ ( in @ SY3675 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2263,plain,
! [SV254: $i,SV772: $i] :
( ( ( ~ ( in @ SV772 @ SV254 ) )
= $true )
| ( ( SV254 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2264,plain,
! [SV521: $i,SV255: $i,SV659: $i] :
( ( ( in @ SV659 @ ( setminus @ SV255 @ SV521 ) )
= $false )
| ( ( in @ SV659 @ SV255 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2265,plain,
! [SV522: $i > $o,SV256: $i] :
( ( ( ~ ! [SY3333: $i] :
~ ~ ( ~ ( in @ SY3333 @ SV256 )
| ~ ( SV522 @ SY3333 ) ) )
= $true )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2010]) ).
thf(2266,plain,
! [SV524: $i,SV773: $i,SV258: $i] :
( ( ( ~ ( breln1 @ SV258 @ SV773 )
| ! [SY3676: $i] :
( ~ ( in @ SY3676 @ SV258 )
| ! [SY3677: $i] :
( ~ ( in @ SY3677 @ SV258 )
| ! [SY3678: $i] :
( ~ ( in @ SY3678 @ SV258 )
| ~ ( in @ ( kpair @ SY3676 @ SY3678 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3678 @ SY3677 ) @ SV773 )
| ( in @ ( kpair @ SY3676 @ SY3677 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2267,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ( breln1 @ SV259 @ SV774 )
| ~ ! [SY3679: $i] :
( ~ ( in @ SY3679 @ SV259 )
| ! [SY3680: $i] :
( ~ ( in @ SY3680 @ SV259 )
| ~ ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV525 )
| ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV774 ) ) )
| ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2268,plain,
! [SV526: $i > $o,SV260: $i,SV660: $i] :
( ( ( in @ SV660
@ ( dsetconstr @ SV260
@ ^ [SY3345: $i] : ( SV526 @ SY3345 ) ) )
= $false )
| ( ( SV526 @ SV660 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2014]) ).
thf(2269,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) )
| ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) ) )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2015]) ).
thf(2270,plain,
! [SV661: $i,SV528: $i,SV262: $i] :
( ( ( func @ SV262 @ SV528 @ SV661 )
= $false )
| ( ( ! [SY3544: $i] :
( ~ ( in @ SY3544 @ SV262 )
| ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3545: $i] : ( in @ ( kpair @ SY3544 @ SY3545 ) @ SV661 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2271,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ~ ( ~ ( SV263 @ SV775 )
| ~ ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2272,plain,
! [SV529: $i,SV264: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV264 ) )
| ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV264 )
| ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SY3684 @ SV776 )
| ~ ( in @ SY3684 @ SV529 ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2273,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ( in @ SV777 @ SV265 ) )
= $true )
| ( ( ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2274,plain,
! [SV530: $i,SV266: $i,SV662: $i] :
( ( ( ~ ( in @ SV662 @ SV266 ) )
= $false )
| ( ( ~ ( in @ SV662 @ ( setminus @ SV266 @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2020]) ).
thf(2275,plain,
! [SV695: $i,SV663: $i,SV531: $i,SV267: $i] :
( ( ( ( kpair @ SV267 @ SV531 )
!= ( kpair @ SV663 @ SV695 ) )
= $true )
| ( ( SV267 = SV663 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2021]) ).
thf(2276,plain,
! [SV268: $i] :
( ( ( ! [SY2868: $i] :
~ ( in @ SY2868 @ SV268 ) )
= $false )
| ( ( SV268 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2022]) ).
thf(2277,plain,
! [SV534: $i,SV272: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV272 ) )
| ~ ( subset @ SV534 @ SV778 )
| ( subset @ ( setminus @ SV272 @ SV778 ) @ ( setminus @ SV272 @ SV534 ) ) )
= $true )
| ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2278,plain,
! [SV535: $i,SV273: $i,SV664: $i] :
( ( ( in @ SV664 @ SV273 )
= $false )
| ( ( ! [SY3547: $i] :
( ~ ( in @ SY3547 @ SV535 )
| ( in @ ( kpair @ SV664 @ SY3547 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2026]) ).
thf(2279,plain,
! [SV665: $i,SV536: $i,SV274: $i] :
( ( ( func @ SV274 @ SV536 @ SV665 )
= $false )
| ( ( ! [SY3548: $i] :
( ~ ( in @ SY3548 @ SV274 )
| ( ( ap @ SV274 @ SV536 @ SV665 @ SY3548 )
= ( ap @ SV274 @ SV536 @ SV665 @ SY3548 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2280,plain,
! [SV537: $i,SV275: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( powerset @ SV275 ) )
| ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV275 )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SY3685 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) ) )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2281,plain,
! [SV666: $i,SV538: $i,SV276: $i] :
( ( ( func @ SV276 @ SV538 @ SV666 )
= $false )
| ( ( ! [SY3549: $i] :
( ~ ( in @ SY3549 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3550: $i] : ( in @ ( kpair @ SY3549 @ SY3550 ) @ SV666 ) ) )
@ SV538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2029]) ).
thf(2282,plain,
! [SV539: $i,SV277: $i,SV667: $i] :
( ( ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) )
= $false )
| ( ( ! [SY3551: $i] :
( ~ ( in @ SY3551 @ SV277 )
| ( in @ ( kpair @ SY3551 @ ( ap @ SV277 @ SV539 @ SV667 @ SY3551 ) ) @ SV667 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2283,plain,
! [SV540: $i > $o,SV278: $i] :
( ( ( ! [SY3367: $i] :
~ ~ ( ~ ( in @ SY3367 @ SV278 )
| ~ ~ ( SV540 @ SY3367 ) ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2031]) ).
thf(2284,plain,
! [SV541: $i,SV279: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV279 )
| ! [SY3686: $i] :
( ~ ( in @ SY3686 @ SV279 )
| ~ ( in @ ( kpair @ SV780 @ SY3686 ) @ SV541 )
| ( in @ ( kpair @ SY3686 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) )
= $true )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2032]) ).
thf(2285,plain,
! [SV542: $i,SV668: $i > $i,SV280: $i] :
( ( ( ! [SY3552: $i] :
( ~ ( in @ SY3552 @ SV280 )
| ( in @ ( SV668 @ SY3552 ) @ SV542 ) ) )
= $false )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2033]) ).
thf(2286,plain,
! [SV543: $i,SV281: $i,SV696: $i,SV669: $i] :
( ( ( ~ ( in @ ( kpair @ SV669 @ SV696 ) @ ( cartprod @ SV281 @ SV543 ) ) )
= $true )
| ( ( in @ SV669 @ SV281 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2034]) ).
thf(2287,plain,
! [SV544: $i,SV670: $i > $i,SV282: $i] :
( ( ( ! [SY3556: $i] :
( ~ ( in @ SY3556 @ SV282 )
| ( in @ ( SV670 @ SY3556 ) @ SV544 ) ) )
= $false )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2288,plain,
! [SV545: $i,SV283: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ ( powerset @ SV283 ) )
| ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SV781 ) ) ) ) )
= $true )
| ( ( in @ SV545 @ ( powerset @ SV283 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2036]) ).
thf(2289,plain,
! [SV284: $i] :
( ( ( ! [SY2910: $i] :
~ ~ ( ~ ( in @ SY2910 @ SV284 )
| ~ $true ) )
= $false )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2290,plain,
! [SV546: $i,SV285: $i,SV671: $i] :
( ( ( in @ SV671 @ SV285 )
= $false )
| ( ( ~ ~ ( in @ SV671 @ SV546 )
| ( SV285 != SV546 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2038]) ).
thf(2291,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) ) )
= $false )
| ( ( ~ ( in @ SV672 @ SV286 )
| ( in @ SV672 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2039]) ).
thf(2292,plain,
! [SV673: $i,SV548: $i,SV287: $i] :
( ( ( func @ SV287 @ SV548 @ SV673 )
= $false )
| ( ( ! [SY3559: $i] :
( ~ ( in @ SY3559 @ SV287 )
| ! [SY3560: $i] :
( ~ ( in @ SY3560 @ SV548 )
| ~ ( in @ ( kpair @ SY3559 @ SY3560 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SY3559 )
= SY3560 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2293,plain,
! [SV549: $o,SV288: $i,SV674: $i] :
( ( ( in @ SV674 @ SV288 )
= $false )
| ( ( ! [SY3561: $i] :
( ~ ( in @ SY3561 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3562: $i] :
( ~ ( ~ SV549
| ( SY3562 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3562 != SY3561 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2041]) ).
thf(2294,plain,
! [SV288: $i,SV675: $i] :
( ( ( in @ SV675 @ SV288 )
= $false )
| ( ( ! [SY3563: $i] :
( ~ ( in @ SY3563 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3564: $i] :
( ~ ( ~ $true
| ( SY3564 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3564 != SY3563 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2042]) ).
thf(2295,plain,
! [SV288: $i,SV676: $i] :
( ( ( in @ SV676 @ SV288 )
= $false )
| ( ( ! [SY3565: $i] :
( ~ ( in @ SY3565 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3566: $i] :
( ~ ( ~ $false
| ( SY3566 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3566 != SY3565 ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2043]) ).
thf(2296,plain,
! [SV550: $i,SV289: $i,SV677: $i] :
( ( ( in @ SV677 @ ( cartprod @ SV289 @ SV550 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV677 ) @ ( ksnd @ SV677 ) )
= SV677 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2044]) ).
thf(2297,plain,
! [SV551: $i,SV290: $i,SV678: $i] :
( ( ( in @ SV678 @ ( setadjoin @ SV290 @ ( setadjoin @ SV551 @ emptyset ) ) )
= $false )
| ( ( ( SV678 = SV290 )
| ( SV678 = SV551 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2298,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ~ ( ~ ( SV291 @ SV782 )
| ~ ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2046]) ).
thf(2299,plain,
! [SV554: $i,SV294: $i,SV679: $i] :
( ( ( in @ SV679 @ SV294 )
= $false )
| ( ( ~ ~ ( in @ SV679 @ SV554 )
| ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2049]) ).
thf(2300,plain,
! [SV555: $o,SV296: $i,SV680: $i] :
( ( ( in @ SV680 @ SV296 )
= $false )
| ( ( ! [SY3567: $i] :
( ~ ( in @ SY3567 @ SV296 )
| ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3568: $i] :
( ~ ( ~ SV555
| ( SY3568 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3568 != SY3567 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2301,plain,
! [SV296: $i,SV681: $i] :
( ( ( in @ SV681 @ SV296 )
= $false )
| ( ( ! [SY3569: $i] :
( ~ ( in @ SY3569 @ SV296 )
| ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3570: $i] :
( ~ ( ~ $true
| ( SY3570 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3570 != SY3569 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2302,plain,
! [SV296: $i,SV682: $i] :
( ( ( in @ SV682 @ SV296 )
= $false )
| ( ( ! [SY3571: $i] :
( ~ ( in @ SY3571 @ SV296 )
| ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3572: $i] :
( ~ ( ~ $false
| ( SY3572 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3572 != SY3571 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2055]) ).
thf(2303,plain,
! [SV320: $i,SV35: $i,SV698: $i] :
( ( ( ~ ( in @ SV698 @ ( powerset @ SV35 ) ) )
= $true )
| ( ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SV698 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SV698 ) ) )
= $true )
| ( ( in @ SV320 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2056]) ).
thf(2304,plain,
! [SV36: $i,SV321: $i,SV559: $i] :
( ( ( in @ SV559 @ SV321 )
= $false )
| ( ( in @ SV559 @ ( setminus @ SV36 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2057]) ).
thf(2305,plain,
! [SV322: $i,SV37: $i,SV699: $i] :
( ( ( ~ ( in @ SV699 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ! [SY3588: $i] :
( ~ ( in @ SY3588 @ ( powerset @ SV37 ) )
| ! [SY3589: $i] :
( ~ ( in @ SY3589 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY3588 )
| ~ ( subset @ SV699 @ SY3589 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SY3588 @ SY3589 ) ) ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2058]) ).
thf(2306,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ( ~ ( SV38 @ SV700 )
| ~ ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) ) )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2307,plain,
! [SV324: $i,SV701: $i,SV40: $i] :
( ( ( ~ ( breln1 @ SV40 @ SV701 ) )
= $true )
| ( ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SV701 ) )
= $true )
| ( ( breln1 @ SV40 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2060]) ).
thf(2308,plain,
! [SV41: $i,SV325: $i,SV560: $i] :
( ( ( ~ ~ ( in @ SV560 @ SV325 ) )
= $true )
| ( ( ~ ( in @ SV560 @ SV41 ) )
= $true )
| ( ( subset @ SV41 @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2309,plain,
! [SV42: $i,SV561: $i,SV326: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV326 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SV783 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) ) )
= $true )
| ( ( in @ SV561 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2062]) ).
thf(2310,plain,
! [SV784: $i > $o,SV702: $i > $o,SV328: $i,SV44: $i] :
( ( ( ~ ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV44 )
| ! [SY3689: $i] :
( ~ ( in @ SY3689 @ SV328 )
| ( SY3688 != SY3689 )
| ~ ( ~ ( ~ ( SV702 @ SY3688 )
| ( SV784 @ SY3689 ) )
| ~ ( ~ ( SV784 @ SY3689 )
| ( SV702 @ SY3688 ) ) ) ) )
| ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2311,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2312,plain,
! [SV45: $i] :
( ( ~ ! [SY3410: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY3410 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3410 ) )
| ~ ! [SY3413: $i] :
~ ~ ! [SY3414: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3413 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3414 @ SY3410 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3413 )
| ~ ( in @ SX5 @ SY3410 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3413 ) )
| ( in @ SY3414 @ SY3416 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2065]) ).
thf(2313,plain,
! [SV329: $i > $o,SV46: $i,SV703: $i] :
( ( ( ~ ( in @ SV703 @ SV46 ) )
= $true )
| ( ( ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV46 )
| ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SY3596 )
| ( SV703 = SY3596 ) ) )
= $true )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2066]) ).
thf(2314,plain,
! [SV49: $i,SV563: $i > $i,SV331: $i] :
( ( ( ~ ( in @ ( sK18_SY3418 @ SV331 @ SV563 @ SV49 ) @ SV49 )
| ( in @ ( SV563 @ ( sK18_SY3418 @ SV331 @ SV563 @ SV49 ) ) @ SV331 ) )
= $false )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2067]) ).
thf(2315,plain,
! [SV50: $i,SV683: $i] :
( ( ( in @ SV683 @ SV50 )
= $false )
| ( ( ( setunion @ SV50 )
= SV683 )
= $true )
| ( ( singleton @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2068]) ).
thf(2316,plain,
! [SV51: $i,SV332: $i] :
( ( ( ~ ( in @ ( sK6_SY2972 @ SV332 @ SV51 ) @ SV51 ) )
= $false )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2317,plain,
! [SV51: $i,SV332: $i] :
( ( ( in @ ( sK6_SY2972 @ SV332 @ SV51 ) @ SV332 )
= $false )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2069]) ).
thf(2318,plain,
! [SV52: $i] :
( ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ~ ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) )
= $true )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2070]) ).
thf(2319,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( setunion @ SV53 ) ) )
= $true )
| ( ( ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2071]) ).
thf(2320,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2072]) ).
thf(2321,plain,
! [SV54: $i,SV564: $i,SV334: $i > $o] :
( ( ( ~ ( SV334 @ SV564 ) )
= $true )
| ( ( ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) )
= $true )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2073]) ).
thf(2322,plain,
! [SV55: $i,SV565: $i > $i,SV335: $i] :
( ( ( ~ ( in @ ( sK19_SY3422 @ SV335 @ SV565 @ SV55 ) @ SV55 )
| ( in @ ( SV565 @ ( sK19_SY3422 @ SV335 @ SV565 @ SV55 ) ) @ SV335 ) )
= $false )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2074]) ).
thf(2323,plain,
! [SV566: $i,SV336: $i,SV56: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV56 )
| ( ( ap @ SV56 @ SV336 @ SV566 @ SV785 )
= ( ap @ SV56 @ SV336 @ SV566 @ SV785 ) ) )
= $true )
| ( ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2324,plain,
! [SV337: $i,SV57: $i,SV704: $i] :
( ( ( ~ ( in @ SV704 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV57 )
| ~ ( in @ SY3597 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SY3597 @ ( setminus @ SV57 @ SV337 ) ) ) )
= $true )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2076]) ).
thf(2325,plain,
! [SV684: $i,SV567: $i,SV338: $i,SV58: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV58 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV58 @ ( setadjoin @ SV338 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV567 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV567 @ ( setadjoin @ SV684 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV338 = SV684 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2077]) ).
thf(2326,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ SV59 ) )
= $true )
| ( ( ~ ~ ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SV705 @ SV339 ) )
= $true )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2078]) ).
thf(2327,plain,
! [SV568: $i,SV341: $i,SV61: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
| ~ ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3692 )
= ( ap @ SV61 @ SV341 @ SV786 @ SY3692 ) ) )
| ( SV568 = SV786 ) )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2328,plain,
! [SV342: $i,SV62: $i,SV706: $i] :
( ( ( ~ ( in @ SV706 @ ( powerset @ SV62 ) ) )
= $true )
| ( ( ~ ( subset @ SV342 @ ( setminus @ SV62 @ SV706 ) )
| ( subset @ SV706 @ ( setminus @ SV62 @ SV342 ) ) )
= $true )
| ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2080]) ).
thf(2329,plain,
! [SV343: $i,SV63: $i,SV707: $i] :
( ( ( ~ ( in @ SV707 @ ( powerset @ SV63 ) ) )
= $true )
| ( ( ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV63 )
| ~ ~ ( in @ SY3598 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SY3598 @ SV707 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2081]) ).
thf(2330,plain,
! [SV344: $i,SV64: $i,SV708: $i] :
( ( ( ~ ( in @ SV708 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ! [SY3599: $i] :
( ~ ( in @ SY3599 @ ( powerset @ SV64 ) )
| ~ ( subset @ SV708 @ SY3599 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SY3599 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2082]) ).
thf(2331,plain,
! [SV345: $i,SV65: $i,SV709: $i] :
( ( ( ~ ( in @ SV709 @ ( powerset @ SV65 ) ) )
= $true )
| ( ( ! [SY3600: $i] :
( ~ ( in @ SY3600 @ SV65 )
| ~ ~ ( in @ SY3600 @ SV709 )
| ~ ( in @ SY3600 @ ( binintersect @ SV345 @ SV709 ) ) ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2332,plain,
! [SV346: $i,SV66: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ SV66 ) )
= $true )
| ( ( ~ ( in @ SV710 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SV710 @ SV346 ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2333,plain,
! [SV347: $i,SV67: $i] :
( ( ( ~ ( in @ ( sK7_SY3000 @ SV67 @ SV347 ) @ SV347 ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2334,plain,
! [SV347: $i,SV67: $i] :
( ( ( in @ ( sK7_SY3000 @ SV67 @ SV347 ) @ SV67 )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2085]) ).
thf(2335,plain,
! [SV348: $i,SV711: $i,SV68: $i] :
( ( ( ~ ( breln1 @ SV68 @ SV711 ) )
= $true )
| ( ( ! [SY3601: $i] :
( ~ ( in @ SY3601 @ SV68 )
| ! [SY3602: $i] :
( ~ ( in @ SY3602 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3602 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3603: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3603 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3603 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3603 @ SY3602 ) @ SV711 ) ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2336,plain,
! [SV349: $i,SV69: $i,SV712: $i] :
( ( ( ~ ( in @ SV712 @ ( powerset @ SV69 ) ) )
= $true )
| ( ( ! [SY3604: $i] :
( ~ ( in @ SY3604 @ SV69 )
| ~ ( in @ SY3604 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SY3604 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2337,plain,
! [SV70: $i,SV569: $i > $i,SV350: $i] :
( ( ( ~ ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 )
| ( in @ ( SV569 @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) ) @ SV350 ) )
= $false )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2088]) ).
thf(2338,plain,
! [SV570: $i > $i > $o,SV351: $i,SV71: $i,SV685: $i] :
( ( ( in @ SV685 @ SV71 )
= $false )
| ( ( ! [SY3573: $i] :
( ~ ( in @ SY3573 @ SV351 )
| ~ ( SV570 @ SV685 @ SY3573 )
| ( in @ ( kpair @ SV685 @ SY3573 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2089]) ).
thf(2339,plain,
! [SV571: $i,SV352: $i,SV72: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV72 )
| ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SV787 ) @ SV352 ) )
= $true )
| ( ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2340,plain,
! [SV572: $i > $i > $o,SV353: $i,SV73: $i,SV713: $i,SV686: $i] :
( ( ( ~ ( in @ ( kpair @ SV686 @ SV713 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SY3439: $i,SY3440: $i] : ( SV572 @ SY3439 @ SY3440 ) ) ) )
= $true )
| ( ( SV572 @ SV686 @ SV713 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2341,plain,
! [SV74: $i,SV354: $i,SV573: $i > $i > $o] :
( ( ( ~ ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
| ~ ! [SY3693: $i] :
~ ~ ( ~ ( in @ SY3693 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SY3693 ) ) )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2092]) ).
thf(2342,plain,
! [SV574: $i,SV355: $i,SV75: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV75 )
| ( in @ ( kpair @ SV788 @ ( ap @ SV75 @ SV355 @ SV574 @ SV788 ) ) @ SV574 ) )
= $true )
| ( ( func @ SV75 @ SV355 @ SV574 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2343,plain,
! [SV356: $i > $o,SV76: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV76 )
| ( SV356 @ SV789 ) )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2344,plain,
! [SV357: $i,SV77: $i,SV575: $i] :
( ( ( ~ ( in @ SV575 @ SV77 ) )
= $true )
| ( ( in @ SV575 @ SV357 )
= $true )
| ( ( subset @ SV77 @ SV357 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2095]) ).
thf(2345,plain,
( ( ~ ( breln1 @ sK1_SX0 @ sK8_SY3448 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2097]) ).
thf(2346,plain,
( ( ! [SY3607: $i] :
( ~ ( in @ SY3607 @ sK1_SX0 )
| ! [SY3608: $i] :
( ~ ( in @ SY3608 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY3607 @ SY3608 ) @ sK8_SY3448 )
| ( in @ ( kpair @ SY3607 @ SY3608 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2097]) ).
thf(2347,plain,
! [SV358: $i,SV78: $i,SV790: $i,SV714: $i] :
( ( ( ( SV714 != SV790 )
| ~ ( in @ SV714 @ SV78 )
| ( in @ SV790 @ SV358 ) )
= $true )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2098]) ).
thf(2348,plain,
! [SV79: $i,SV359: $i] :
( ( ( subset @ SV359 @ SV79 )
= $false )
| ( ( SV79 = SV359 )
= $true )
| ( ( subset @ SV79 @ SV359 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2349,plain,
! [SV687: $i,SV576: $i,SV360: $i,SV80: $i] :
( ( ( ( kpair @ SV80 @ SV360 )
= ( kpair @ SV576 @ SV687 ) )
= $false )
| ( ( SV360 = SV687 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2350,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i] :
( ( ( ~ ( func @ SV81 @ SV361 @ SV791 )
| ~ ! [SY3694: $i] :
( ~ ( in @ SY3694 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3694 )
= ( ap @ SV81 @ SV361 @ SV791 @ SY3694 ) ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2351,plain,
! [SV82: $i,SV362: $i] :
( ( ( ~ ( in @ SV362 @ ( powerset @ SV82 ) ) )
= $true )
| ( ( ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2352,plain,
! [SV82: $i,SV362: $i] :
( ( ( ~ ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2353,plain,
! [SV363: $i,SV83: $i,SV792: $i,SV715: $i] :
( ( ( ( SV715 != SV792 )
| ~ ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) )
| ~ ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) ) ) )
= $true )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2354,plain,
! [SV365: $i,SV85: $i,SV716: $i] :
( ( ( ~ ( in @ SV716 @ ( powerset @ SV85 ) ) )
= $true )
| ( ( ! [SY3611: $o,SY3612: $i] :
( ~ ( in @ SY3612 @ SV85 )
| ~ ( in @ SY3612 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SY3612 @ SV365 )
| SY3611 )
| ~ ( ~ ( in @ SY3612 @ SV716 )
| SY3611 )
| SY3611 ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2355,plain,
! [SV688: $o,SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| SV688 )
| ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2106]) ).
thf(2356,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $true )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2357,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $false )
| ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2108]) ).
thf(2358,plain,
! [SV87: $i,SV367: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ SV367 ) )
= $true )
| ( ( ~ ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) ) )
= $true )
| ( ( in @ SV579 @ SV87 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2359,plain,
! [SV89: $i,SV581: $i,SV369: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV369 )
| ( ( ksnd @ ( kpair @ SV581 @ SV793 ) )
= SV793 ) )
= $true )
| ( ( in @ SV581 @ SV89 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2360,plain,
! [SV92: $i,SV583: $i,SV372: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV372 )
| ( ( kpair @ SV583 @ SV794 )
= ( kpair @ SV583 @ SV794 ) ) )
= $true )
| ( ( in @ SV583 @ SV92 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2361,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SV795 )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2114]) ).
thf(2362,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $true )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2114]) ).
thf(2363,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $false )
| ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2114]) ).
thf(2364,plain,
! [SV94: $i,SV374: $i,SV585: $i] :
( ( ( ~ ~ ( in @ SV585 @ SV374 ) )
= $true )
| ( ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) )
= $true )
| ( ( in @ SV585 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2115]) ).
thf(2365,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ SV717 )
= $false )
| ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) )
| ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2116]) ).
thf(2366,plain,
! [SV375: $i,SV96: $i,SV796: $i,SV718: $i] :
( ( ( ( SV718 != SV796 )
| ( ( setadjoin @ SV96 @ SV718 )
= ( setadjoin @ SV375 @ SV796 ) ) )
= $true )
| ( ( SV96 = SV375 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2367,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ( ( sK9_SY3069 @ SV376 @ SV97 )
!= ( sK22_SY3614 @ SV97 @ SV376 ) )
| ~ ( ~ ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
| ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2118]) ).
thf(2368,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2369,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3615: $i] :
( ~ ( in @ SY3615 @ SV98 )
| ~ ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
| ~ ( SV377 @ SY3615 )
| ( ( sK10_SY3077 @ SV377 @ SV98 )
= SY3615 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2370,plain,
! [SV100: $i,SV586: $i,SV381: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV381 )
| ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SV797 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) ) )
= $true )
| ( ( in @ SV586 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2371,plain,
! [SV382: $i,SV101: $i,SV719: $i] :
( ( ( ~ ( in @ SV719 @ ( powerset @ SV101 ) ) )
= $true )
| ( ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SV719 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) )
= $true )
| ( ( in @ SV382 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2372,plain,
! [SV383: $i,SV102: $i,SV720: $i] :
( ( ( ~ ( in @ SV720 @ ( powerset @ SV102 ) ) )
= $true )
| ( ( ~ ( subset @ ( setminus @ SV102 @ SV720 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SV720 ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2122]) ).
thf(2373,plain,
! [SV385: $i,SV104: $i,SV721: $i] :
( ( ( ~ ( in @ SV721 @ ( powerset @ SV104 ) ) )
= $true )
| ( ( ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3616 ) @ ( binunion @ SV721 @ SY3616 ) ) ) ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2124]) ).
thf(2374,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ( ~ ( SV105 @ SV722 )
| ~ ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) ) )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2125]) ).
thf(2375,plain,
! [SV386: $i > $o,SV106: $i] :
( ( ( ! [SY3088: $i] :
~ ~ ( ~ ( in @ SY3088 @ SV106 )
| ~ ( SV386 @ SY3088 ) ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2376,plain,
! [SV387: $i,SV107: $i,SV723: $i] :
( ( ( ~ ( in @ SV723 @ ( powerset @ SV107 ) ) )
= $true )
| ( ( ! [SY3618: $i] :
( ~ ( in @ SY3618 @ SV107 )
| ~ ~ ( in @ SY3618 @ SV387 )
| ~ ( in @ SY3618 @ ( binintersect @ SV387 @ SV723 ) ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2377,plain,
! [SV588: $i,SV388: $o,SV108: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV108 )
| ( in @ ( if @ SV108 @ SV388 @ SV588 @ SV798 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SV798 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV588 @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2378,plain,
! [SV589: $i,SV108: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV108 )
| ( in @ ( if @ SV108 @ $true @ SV589 @ SV799 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SV799 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV589 @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2379,plain,
! [SV590: $i,SV108: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV108 )
| ( in @ ( if @ SV108 @ $false @ SV590 @ SV800 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SV800 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV590 @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2380,plain,
! [SV391: $i,SV111: $i,SV724: $i] :
( ( ( ~ ( in @ SV724 @ ( powerset @ SV111 ) ) )
= $true )
| ( ( ~ ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV111 )
| ~ ( in @ SY3619 @ SV391 )
| ( in @ SY3619 @ SV724 ) )
| ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2381,plain,
! [SV392: $i,SV112: $i,SV725: $i] :
( ( ( ~ ( in @ SV725 @ ( powerset @ SV112 ) ) )
= $true )
| ( ( ! [SY3621: $i] :
( ~ ( in @ SY3621 @ SV112 )
| ~ ~ ( in @ SY3621 @ SV392 )
| ~ ~ ( in @ SY3621 @ SV725 )
| ~ ( in @ SY3621 @ ( binunion @ SV392 @ SV725 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2133]) ).
thf(2382,plain,
! [SV113: $i,SV393: $i] :
( ( ( ~ ( in @ ( sK11_SY3100 @ SV393 @ SV113 ) @ SV113 ) )
= $false )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2383,plain,
! [SV113: $i,SV393: $i] :
( ( ( in @ ( sK11_SY3100 @ SV393 @ SV113 ) @ SV393 )
= $false )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2134]) ).
thf(2384,plain,
! [SV394: $i,SV114: $i,SV592: $i] :
( ( ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
= $true )
| ( ( ~ ~ ( in @ SV592 @ SV394 )
| ~ ( in @ SV592 @ SV114 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2135]) ).
thf(2385,plain,
! [SV593: $i,SV396: $o,SV117: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV117 )
| ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) ) )
= $true )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2386,plain,
! [SV594: $i,SV117: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV117 )
| ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) ) )
= $true )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2387,plain,
! [SV595: $i,SV117: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV117 )
| ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) ) )
= $true )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2388,plain,
! [SV397: $i,SV118: $i,SV726: $i] :
( ( ( ~ ( in @ SV726 @ ( powerset @ SV118 ) ) )
= $true )
| ( ( ! [SY3622: $i] :
( ~ ( in @ SY3622 @ ( binintersect @ SV397 @ SV726 ) )
| ( in @ SY3622 @ SV118 ) ) )
= $true )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2139]) ).
thf(2389,plain,
! [SV121: $i,SV400: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 ) )
= $false )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2390,plain,
! [SV121: $i,SV400: $i > $o] :
( ( ( ~ ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) ) )
= $false )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2142]) ).
thf(2391,plain,
! [SV401: $i,SV122: $i,SV727: $i] :
( ( ( ~ ( in @ SV727 @ ( powerset @ SV122 ) ) )
= $true )
| ( ( ! [SY3623: $i] :
( ~ ( in @ SY3623 @ SV122 )
| ~ ( in @ SY3623 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SY3623 @ ( setminus @ SV122 @ SV401 ) ) ) )
= $true )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2143]) ).
thf(2392,plain,
! [SV598: $i > $i > $o,SV402: $i,SV123: $i,SV728: $i,SV689: $i] :
( ( ( ~ ( in @ ( kpair @ SV689 @ SV728 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SY3472: $i,SY3473: $i] : ( SV598 @ SY3472 @ SY3473 ) ) ) )
= $true )
| ( ( in @ SV689 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2144]) ).
thf(2393,plain,
! [SV600: $i,SV404: $i,SV125: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV125 )
| ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SV804 ) @ SV404 ) )
= $true )
| ( ( func @ SV125 @ SV404 @ SV600 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2394,plain,
! [SV805: $i > $o,SV601: $i,SV405: $i,SV126: $i] :
( ( ( ~ ! [SY3700: $i] :
( ~ ( in @ SY3700 @ SV126 )
| ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV405 )
| ~ ( in @ ( kpair @ SY3700 @ SY3701 ) @ SV601 )
| ( SV805 @ ( kpair @ SY3700 @ SY3701 ) ) ) )
| ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2395,plain,
! [SV406: $i,SV127: $i,SV729: $i] :
( ( ( ~ ( in @ SV729 @ ( powerset @ SV127 ) ) )
= $true )
| ( ( ! [SY3626: $i] :
( ~ ( in @ SY3626 @ SV127 )
| ~ ( in @ SY3626 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3626 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) ) )
= $true )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2148]) ).
thf(2396,plain,
! [SV407: $i,SV128: $i,SV602: $i] :
( ( ( in @ SV602 @ SV128 )
= $true )
| ( ( ~ ( in @ SV602 @ SV407 )
| ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2397,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( ~ ( SV129 @ SV730 )
| ~ ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) ) )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2150]) ).
thf(2398,plain,
! [SV408: $i,SV130: $i,SV603: $i] :
( ( ( SV603 = SV130 )
= $true )
| ( ( in @ SV603 @ SV408 )
= $true )
| ( ( in @ SV603 @ ( setadjoin @ SV130 @ SV408 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2151]) ).
thf(2399,plain,
! [SV409: $i,SV132: $i,SV731: $i] :
( ( ( ~ ( in @ SV731 @ ( powerset @ SV132 ) ) )
= $true )
| ( ( ! [SY3628: $i] :
( ~ ( in @ SY3628 @ SV132 )
| ~ ( in @ SY3628 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SY3628 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) ) )
= $true )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2152]) ).
thf(2400,plain,
! [SV411: $i,SV134: $i,SV732: $i] :
( ( ( ~ ( in @ SV732 @ ( powerset @ SV134 ) ) )
= $true )
| ( ( ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SY3629 @ SV411 )
| ( in @ SY3629 @ SV732 ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2401,plain,
! [SV605: $i,SV806: $i,SV413: $i,SV137: $i] :
( ( ( ~ ( func @ SV137 @ SV413 @ SV806 )
| ~ ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3703 )
= ( ap @ SV137 @ SV413 @ SV806 @ SY3703 ) ) )
| ( SV605 = SV806 ) )
= $true )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2402,plain,
! [SV606: $i,SV414: $o,SV138: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ SV138 )
| ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3704: $i] :
( ~ ( ~ SV414
| ( SY3704 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3704 != SV807 ) ) ) ) ) )
= $true )
| ( ( in @ SV606 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2403,plain,
! [SV607: $i,SV138: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ SV138 )
| ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3705: $i] :
( ~ ( ~ $true
| ( SY3705 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3705 != SV808 ) ) ) ) ) )
= $true )
| ( ( in @ SV607 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2404,plain,
! [SV608: $i,SV138: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV138 )
| ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3706: $i] :
( ~ ( ~ $false
| ( SY3706 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3706 != SV809 ) ) ) ) ) )
= $true )
| ( ( in @ SV608 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2405,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ( ~ ( SV139 @ SV733 )
| ~ ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) ) )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2406,plain,
! [SV140: $i,SV609: $i,SV415: $i > $o] :
( ( ( ~ ( SV415 @ SV609 ) )
= $true )
| ( ( in @ SV609
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) )
= $true )
| ( ( in @ SV609 @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2161]) ).
thf(2407,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ( ( sK13_SY3143 @ SV416 @ SV141 )
!= ( sK23_SY3631 @ SV141 @ SV416 ) )
| ~ ( ~ ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
| ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2162]) ).
thf(2408,plain,
! [SV610: $i,SV417: $i,SV142: $i] :
( ( ( ! [SY3488: $i] :
~ ~ ( ~ ( in @ SY3488 @ SV142 )
| ~ ~ ! [SY3489: $i] :
~ ~ ( ~ ( in @ SY3489 @ SV417 )
| ( SV610
!= ( kpair @ SY3488 @ SY3489 ) ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2163]) ).
thf(2409,plain,
! [SV418: $i,SV143: $i,SV734: $i] :
( ( ( ~ ( in @ SV734 @ ( powerset @ SV143 ) ) )
= $true )
| ( ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SV734 ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2164]) ).
thf(2410,plain,
! [SV735: $i > $o,SV419: $i,SV144: $i] :
( ( ( ~ ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV144 )
| ! [SY3633: $i] :
( ~ ( in @ SY3633 @ SV144 )
| ~ ( in @ ( kpair @ SY3632 @ SY3633 ) @ SV419 )
| ( SV735 @ ( kpair @ SY3632 @ SY3633 ) ) ) ) )
= $true )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2165]) ).
thf(2411,plain,
! [SV420: $i,SV145: $i,SV736: $i] :
( ( ( ~ ( in @ SV736 @ ( powerset @ SV145 ) ) )
= $true )
| ( ( ! [SY3635: $i] :
( ~ ( in @ SY3635 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3635 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SY3635 ) ) )
= $true )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2166]) ).
thf(2412,plain,
! [SV611: $i,SV422: $o,SV147: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ SV147 )
| ~ ~ SV422
| ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) ) )
= $true )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2413,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ SV147 )
| ~ ~ $true
| ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) ) )
= $true )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2414,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV147 )
| ~ ~ $false
| ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2415,plain,
! [SV614: $i,SV423: $o,SV149: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV149 )
| ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 ) )
= $true )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2416,plain,
! [SV615: $i,SV149: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV149 )
| ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 ) )
= $true )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2417,plain,
! [SV616: $i,SV149: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV149 )
| ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 ) )
= $true )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2418,plain,
! [SV150: $i,SV424: $i,SV617: $i] :
( ( ( ~ ( subset @ SV617 @ SV424 ) )
= $true )
| ( ( subset @ SV617 @ ( binintersect @ SV150 @ SV424 ) )
= $true )
| ( ( subset @ SV617 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2419,plain,
! [SV425: $i,SV151: $i,SV737: $i] :
( ( ( ~ ( in @ SV737 @ ( powerset @ SV151 ) ) )
= $true )
| ( ( ~ ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
| ! [SY3636: $i] :
( ~ ( in @ SY3636 @ SV151 )
| ~ ( in @ SY3636 @ SV737 )
| ( in @ SY3636 @ ( setminus @ SV151 @ SV425 ) ) ) )
= $true )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2174]) ).
thf(2420,plain,
! [SV426: $i,SV152: $i,SV738: $i] :
( ( ( ~ ( in @ SV738 @ ( powerset @ SV152 ) ) )
= $true )
| ( ( ! [SY3637: $i] :
( ~ ( in @ SY3637 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SY3637 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SY3637 ) ) ) )
= $true )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2175]) ).
thf(2421,plain,
! [SV427: $i,SV154: $i,SV739: $i] :
( ( ( ~ ( in @ SV739 @ ( powerset @ SV154 ) ) )
= $true )
| ( ( ! [SY3638: $i] :
( ~ ( in @ SY3638 @ ( powerset @ SV154 ) )
| ! [SY3639: $i] :
( ~ ( in @ SY3639 @ SV154 )
| ~ ( in @ SY3639 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3639 @ ( binunion @ SV427 @ SY3638 ) ) ) ) )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2176]) ).
thf(2422,plain,
! [SV428: $i > $o,SV155: $i,SV816: $i] :
( ( ( ~ ~ ( ~ ( in @ SV816 @ SV155 )
| ~ ( SV428 @ SV816 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2423,plain,
! [SV429: $i,SV156: $i,SV740: $i] :
( ( ( ~ ( in @ SV740 @ ( powerset @ SV156 ) ) )
= $true )
| ( ( ! [SY3640: $i] :
( ~ ( in @ SY3640 @ SV156 )
| ~ ( in @ SY3640 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3640 @ ( binintersect @ SV429 @ SV740 ) ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2178]) ).
thf(2424,plain,
! [SV158: $i,SV618: $i,SV431: $i] :
( ( ( ~ ( subset @ SV431 @ SV618 ) )
= $true )
| ( ( subset @ SV158 @ SV618 )
= $true )
| ( ( subset @ SV158 @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2179]) ).
thf(2425,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2426,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3641: $i] :
( ~ ( in @ SY3641 @ SV159 )
| ~ ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
| ~ ( SV432 @ SY3641 )
| ( ( sK14_SY3181 @ SV432 @ SV159 )
= SY3641 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2427,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( ~ ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) )
| ~ ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) )
= $false )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2428,plain,
! [SV161: $i,SV620: $i,SV434: $i > $o] :
( ( ( ~ ( SV434 @ SV620 ) )
= $true )
| ( ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset )
= $true )
| ( ( in @ SV620 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2182]) ).
thf(2429,plain,
! [SV436: $i,SV163: $i,SV690: $i,SV622: $i] :
( ( ( in @ ( kpair @ SV622 @ SV690 ) @ ( cartprod @ SV163 @ SV436 ) )
= $false )
| ( ( in @ SV690 @ SV436 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2184]) ).
thf(2430,plain,
! [SV165: $i,SV623: $i,SV437: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV437 )
| ( in @ ( kpair @ SV623 @ SV817 ) @ ( cartprod @ SV165 @ SV437 ) ) )
= $true )
| ( ( in @ SV623 @ SV165 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2431,plain,
! [SV438: $i,SV166: $i,SV741: $i] :
( ( ( ~ ( in @ SV741 @ ( powerset @ SV166 ) ) )
= $true )
| ( ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SV741 ) ) ) )
= $true )
| ( ( in @ SV438 @ ( powerset @ SV166 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2186]) ).
thf(2432,plain,
! [SV167: $i,SV624: $i,SV439: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV439 )
| ( ( kfst @ ( kpair @ SV624 @ SV818 ) )
= SV624 ) )
= $true )
| ( ( in @ SV624 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2433,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK24_SY3199 @ SV440 @ SV168 ) @ SV168 )
| ~ ( SV440 @ ( sK24_SY3199 @ SV440 @ SV168 ) ) ) )
= $false )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2188]) ).
thf(2434,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
| ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2435,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ~ ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
| ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2190]) ).
thf(2436,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 ) )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2191]) ).
thf(2437,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ! [SY3642: $i] :
~ ~ ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3642 )
| ~ ! [SY3643: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3643 )
| ( SY3642 = SY3643 ) ) ) )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2191]) ).
thf(2438,plain,
! [SV443: $i,SV171: $i,SV626: $i] :
( ( ( ~ ( in @ SV626 @ SV171 ) )
= $true )
| ( ( in @ SV443 @ ( setunion @ SV171 ) )
= $true )
| ( ( in @ SV443 @ SV626 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2192]) ).
thf(2439,plain,
! [SV819: $i > $o,SV627: $i,SV445: $i,SV173: $i] :
( ( ( ~ ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV173 )
| ! [SY3711: $i] :
( ~ ( in @ SY3711 @ SV445 )
| ~ ( in @ ( kpair @ SY3710 @ SY3711 ) @ SV627 )
| ( SV819 @ ( kpair @ SY3710 @ SY3711 ) ) ) )
| ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2440,plain,
! [SV691: $i,SV628: $i,SV446: $i,SV174: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV174 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV174 @ ( setadjoin @ SV446 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV628 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV628 @ ( setadjoin @ SV691 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV174 = SV628 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2441,plain,
! [SV177: $i,SV449: $i] :
( ( ( ~ ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 ) )
= $false )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2442,plain,
! [SV177: $i,SV449: $i] :
( ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2195]) ).
thf(2443,plain,
! [SV692: $i,SV630: $i,SV451: $i,SV179: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SV692 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV630 != SV692 )
| ( SV451 = SV692 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2197]) ).
thf(2444,plain,
! [SV631: $i,SV452: $i,SV180: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV180 )
| ! [SY3713: $i] :
( ~ ( in @ SY3713 @ SV452 )
| ~ ( in @ ( kpair @ SV820 @ SY3713 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SY3713 ) ) )
= $true )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2445,plain,
! [SV454: $i,SV183: $i,SV742: $i] :
( ( ( ~ ( in @ SV742 @ ( powerset @ SV183 ) ) )
= $true )
| ( ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SV742 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV183 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2200]) ).
thf(2446,plain,
! [SV455: $i,SV743: $i,SV185: $i] :
( ( ( ~ ( breln1 @ SV185 @ SV743 ) )
= $true )
| ( ( ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SV185 )
| ! [SY3645: $i] :
( ~ ( in @ SY3645 @ SV185 )
| ~ ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV455 )
| ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV743 ) ) )
| ( subset @ SV455 @ SV743 ) )
= $true )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2202]) ).
thf(2447,plain,
! [SV186: $i,SV456: $i,SV633: $i] :
( ( ( ~ ( in @ SV633 @ SV456 ) )
= $true )
| ( ( in @ SV633 @ ( binintersect @ SV186 @ SV456 ) )
= $true )
| ( ( in @ SV633 @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2203]) ).
thf(2448,plain,
! [SV457: $i,SV187: $i,SV744: $i] :
( ( ( ~ ( in @ SV744 @ ( powerset @ SV187 ) ) )
= $true )
| ( ( ! [SY3646: $i] :
( ~ ( in @ SY3646 @ ( powerset @ SV187 ) )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV187 )
| ~ ( in @ SY3647 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3647 @ ( binintersect @ ( binunion @ SV457 @ SY3646 ) @ ( binunion @ SV744 @ SY3646 ) ) ) ) ) )
= $true )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2204]) ).
thf(2449,plain,
! [SV458: $i,SV188: $i,SV745: $i] :
( ( ( ~ ( in @ SV745 @ SV188 ) )
= $true )
| ( ( ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV188 )
| ~ ( in @ ( kpair @ SY3648 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SY3648 ) @ SV458 ) ) )
= $true )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2205]) ).
thf(2450,plain,
! [SV746: $o,SV189: $i,SV459: $i] :
( ( ( ~ ! [SY3649: $i] :
( ~ ( in @ SV459 @ SY3649 )
| ~ ( in @ SY3649 @ SV189 )
| SV746 ) )
= $true )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2451,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2207]) ).
thf(2452,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2453,plain,
! [SV462: $i,SV192: $i,SV747: $i] :
( ( ( ~ ( in @ SV747 @ ( powerset @ SV192 ) ) )
= $true )
| ( ( ! [SY3650: $i] :
( ~ ( in @ SY3650 @ SV192 )
| ~ ~ ( in @ SY3650 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SY3650 @ SV462 ) ) )
= $true )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2454,plain,
! [SV463: $i,SV193: $i,SV748: $i] :
( ( ( ~ ( in @ SV748 @ ( powerset @ SV193 ) ) )
= $true )
| ( ( ! [SY3651: $i] :
( ~ ( in @ SY3651 @ SV193 )
| ~ ( in @ SY3651 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SY3651 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2455,plain,
! [SV464: $i,SV194: $i,SV749: $i] :
( ( ( ~ ( in @ SV749 @ ( powerset @ SV194 ) ) )
= $true )
| ( ( ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3652 ) @ ( binunion @ SV749 @ SY3652 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2212]) ).
thf(2456,plain,
! [SV465: $i,SV821: $o,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| SV821 )
| ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2213]) ).
thf(2457,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| $true )
| ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2213]) ).
thf(2458,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| $false )
| ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2213]) ).
thf(2459,plain,
! [SV467: $i,SV197: $i] :
( ( ( ! [SY3248: $i] :
~ ~ ( ~ ( in @ SY3248 @ SV197 )
| ~ ( in @ SY3248 @ SV467 ) ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2460,plain,
! [SV469: $i,SV199: $i,SV750: $i] :
( ( ( ~ ( in @ SV750 @ ( powerset @ SV199 ) ) )
= $true )
| ( ( in @ ( setminus @ SV469 @ SV750 ) @ ( powerset @ SV199 ) )
= $true )
| ( ( in @ SV469 @ ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2216]) ).
thf(2461,plain,
! [SV200: $i,SV637: $i > $i,SV470: $i] :
( ( ( ~ ( in @ ( sK25_SY3515 @ SV470 @ SV637 @ SV200 ) @ SV200 )
| ( in @ ( SV637 @ ( sK25_SY3515 @ SV470 @ SV637 @ SV200 ) ) @ SV470 ) )
= $false )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2217]) ).
thf(2462,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK26_SY3253 @ SV471 @ SV201 ) @ SV201 )
| ~ ( in @ SV471 @ ( sK26_SY3253 @ SV471 @ SV201 ) ) ) )
= $false )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2218]) ).
thf(2463,plain,
! [SV473: $i,SV203: $i,SV751: $i] :
( ( ( ~ ( in @ SV751 @ ( powerset @ SV203 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV473 @ SV751 ) @ ( powerset @ SV203 ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV203 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2464,plain,
! [SV474: $i,SV204: $i,SV752: $i] :
( ( ( ~ ( in @ SV752 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( ! [SY3653: $i] :
( ~ ( in @ SY3653 @ ( powerset @ SV204 ) )
| ! [SY3654: $i] :
( ~ ( in @ SY3654 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SY3653 @ SY3654 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3653 ) @ ( setminus @ SV204 @ SY3654 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2465,plain,
! [SV475: $i,SV206: $i,SV638: $i] :
( ( ( in @ SV638 @ SV206 )
= $true )
| ( ( in @ SV638 @ SV475 )
= $true )
| ( ( in @ SV638 @ ( binunion @ SV206 @ SV475 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2221]) ).
thf(2466,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( SV207 @ SV753 )
| ~ ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) ) )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2222]) ).
thf(2467,plain,
! [SV209: $i,SV477: $i] :
( ( ( in @ SV477 @ ( setadjoin @ SV209 @ emptyset ) )
= $false )
| ( ( SV209 = SV477 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2468,plain,
! [SV211: $i,SV639: $i,SV479: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV479 )
| ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SV822 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) ) )
= $true )
| ( ( in @ SV639 @ SV211 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2469,plain,
! [SV480: $i,SV754: $i,SV212: $i] :
( ( ( ~ ( breln1 @ SV212 @ SV754 ) )
= $true )
| ( ( breln1 @ SV212 @ ( binunion @ SV480 @ SV754 ) )
= $true )
| ( ( breln1 @ SV212 @ SV480 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2225]) ).
thf(2470,plain,
! [SV641: $i,SV482: $o,SV214: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ SV214 )
| ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SV823 )
= SV641 ) )
= $true )
| ( ( in @ SV641 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2471,plain,
! [SV642: $i,SV214: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ SV214 )
| ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SV824 )
= SV642 ) )
= $true )
| ( ( in @ SV642 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2472,plain,
! [SV643: $i,SV214: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV214 )
| ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SV825 )
= SV643 ) )
= $true )
| ( ( in @ SV643 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2473,plain,
! [SV483: $i,SV755: $i,SV215: $i] :
( ( ( ~ ( breln1 @ SV215 @ SV755 ) )
= $true )
| ( ( ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV215 )
| ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV215 )
| ~ ( in @ ( kpair @ SY3656 @ SY3657 ) @ SV483 )
| ( in @ ( kpair @ SY3656 @ SY3657 ) @ ( binunion @ SV483 @ SV755 ) ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2230]) ).
thf(2474,plain,
! [SV484: $i,SV216: $i,SV756: $i] :
( ( ( ~ ( in @ SV756 @ ( powerset @ SV216 ) ) )
= $true )
| ( ( ~ ( subset @ SV484 @ ( setminus @ SV216 @ SV756 ) )
| ( subset @ SV756 @ ( setminus @ SV216 @ SV484 ) ) )
= $true )
| ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2231]) ).
thf(2475,plain,
! [SV644: $i > $i > $o,SV485: $i,SV217: $i,SV757: $i,SV693: $i] :
( ( ( ~ ( in @ ( kpair @ SV693 @ SV757 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SY3523: $i,SY3524: $i] : ( SV644 @ SY3523 @ SY3524 ) ) ) )
= $true )
| ( ( in @ SV757 @ SV485 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2476,plain,
! [SV486: $i,SV218: $i,SV758: $i] :
( ( ( ~ ( in @ SV758 @ ( powerset @ SV218 ) ) )
= $true )
| ( ( ( setminus @ SV218 @ ( binunion @ SV486 @ SV758 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SV758 ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV218 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2477,plain,
! [SV487: $i,SV219: $i,SV645: $i] :
( ( ( in @ SV645 @ SV219 )
= $true )
| ( ( ~ ~ ( in @ SV645 @ SV487 )
| ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2234]) ).
thf(2478,plain,
! [SV488: $i,SV220: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV220 ) )
= $true )
| ( ( ~ ( in @ SV759 @ SV488 )
| ~ ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) ) )
= $true )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2235]) ).
thf(2479,plain,
! [SV489: $i > $o,SV221: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ SV221 )
| ( SV489 @ SV826 ) )
= $true )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2236]) ).
thf(2480,plain,
! [SV491: $i,SV223: $i,SV760: $i] :
( ( ( ~ ( in @ SV760 @ ( powerset @ SV223 ) ) )
= $true )
| ( ( ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV223 )
| ~ ( in @ SY3660 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SY3660 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2237]) ).
thf(2481,plain,
! [SV492: $i,SV224: $i,SV646: $i] :
( ( ( in @ SV646 @ ( setminus @ SV224 @ SV492 ) )
= $false )
| ( ( in @ SV646 @ SV492 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2238]) ).
thf(2482,plain,
! [SV225: $i,SV493: $i,SV647: $i] :
( ( ( ~ ~ ( in @ SV647 @ SV493 ) )
= $true )
| ( ( ~ ( subset @ SV225 @ SV493 ) )
= $true )
| ( ( in @ SV647 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2239]) ).
thf(2483,plain,
! [SV648: $i,SV827: $i,SV494: $i,SV226: $i] :
( ( ( ~ ( breln @ SV226 @ SV494 @ SV827 )
| ~ ! [SY3714: $i] :
( ~ ( in @ SY3714 @ SV226 )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV494 )
| ~ ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV648 )
| ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV827 ) ) )
| ( subset @ SV648 @ SV827 ) )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2240]) ).
thf(2484,plain,
! [SV495: $i,SV227: $i,SV761: $i] :
( ( ( ~ ( in @ SV761 @ ( powerset @ SV227 ) ) )
= $true )
| ( ( in @ ( binunion @ SV495 @ SV761 ) @ ( powerset @ SV227 ) )
= $true )
| ( ( in @ SV495 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2241]) ).
thf(2485,plain,
! [SV228: $i,SV496: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ SV496 ) )
= $true )
| ( ( in @ SV649 @ SV228 )
= $true )
| ( ( in @ SV496 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2242]) ).
thf(2486,plain,
! [SV231: $i,SV650: $i,SV499: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ SV499 )
| ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SV828 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) ) )
= $true )
| ( ( in @ SV650 @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2487,plain,
! [SV500: $i,SV232: $i,SV762: $i] :
( ( ( ~ ( in @ SV762 @ ( powerset @ SV232 ) ) )
= $true )
| ( ( ~ ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV232 )
| ~ ( in @ SY3661 @ SV500 )
| ( in @ SY3661 @ SV762 ) )
| ( subset @ SV500 @ SV762 ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2244]) ).
thf(2488,plain,
! [SV501: $i,SV233: $i,SV763: $i] :
( ( ( ~ ( in @ SV763 @ ( powerset @ SV233 ) ) )
= $true )
| ( ( ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV233 )
| ~ ( in @ SY3662 @ SV501 )
| ( in @ SY3662 @ SV763 ) )
| ( in @ SV501 @ ( powerset @ SV763 ) ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2489,plain,
! [SV502: $i,SV234: $i,SV651: $i] :
( ( ( SV651 = SV234 )
= $true )
| ( ( SV651 = SV502 )
= $true )
| ( ( in @ SV651 @ ( setadjoin @ SV234 @ ( setadjoin @ SV502 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2246]) ).
thf(2490,plain,
! [SV503: $i,SV235: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV235 ) )
= $true )
| ( ( ~ ( in @ SV764 @ SV503 )
| ( in @ SV764 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) )
= $true )
| ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2247]) ).
thf(2491,plain,
! [SV504: $i,SV236: $i] :
( ( ( SV236 = SV504 )
= $false )
| ( ( subset @ SV236 @ SV504 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2492,plain,
! [SV652: $i,SV505: $o,SV237: $i,SV829: $i] :
( ( ( ~ ( in @ SV829 @ SV237 )
| ( in @ ( if @ SV237 @ SV505 @ SV652 @ SV829 ) @ SV237 ) )
= $true )
| ( ( in @ SV652 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2249]) ).
thf(2493,plain,
! [SV653: $i,SV237: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ SV237 )
| ( in @ ( if @ SV237 @ $true @ SV653 @ SV830 ) @ SV237 ) )
= $true )
| ( ( in @ SV653 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2250]) ).
thf(2494,plain,
! [SV654: $i,SV237: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ SV237 )
| ( in @ ( if @ SV237 @ $false @ SV654 @ SV831 ) @ SV237 ) )
= $true )
| ( ( in @ SV654 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2251]) ).
thf(2495,plain,
! [SV506: $i,SV238: $i,SV765: $i] :
( ( ( ~ ( in @ SV765 @ ( powerset @ SV238 ) ) )
= $true )
| ( ( ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( powerset @ SV238 ) )
| ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV238 )
| ~ ( in @ SY3664 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3664 @ ( binunion @ SV765 @ SY3663 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2496,plain,
! [SV508: $i,SV766: $i,SV240: $i] :
( ( ( ~ ( breln1 @ SV240 @ SV766 ) )
= $true )
| ( ( ! [SY3665: $i] :
( ~ ( in @ SY3665 @ SV240 )
| ! [SY3666: $i] :
( ~ ( in @ SY3666 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3666 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3667: $o] :
( ~ ! [SY3668: $i] :
( ~ ( in @ SY3668 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3668 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3668 @ SY3666 ) @ SV766 )
| SY3667 )
| SY3667 ) ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2497,plain,
! [SV767: $i > $o,SV509: $i,SV241: $i] :
( ( ( ~ ! [SY3669: $i] :
( ~ ( in @ SY3669 @ SV241 )
| ! [SY3670: $i] :
( ~ ( in @ SY3670 @ SV241 )
| ~ ( in @ ( kpair @ SY3669 @ SY3670 ) @ SV509 )
| ( SV767 @ ( kpair @ SY3669 @ SY3670 ) ) ) ) )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2498,plain,
! [SV510: $i,SV242: $i,SV768: $i] :
( ( ( ~ ( in @ SV768 @ ( powerset @ SV242 ) ) )
= $true )
| ( ( ! [SY3672: $i] :
( ~ ( in @ SY3672 @ SV242 )
| ~ ( in @ SY3672 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SY3672 @ SV510 ) ) )
= $true )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2499,plain,
! [SV511: $i,SV243: $i,SV769: $i] :
( ( ( ~ ( in @ SV769 @ ( powerset @ SV243 ) ) )
= $true )
| ( ( ! [SY3673: $i] :
( ~ ( in @ SY3673 @ SV243 )
| ~ ( in @ SY3673 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SY3673 @ ( setminus @ SV243 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2500,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i,SV694: $i] :
( ( ( in @ SV694 @ SV249 )
= $false )
| ( ( ! [SY3585: $i] :
( ~ ( in @ SY3585 @ SV517 )
| ~ ( in @ ( kpair @ SV694 @ SY3585 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SY3585 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2501,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY3674: $i] :
~ ( ~ ( ~ ( SV250 @ SY3674 )
| ( SY3674 = SV770 ) )
| ~ ( ( SY3674 != SV770 )
| ( SV250 @ SY3674 ) ) ) )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2260]) ).
thf(2502,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ( breln @ SV251 @ SV518 @ SV832 )
| ~ ! [SY3716: $i] :
( ~ ( in @ SY3716 @ SV251 )
| ! [SY3717: $i] :
( ~ ( in @ SY3717 @ SV518 )
| ~ ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV658 )
| ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV832 ) ) )
| ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2261]) ).
thf(2503,plain,
! [SV519: $i,SV252: $i,SV771: $i] :
( ( ( ~ ( in @ SV771 @ ( powerset @ SV252 ) ) )
= $true )
| ( ( ! [SY3675: $i] :
( ~ ( in @ SY3675 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SY3675 @ SV771 )
| ~ ( in @ SY3675 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2504,plain,
! [SV254: $i,SV772: $i] :
( ( ( in @ SV772 @ SV254 )
= $false )
| ( ( SV254 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2505,plain,
! [SV522: $i > $o,SV256: $i] :
( ( ( ! [SY3333: $i] :
~ ~ ( ~ ( in @ SY3333 @ SV256 )
| ~ ( SV522 @ SY3333 ) ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2265]) ).
thf(2506,plain,
! [SV524: $i,SV773: $i,SV258: $i] :
( ( ( ~ ( breln1 @ SV258 @ SV773 ) )
= $true )
| ( ( ! [SY3676: $i] :
( ~ ( in @ SY3676 @ SV258 )
| ! [SY3677: $i] :
( ~ ( in @ SY3677 @ SV258 )
| ! [SY3678: $i] :
( ~ ( in @ SY3678 @ SV258 )
| ~ ( in @ ( kpair @ SY3676 @ SY3678 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3678 @ SY3677 ) @ SV773 )
| ( in @ ( kpair @ SY3676 @ SY3677 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2266]) ).
thf(2507,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ( breln1 @ SV259 @ SV774 ) )
= $true )
| ( ( ~ ! [SY3679: $i] :
( ~ ( in @ SY3679 @ SV259 )
| ! [SY3680: $i] :
( ~ ( in @ SY3680 @ SV259 )
| ~ ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV525 )
| ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV774 ) ) )
| ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2267]) ).
thf(2508,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) )
| ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2269]) ).
thf(2509,plain,
! [SV661: $i,SV528: $i,SV262: $i,SV833: $i] :
( ( ( ~ ( in @ SV833 @ SV262 )
| ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3720: $i] : ( in @ ( kpair @ SV833 @ SY3720 ) @ SV661 ) ) ) )
= $true )
| ( ( func @ SV262 @ SV528 @ SV661 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2510,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ SV775 )
| ~ ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) ) )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2511,plain,
! [SV529: $i,SV264: $i,SV776: $i] :
( ( ( ~ ( in @ SV776 @ ( powerset @ SV264 ) ) )
= $true )
| ( ( ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV264 )
| ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SY3684 @ SV776 )
| ~ ( in @ SY3684 @ SV529 ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2272]) ).
thf(2512,plain,
! [SV265: $i,SV777: $i] :
( ( ( in @ SV777 @ SV265 )
= $false )
| ( ( ~ ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2513,plain,
! [SV530: $i,SV266: $i,SV662: $i] :
( ( ( in @ SV662 @ SV266 )
= $true )
| ( ( ~ ( in @ SV662 @ ( setminus @ SV266 @ SV530 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2514,plain,
! [SV695: $i,SV663: $i,SV531: $i,SV267: $i] :
( ( ( ( kpair @ SV267 @ SV531 )
= ( kpair @ SV663 @ SV695 ) )
= $false )
| ( ( SV267 = SV663 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2275]) ).
thf(2515,plain,
! [SV268: $i] :
( ( ( ~ ( in @ ( sK27_SY2868 @ SV268 ) @ SV268 ) )
= $false )
| ( ( SV268 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2276]) ).
thf(2516,plain,
! [SV534: $i,SV272: $i,SV778: $i] :
( ( ( ~ ( in @ SV778 @ ( powerset @ SV272 ) ) )
= $true )
| ( ( ~ ( subset @ SV534 @ SV778 )
| ( subset @ ( setminus @ SV272 @ SV778 ) @ ( setminus @ SV272 @ SV534 ) ) )
= $true )
| ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2517,plain,
! [SV273: $i,SV664: $i,SV535: $i,SV834: $i] :
( ( ( ~ ( in @ SV834 @ SV535 )
| ( in @ ( kpair @ SV664 @ SV834 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) ) )
= $true )
| ( ( in @ SV664 @ SV273 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2278]) ).
thf(2518,plain,
! [SV665: $i,SV536: $i,SV274: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ SV274 )
| ( ( ap @ SV274 @ SV536 @ SV665 @ SV835 )
= ( ap @ SV274 @ SV536 @ SV665 @ SV835 ) ) )
= $true )
| ( ( func @ SV274 @ SV536 @ SV665 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2279]) ).
thf(2519,plain,
! [SV537: $i,SV275: $i,SV779: $i] :
( ( ( ~ ( in @ SV779 @ ( powerset @ SV275 ) ) )
= $true )
| ( ( ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV275 )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SY3685 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) ) )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2280]) ).
thf(2520,plain,
! [SV666: $i,SV538: $i,SV276: $i,SV836: $i] :
( ( ( ~ ( in @ SV836 @ SV276 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3721: $i] : ( in @ ( kpair @ SV836 @ SY3721 ) @ SV666 ) ) )
@ SV538 ) )
= $true )
| ( ( func @ SV276 @ SV538 @ SV666 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2521,plain,
! [SV667: $i,SV539: $i,SV277: $i,SV837: $i] :
( ( ( ~ ( in @ SV837 @ SV277 )
| ( in @ ( kpair @ SV837 @ ( ap @ SV277 @ SV539 @ SV667 @ SV837 ) ) @ SV667 ) )
= $true )
| ( ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2282]) ).
thf(2522,plain,
! [SV540: $i > $o,SV278: $i,SV838: $i] :
( ( ( ~ ~ ( ~ ( in @ SV838 @ SV278 )
| ~ ~ ( SV540 @ SV838 ) ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2283]) ).
thf(2523,plain,
! [SV541: $i,SV279: $i,SV780: $i] :
( ( ( ~ ( in @ SV780 @ SV279 ) )
= $true )
| ( ( ! [SY3686: $i] :
( ~ ( in @ SY3686 @ SV279 )
| ~ ( in @ ( kpair @ SV780 @ SY3686 ) @ SV541 )
| ( in @ ( kpair @ SY3686 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) )
= $true )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2284]) ).
thf(2524,plain,
! [SV280: $i,SV668: $i > $i,SV542: $i] :
( ( ( ~ ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 )
| ( in @ ( SV668 @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) ) @ SV542 ) )
= $false )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2285]) ).
thf(2525,plain,
! [SV543: $i,SV281: $i,SV696: $i,SV669: $i] :
( ( ( in @ ( kpair @ SV669 @ SV696 ) @ ( cartprod @ SV281 @ SV543 ) )
= $false )
| ( ( in @ SV669 @ SV281 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2286]) ).
thf(2526,plain,
! [SV282: $i,SV670: $i > $i,SV544: $i] :
( ( ( ~ ( in @ ( sK29_SY3556 @ SV544 @ SV670 @ SV282 ) @ SV282 )
| ( in @ ( SV670 @ ( sK29_SY3556 @ SV544 @ SV670 @ SV282 ) ) @ SV544 ) )
= $false )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2287]) ).
thf(2527,plain,
! [SV545: $i,SV283: $i,SV781: $i] :
( ( ( ~ ( in @ SV781 @ ( powerset @ SV283 ) ) )
= $true )
| ( ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SV781 ) ) ) )
= $true )
| ( ( in @ SV545 @ ( powerset @ SV283 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2528,plain,
! [SV284: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_SY2910 @ SV284 ) @ SV284 )
| ~ $true ) )
= $false )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2289]) ).
thf(2529,plain,
! [SV285: $i,SV546: $i,SV671: $i] :
( ( ( ~ ~ ( in @ SV671 @ SV546 ) )
= $true )
| ( ( SV285 != SV546 )
= $true )
| ( ( in @ SV671 @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2530,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) )
= $true )
| ( ( ~ ( in @ SV672 @ SV286 )
| ( in @ SV672 @ SV547 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2531,plain,
! [SV673: $i,SV548: $i,SV287: $i,SV839: $i] :
( ( ( ~ ( in @ SV839 @ SV287 )
| ! [SY3722: $i] :
( ~ ( in @ SY3722 @ SV548 )
| ~ ( in @ ( kpair @ SV839 @ SY3722 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SY3722 ) ) )
= $true )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2532,plain,
! [SV674: $i,SV549: $o,SV288: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3723: $i] :
( ~ ( ~ SV549
| ( SY3723 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3723 != SV840 ) ) ) ) ) )
= $true )
| ( ( in @ SV674 @ SV288 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2293]) ).
thf(2533,plain,
! [SV675: $i,SV288: $i,SV841: $i] :
( ( ( ~ ( in @ SV841 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3724: $i] :
( ~ ( ~ $true
| ( SY3724 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3724 != SV841 ) ) ) ) ) )
= $true )
| ( ( in @ SV675 @ SV288 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2534,plain,
! [SV676: $i,SV288: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ SV288 )
| ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3725: $i] :
( ~ ( ~ $false
| ( SY3725 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3725 != SV842 ) ) ) ) ) )
= $true )
| ( ( in @ SV676 @ SV288 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2295]) ).
thf(2535,plain,
! [SV551: $i,SV290: $i,SV678: $i] :
( ( ( SV678 = SV290 )
= $true )
| ( ( SV678 = SV551 )
= $true )
| ( ( in @ SV678 @ ( setadjoin @ SV290 @ ( setadjoin @ SV551 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2297]) ).
thf(2536,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( ~ ( SV291 @ SV782 )
| ~ ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) ) )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2298]) ).
thf(2537,plain,
! [SV294: $i,SV554: $i,SV679: $i] :
( ( ( ~ ~ ( in @ SV679 @ SV554 ) )
= $true )
| ( ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) )
= $true )
| ( ( in @ SV679 @ SV294 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2299]) ).
thf(2538,plain,
! [SV680: $i,SV555: $o,SV296: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ SV296 )
| ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3726: $i] :
( ~ ( ~ SV555
| ( SY3726 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3726 != SV843 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) )
= $true )
| ( ( in @ SV680 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2539,plain,
! [SV681: $i,SV296: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ SV296 )
| ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3727: $i] :
( ~ ( ~ $true
| ( SY3727 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3727 != SV844 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) )
= $true )
| ( ( in @ SV681 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2301]) ).
thf(2540,plain,
! [SV682: $i,SV296: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ SV296 )
| ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3728: $i] :
( ~ ( ~ $false
| ( SY3728 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3728 != SV845 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) )
= $true )
| ( ( in @ SV682 @ SV296 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2541,plain,
! [SV320: $i,SV35: $i,SV698: $i] :
( ( ( in @ SV698 @ ( powerset @ SV35 ) )
= $false )
| ( ( ( setminus @ SV35 @ ( binintersect @ SV320 @ SV698 ) )
= ( binunion @ ( setminus @ SV35 @ SV320 ) @ ( setminus @ SV35 @ SV698 ) ) )
= $true )
| ( ( in @ SV320 @ ( powerset @ SV35 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2303]) ).
thf(2542,plain,
! [SV322: $i,SV37: $i,SV699: $i] :
( ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( ! [SY3588: $i] :
( ~ ( in @ SY3588 @ ( powerset @ SV37 ) )
| ! [SY3589: $i] :
( ~ ( in @ SY3589 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SY3588 )
| ~ ( subset @ SV699 @ SY3589 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SY3588 @ SY3589 ) ) ) ) )
= $true )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2543,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ( SV38 @ SV700 )
| ~ ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2306]) ).
thf(2544,plain,
! [SV324: $i,SV701: $i,SV40: $i] :
( ( ( breln1 @ SV40 @ SV701 )
= $false )
| ( ( breln1 @ SV40 @ ( breln1compset @ SV40 @ SV324 @ SV701 ) )
= $true )
| ( ( breln1 @ SV40 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2307]) ).
thf(2545,plain,
! [SV41: $i,SV325: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ SV325 ) )
= $false )
| ( ( ~ ( in @ SV560 @ SV41 ) )
= $true )
| ( ( subset @ SV41 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2546,plain,
! [SV42: $i,SV561: $i,SV326: $i,SV783: $i] :
( ( ( ~ ( in @ SV783 @ SV326 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SV783 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) )
= $true )
| ( ( in @ SV561 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2547,plain,
! [SV784: $i > $o,SV702: $i > $o,SV328: $i,SV44: $i] :
( ( ( ~ ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV44 )
| ! [SY3689: $i] :
( ~ ( in @ SY3689 @ SV328 )
| ( SY3688 != SY3689 )
| ~ ( ~ ( ~ ( SV702 @ SY3688 )
| ( SV784 @ SY3689 ) )
| ~ ( ~ ( SV784 @ SY3689 )
| ( SV702 @ SY3688 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2310]) ).
thf(2548,plain,
! [SV45: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2311]) ).
thf(2549,plain,
! [SV45: $i] :
( ( ! [SY3410: $i] :
( ~ ~ ( ~ ! [SY2235: $i] :
( ~ ( in @ SY2235 @ SY3410 )
| ( in @ SY2235 @ SV45 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY3410 ) )
| ~ ! [SY3413: $i] :
~ ~ ! [SY3414: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3413 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3414 @ SY3410 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY3413 )
| ~ ( in @ SX5 @ SY3410 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3413 ) )
| ( in @ SY3414 @ SY3416 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2312]) ).
thf(2550,plain,
! [SV329: $i > $o,SV46: $i,SV703: $i] :
( ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ! [SY3596: $i] :
( ~ ( in @ SY3596 @ SV46 )
| ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SY3596 )
| ( SV703 = SY3596 ) ) )
= $true )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2313]) ).
thf(2551,plain,
! [SV49: $i,SV563: $i > $i,SV331: $i] :
( ( ( ~ ( in @ ( sK18_SY3418 @ SV331 @ SV563 @ SV49 ) @ SV49 ) )
= $false )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2552,plain,
! [SV49: $i,SV331: $i,SV563: $i > $i] :
( ( ( in @ ( SV563 @ ( sK18_SY3418 @ SV331 @ SV563 @ SV49 ) ) @ SV331 )
= $false )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2553,plain,
! [SV51: $i,SV332: $i] :
( ( ( in @ ( sK6_SY2972 @ SV332 @ SV51 ) @ SV51 )
= $true )
| ( ( subset @ SV51 @ SV332 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2316]) ).
thf(2554,plain,
! [SV52: $i] :
( ( ( ! [SY2254: $i] :
( ~ ~ ( ~ ( in @ SY2254 @ omega )
| ~ ( in @ SY2254 @ SV52 ) )
| ( in @ ( setadjoin @ SY2254 @ SY2254 ) @ SV52 ) ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2318]) ).
thf(2555,plain,
! [SV53: $i,SV333: $i] :
( ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false )
| ( ( ~ ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2319]) ).
thf(2556,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2320]) ).
thf(2557,plain,
! [SV54: $i,SV564: $i,SV334: $i > $o] :
( ( ( SV334 @ SV564 )
= $false )
| ( ( ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) )
| ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) ) )
= $true )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2321]) ).
thf(2558,plain,
! [SV55: $i,SV565: $i > $i,SV335: $i] :
( ( ( ~ ( in @ ( sK19_SY3422 @ SV335 @ SV565 @ SV55 ) @ SV55 ) )
= $false )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2559,plain,
! [SV55: $i,SV335: $i,SV565: $i > $i] :
( ( ( in @ ( SV565 @ ( sK19_SY3422 @ SV335 @ SV565 @ SV55 ) ) @ SV335 )
= $false )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2322]) ).
thf(2560,plain,
! [SV566: $i,SV336: $i,SV56: $i,SV785: $i] :
( ( ( ~ ( in @ SV785 @ SV56 ) )
= $true )
| ( ( ( ap @ SV56 @ SV336 @ SV566 @ SV785 )
= ( ap @ SV56 @ SV336 @ SV566 @ SV785 ) )
= $true )
| ( ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2323]) ).
thf(2561,plain,
! [SV337: $i,SV57: $i,SV704: $i] :
( ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( ! [SY3597: $i] :
( ~ ( in @ SY3597 @ SV57 )
| ~ ( in @ SY3597 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SY3597 @ ( setminus @ SV57 @ SV337 ) ) ) )
= $true )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2562,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( in @ SV705 @ SV59 )
= $false )
| ( ( ~ ~ ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) )
| ( in @ SV705 @ SV339 ) )
= $true )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2563,plain,
! [SV568: $i,SV341: $i,SV61: $i,SV786: $i] :
( ( ( ~ ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) ) )
= $true )
| ( ( ~ ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3692 )
= ( ap @ SV61 @ SV341 @ SV786 @ SY3692 ) ) )
| ( SV568 = SV786 ) )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2327]) ).
thf(2564,plain,
! [SV342: $i,SV62: $i,SV706: $i] :
( ( ( in @ SV706 @ ( powerset @ SV62 ) )
= $false )
| ( ( ~ ( subset @ SV342 @ ( setminus @ SV62 @ SV706 ) )
| ( subset @ SV706 @ ( setminus @ SV62 @ SV342 ) ) )
= $true )
| ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2565,plain,
! [SV343: $i,SV63: $i,SV707: $i] :
( ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( ! [SY3598: $i] :
( ~ ( in @ SY3598 @ SV63 )
| ~ ~ ( in @ SY3598 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SY3598 @ SV707 ) ) )
= $true )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2329]) ).
thf(2566,plain,
! [SV344: $i,SV64: $i,SV708: $i] :
( ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( ! [SY3599: $i] :
( ~ ( in @ SY3599 @ ( powerset @ SV64 ) )
| ~ ( subset @ SV708 @ SY3599 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SY3599 ) ) )
= $true )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2330]) ).
thf(2567,plain,
! [SV345: $i,SV65: $i,SV709: $i] :
( ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( ! [SY3600: $i] :
( ~ ( in @ SY3600 @ SV65 )
| ~ ~ ( in @ SY3600 @ SV709 )
| ~ ( in @ SY3600 @ ( binintersect @ SV345 @ SV709 ) ) ) )
= $true )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2568,plain,
! [SV346: $i,SV66: $i,SV710: $i] :
( ( ( in @ SV710 @ SV66 )
= $false )
| ( ( ~ ( in @ SV710 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
| ( in @ SV710 @ SV346 ) )
= $true )
| ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2332]) ).
thf(2569,plain,
! [SV347: $i,SV67: $i] :
( ( ( in @ ( sK7_SY3000 @ SV67 @ SV347 ) @ SV347 )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV67 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2333]) ).
thf(2570,plain,
! [SV348: $i,SV711: $i,SV68: $i] :
( ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( ! [SY3601: $i] :
( ~ ( in @ SY3601 @ SV68 )
| ! [SY3602: $i] :
( ~ ( in @ SY3602 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3602 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3603: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3603 @ SV68 )
| ~ ( in @ ( kpair @ SY3601 @ SY3603 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3603 @ SY3602 ) @ SV711 ) ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2571,plain,
! [SV349: $i,SV69: $i,SV712: $i] :
( ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( ! [SY3604: $i] :
( ~ ( in @ SY3604 @ SV69 )
| ~ ( in @ SY3604 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SY3604 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) ) )
= $true )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2336]) ).
thf(2572,plain,
! [SV70: $i,SV569: $i > $i,SV350: $i] :
( ( ( ~ ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 ) )
= $false )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2573,plain,
! [SV70: $i,SV350: $i,SV569: $i > $i] :
( ( ( in @ ( SV569 @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) ) @ SV350 )
= $false )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2337]) ).
thf(2574,plain,
! [SV71: $i,SV685: $i,SV570: $i > $i > $o,SV351: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ SV351 )
| ~ ( SV570 @ SV685 @ SV846 )
| ( in @ ( kpair @ SV685 @ SV846 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) )
= $true )
| ( ( in @ SV685 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2338]) ).
thf(2575,plain,
! [SV571: $i,SV352: $i,SV72: $i,SV787: $i] :
( ( ( ~ ( in @ SV787 @ SV72 ) )
= $true )
| ( ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SV787 ) @ SV352 )
= $true )
| ( ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2576,plain,
! [SV572: $i > $i > $o,SV353: $i,SV73: $i,SV713: $i,SV686: $i] :
( ( ( in @ ( kpair @ SV686 @ SV713 )
@ ( dpsetconstr @ SV73 @ SV353
@ ^ [SY3439: $i,SY3440: $i] : ( SV572 @ SY3439 @ SY3440 ) ) )
= $false )
| ( ( SV572 @ SV686 @ SV713 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2577,plain,
! [SV74: $i,SV354: $i,SV573: $i > $i > $o] :
( ( ( ~ ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 ) )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2578,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i] :
( ( ( ~ ! [SY3693: $i] :
~ ~ ( ~ ( in @ SY3693 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SY3693 ) ) )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2341]) ).
thf(2579,plain,
! [SV574: $i,SV355: $i,SV75: $i,SV788: $i] :
( ( ( ~ ( in @ SV788 @ SV75 ) )
= $true )
| ( ( in @ ( kpair @ SV788 @ ( ap @ SV75 @ SV355 @ SV574 @ SV788 ) ) @ SV574 )
= $true )
| ( ( func @ SV75 @ SV355 @ SV574 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2580,plain,
! [SV356: $i > $o,SV76: $i,SV789: $i] :
( ( ( ~ ( in @ SV789 @ SV76 ) )
= $true )
| ( ( SV356 @ SV789 )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2343]) ).
thf(2581,plain,
! [SV357: $i,SV77: $i,SV575: $i] :
( ( ( in @ SV575 @ SV77 )
= $false )
| ( ( in @ SV575 @ SV357 )
= $true )
| ( ( subset @ SV77 @ SV357 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2582,plain,
( ( breln1 @ sK1_SX0 @ sK8_SY3448 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2583,plain,
( ( ~ ( in @ sK31_SY3607 @ sK1_SX0 )
| ! [SY3731: $i] :
( ~ ( in @ SY3731 @ sK1_SX0 )
| ~ ( in @ ( kpair @ sK31_SY3607 @ SY3731 ) @ sK8_SY3448 )
| ( in @ ( kpair @ sK31_SY3607 @ SY3731 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2346]) ).
thf(2584,plain,
! [SV358: $i,SV78: $i,SV790: $i,SV714: $i] :
( ( ( SV714 != SV790 )
= $true )
| ( ( ~ ( in @ SV714 @ SV78 )
| ( in @ SV790 @ SV358 ) )
= $true )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2347]) ).
thf(2585,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i] :
( ( ( ~ ( func @ SV81 @ SV361 @ SV791 ) )
= $true )
| ( ( ~ ! [SY3694: $i] :
( ~ ( in @ SY3694 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3694 )
= ( ap @ SV81 @ SV361 @ SV791 @ SY3694 ) ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2350]) ).
thf(2586,plain,
! [SV82: $i,SV362: $i] :
( ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $false )
| ( ( ! [SY3048: $i] :
( ~ ( in @ SY3048 @ SV362 )
| ( in @ SY3048 @ SV82 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2351]) ).
thf(2587,plain,
! [SV82: $i,SV362: $i] :
( ( ( ! [SY3049: $i] :
( ~ ( in @ SY3049 @ SV362 )
| ( in @ SY3049 @ SV82 ) ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2588,plain,
! [SV363: $i,SV83: $i,SV792: $i,SV715: $i] :
( ( ( SV715 != SV792 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) )
| ~ ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) ) ) )
= $true )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2353]) ).
thf(2589,plain,
! [SV365: $i,SV85: $i,SV716: $i] :
( ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( ! [SY3611: $o,SY3612: $i] :
( ~ ( in @ SY3612 @ SV85 )
| ~ ( in @ SY3612 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SY3612 @ SV365 )
| SY3611 )
| ~ ( ~ ( in @ SY3612 @ SV716 )
| SY3611 )
| SY3611 ) )
= $true )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2354]) ).
thf(2590,plain,
! [SV366: $i,SV688: $o,SV86: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| SV688 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2355]) ).
thf(2591,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2592,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV86 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2593,plain,
! [SV87: $i,SV367: $i,SV579: $i] :
( ( ( in @ SV579 @ SV367 )
= $false )
| ( ( ~ ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) ) )
= $true )
| ( ( in @ SV579 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2594,plain,
! [SV89: $i,SV581: $i,SV369: $i,SV793: $i] :
( ( ( ~ ( in @ SV793 @ SV369 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV581 @ SV793 ) )
= SV793 )
= $true )
| ( ( in @ SV581 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2595,plain,
! [SV92: $i,SV583: $i,SV372: $i,SV794: $i] :
( ( ( ~ ( in @ SV794 @ SV372 ) )
= $true )
| ( ( ( kpair @ SV583 @ SV794 )
= ( kpair @ SV583 @ SV794 ) )
= $true )
| ( ( in @ SV583 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2596,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SV795 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2597,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2598,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2363]) ).
thf(2599,plain,
! [SV94: $i,SV374: $i,SV585: $i] :
( ( ( ~ ( in @ SV585 @ SV374 ) )
= $false )
| ( ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) )
= $true )
| ( ( in @ SV585 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2600,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) ) )
= $true )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2601,plain,
! [SV375: $i,SV96: $i,SV796: $i,SV718: $i] :
( ( ( SV718 != SV796 )
= $true )
| ( ( ( setadjoin @ SV96 @ SV718 )
= ( setadjoin @ SV375 @ SV796 ) )
= $true )
| ( ( SV96 = SV375 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2602,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ( sK9_SY3069 @ SV376 @ SV97 )
!= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2603,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
| ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2367]) ).
thf(2604,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2368]) ).
thf(2605,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
| ~ ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
| ~ ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
| ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2369]) ).
thf(2606,plain,
! [SV100: $i,SV586: $i,SV381: $i,SV797: $i] :
( ( ( ~ ( in @ SV797 @ SV381 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SV797 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) )
= $true )
| ( ( in @ SV586 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2607,plain,
! [SV382: $i,SV101: $i,SV719: $i] :
( ( ( in @ SV719 @ ( powerset @ SV101 ) )
= $false )
| ( ( in @ ( setminus @ SV101 @ ( binunion @ SV382 @ SV719 ) ) @ ( powerset @ ( setminus @ SV101 @ SV382 ) ) )
= $true )
| ( ( in @ SV382 @ ( powerset @ SV101 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2371]) ).
thf(2608,plain,
! [SV383: $i,SV102: $i,SV720: $i] :
( ( ( in @ SV720 @ ( powerset @ SV102 ) )
= $false )
| ( ( ~ ( subset @ ( setminus @ SV102 @ SV720 ) @ ( setminus @ SV102 @ SV383 ) )
| ( subset @ SV383 @ SV720 ) )
= $true )
| ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2372]) ).
thf(2609,plain,
! [SV385: $i,SV104: $i,SV721: $i] :
( ( ( in @ SV721 @ ( powerset @ SV104 ) )
= $false )
| ( ( ! [SY3616: $i] :
( ~ ( in @ SY3616 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SY3616 ) @ ( binunion @ SV721 @ SY3616 ) ) ) ) ) )
= $true )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2610,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV722 )
| ~ ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2374]) ).
thf(2611,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
| ~ ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) ) ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2375]) ).
thf(2612,plain,
! [SV387: $i,SV107: $i,SV723: $i] :
( ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( ! [SY3618: $i] :
( ~ ( in @ SY3618 @ SV107 )
| ~ ~ ( in @ SY3618 @ SV387 )
| ~ ( in @ SY3618 @ ( binintersect @ SV387 @ SV723 ) ) ) )
= $true )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2376]) ).
thf(2613,plain,
! [SV588: $i,SV388: $o,SV108: $i,SV798: $i] :
( ( ( ~ ( in @ SV798 @ SV108 ) )
= $true )
| ( ( in @ ( if @ SV108 @ SV388 @ SV588 @ SV798 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SV798 @ emptyset ) ) )
= $true )
| ( ( in @ SV588 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2377]) ).
thf(2614,plain,
! [SV589: $i,SV108: $i,SV799: $i] :
( ( ( ~ ( in @ SV799 @ SV108 ) )
= $true )
| ( ( in @ ( if @ SV108 @ $true @ SV589 @ SV799 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SV799 @ emptyset ) ) )
= $true )
| ( ( in @ SV589 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2378]) ).
thf(2615,plain,
! [SV590: $i,SV108: $i,SV800: $i] :
( ( ( ~ ( in @ SV800 @ SV108 ) )
= $true )
| ( ( in @ ( if @ SV108 @ $false @ SV590 @ SV800 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SV800 @ emptyset ) ) )
= $true )
| ( ( in @ SV590 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2379]) ).
thf(2616,plain,
! [SV391: $i,SV111: $i,SV724: $i] :
( ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( ~ ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV111 )
| ~ ( in @ SY3619 @ SV391 )
| ( in @ SY3619 @ SV724 ) )
| ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2380]) ).
thf(2617,plain,
! [SV392: $i,SV112: $i,SV725: $i] :
( ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( ! [SY3621: $i] :
( ~ ( in @ SY3621 @ SV112 )
| ~ ~ ( in @ SY3621 @ SV392 )
| ~ ~ ( in @ SY3621 @ SV725 )
| ~ ( in @ SY3621 @ ( binunion @ SV392 @ SV725 ) ) ) )
= $true )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2381]) ).
thf(2618,plain,
! [SV113: $i,SV393: $i] :
( ( ( in @ ( sK11_SY3100 @ SV393 @ SV113 ) @ SV113 )
= $true )
| ( ( subset @ SV113 @ SV393 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2382]) ).
thf(2619,plain,
! [SV114: $i,SV394: $i,SV592: $i] :
( ( ( ~ ~ ( in @ SV592 @ SV394 ) )
= $true )
| ( ( ~ ( in @ SV592 @ SV114 ) )
= $true )
| ( ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2384]) ).
thf(2620,plain,
! [SV593: $i,SV396: $o,SV117: $i,SV801: $i] :
( ( ( ~ ( in @ SV801 @ SV117 ) )
= $true )
| ( ( ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) ) )
= $true )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2385]) ).
thf(2621,plain,
! [SV594: $i,SV117: $i,SV802: $i] :
( ( ( ~ ( in @ SV802 @ SV117 ) )
= $true )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) ) )
= $true )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2622,plain,
! [SV595: $i,SV117: $i,SV803: $i] :
( ( ( ~ ( in @ SV803 @ SV117 ) )
= $true )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) ) )
= $true )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2387]) ).
thf(2623,plain,
! [SV397: $i,SV118: $i,SV726: $i] :
( ( ( in @ SV726 @ ( powerset @ SV118 ) )
= $false )
| ( ( ! [SY3622: $i] :
( ~ ( in @ SY3622 @ ( binintersect @ SV397 @ SV726 ) )
| ( in @ SY3622 @ SV118 ) ) )
= $true )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2624,plain,
! [SV121: $i,SV400: $i > $o] :
( ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2389]) ).
thf(2625,plain,
! [SV121: $i,SV400: $i > $o] :
( ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true )
| ( ( ~ ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2390]) ).
thf(2626,plain,
! [SV401: $i,SV122: $i,SV727: $i] :
( ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( ! [SY3623: $i] :
( ~ ( in @ SY3623 @ SV122 )
| ~ ( in @ SY3623 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SY3623 @ ( setminus @ SV122 @ SV401 ) ) ) )
= $true )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2627,plain,
! [SV598: $i > $i > $o,SV402: $i,SV123: $i,SV728: $i,SV689: $i] :
( ( ( in @ ( kpair @ SV689 @ SV728 )
@ ( dpsetconstr @ SV123 @ SV402
@ ^ [SY3472: $i,SY3473: $i] : ( SV598 @ SY3472 @ SY3473 ) ) )
= $false )
| ( ( in @ SV689 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2628,plain,
! [SV600: $i,SV404: $i,SV125: $i,SV804: $i] :
( ( ( ~ ( in @ SV804 @ SV125 ) )
= $true )
| ( ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SV804 ) @ SV404 )
= $true )
| ( ( func @ SV125 @ SV404 @ SV600 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2393]) ).
thf(2629,plain,
! [SV805: $i > $o,SV601: $i,SV405: $i,SV126: $i] :
( ( ( ~ ! [SY3700: $i] :
( ~ ( in @ SY3700 @ SV126 )
| ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV405 )
| ~ ( in @ ( kpair @ SY3700 @ SY3701 ) @ SV601 )
| ( SV805 @ ( kpair @ SY3700 @ SY3701 ) ) ) ) )
= $true )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2630,plain,
! [SV406: $i,SV127: $i,SV729: $i] :
( ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( ! [SY3626: $i] :
( ~ ( in @ SY3626 @ SV127 )
| ~ ( in @ SY3626 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SY3626 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) ) )
= $true )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2631,plain,
! [SV128: $i,SV407: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV407 ) )
= $true )
| ( ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) )
= $true )
| ( ( in @ SV602 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2396]) ).
thf(2632,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV730 )
| ~ ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2633,plain,
! [SV409: $i,SV132: $i,SV731: $i] :
( ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( ! [SY3628: $i] :
( ~ ( in @ SY3628 @ SV132 )
| ~ ( in @ SY3628 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SY3628 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) ) )
= $true )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2399]) ).
thf(2634,plain,
! [SV411: $i,SV134: $i,SV732: $i] :
( ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( ! [SY3629: $i] :
( ~ ( in @ SY3629 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SY3629 @ SV411 )
| ( in @ SY3629 @ SV732 ) ) )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2635,plain,
! [SV605: $i,SV806: $i,SV413: $i,SV137: $i] :
( ( ( ~ ( func @ SV137 @ SV413 @ SV806 ) )
= $true )
| ( ( ~ ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3703 )
= ( ap @ SV137 @ SV413 @ SV806 @ SY3703 ) ) )
| ( SV605 = SV806 ) )
= $true )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2636,plain,
! [SV606: $i,SV414: $o,SV138: $i,SV807: $i] :
( ( ( ~ ( in @ SV807 @ SV138 ) )
= $true )
| ( ( ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3704: $i] :
( ~ ( ~ SV414
| ( SY3704 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3704 != SV807 ) ) ) ) ) )
= $true )
| ( ( in @ SV606 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2637,plain,
! [SV607: $i,SV138: $i,SV808: $i] :
( ( ( ~ ( in @ SV808 @ SV138 ) )
= $true )
| ( ( ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3705: $i] :
( ~ ( ~ $true
| ( SY3705 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3705 != SV808 ) ) ) ) ) )
= $true )
| ( ( in @ SV607 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2403]) ).
thf(2638,plain,
! [SV608: $i,SV138: $i,SV809: $i] :
( ( ( ~ ( in @ SV809 @ SV138 ) )
= $true )
| ( ( ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3706: $i] :
( ~ ( ~ $false
| ( SY3706 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3706 != SV809 ) ) ) ) ) )
= $true )
| ( ( in @ SV608 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2404]) ).
thf(2639,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV733 )
| ~ ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2640,plain,
! [SV140: $i,SV609: $i,SV415: $i > $o] :
( ( ( SV415 @ SV609 )
= $false )
| ( ( in @ SV609
@ ( dsetconstr @ SV140
@ ^ [SY3142: $i] : ( SV415 @ SY3142 ) ) )
= $true )
| ( ( in @ SV609 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2406]) ).
thf(2641,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ( sK13_SY3143 @ SV416 @ SV141 )
!= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2642,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
| ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2407]) ).
thf(2643,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SV142 )
| ~ ~ ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2408]) ).
thf(2644,plain,
! [SV418: $i,SV143: $i,SV734: $i] :
( ( ( in @ SV734 @ ( powerset @ SV143 ) )
= $false )
| ( ( subset @ ( setminus @ SV143 @ SV418 ) @ ( setminus @ SV143 @ ( binintersect @ SV418 @ SV734 ) ) )
= $true )
| ( ( in @ SV418 @ ( powerset @ SV143 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2645,plain,
! [SV735: $i > $o,SV419: $i,SV144: $i] :
( ( ( ! [SY3632: $i] :
( ~ ( in @ SY3632 @ SV144 )
| ! [SY3633: $i] :
( ~ ( in @ SY3633 @ SV144 )
| ~ ( in @ ( kpair @ SY3632 @ SY3633 ) @ SV419 )
| ( SV735 @ ( kpair @ SY3632 @ SY3633 ) ) ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2646,plain,
! [SV420: $i,SV145: $i,SV736: $i] :
( ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( ! [SY3635: $i] :
( ~ ( in @ SY3635 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SY3635 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SY3635 ) ) )
= $true )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2411]) ).
thf(2647,plain,
! [SV611: $i,SV422: $o,SV147: $i,SV810: $i] :
( ( ( ~ ( in @ SV810 @ SV147 ) )
= $true )
| ( ( ~ ~ SV422
| ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) ) )
= $true )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2648,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( ( ~ ( in @ SV811 @ SV147 ) )
= $true )
| ( ( ~ ~ $true
| ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) ) )
= $true )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2413]) ).
thf(2649,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( ( ~ ( in @ SV812 @ SV147 ) )
= $true )
| ( ( ~ ~ $false
| ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2414]) ).
thf(2650,plain,
! [SV614: $i,SV423: $o,SV149: $i,SV813: $i] :
( ( ( ~ ( in @ SV813 @ SV149 ) )
= $true )
| ( ( ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 ) )
= $true )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2651,plain,
! [SV615: $i,SV149: $i,SV814: $i] :
( ( ( ~ ( in @ SV814 @ SV149 ) )
= $true )
| ( ( ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 ) )
= $true )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2652,plain,
! [SV616: $i,SV149: $i,SV815: $i] :
( ( ( ~ ( in @ SV815 @ SV149 ) )
= $true )
| ( ( ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 ) )
= $true )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2653,plain,
! [SV150: $i,SV424: $i,SV617: $i] :
( ( ( subset @ SV617 @ SV424 )
= $false )
| ( ( subset @ SV617 @ ( binintersect @ SV150 @ SV424 ) )
= $true )
| ( ( subset @ SV617 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2654,plain,
! [SV425: $i,SV151: $i,SV737: $i] :
( ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( ~ ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
| ! [SY3636: $i] :
( ~ ( in @ SY3636 @ SV151 )
| ~ ( in @ SY3636 @ SV737 )
| ( in @ SY3636 @ ( setminus @ SV151 @ SV425 ) ) ) )
= $true )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2419]) ).
thf(2655,plain,
! [SV426: $i,SV152: $i,SV738: $i] :
( ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( ! [SY3637: $i] :
( ~ ( in @ SY3637 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SY3637 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SY3637 ) ) ) )
= $true )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2420]) ).
thf(2656,plain,
! [SV427: $i,SV154: $i,SV739: $i] :
( ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( ! [SY3638: $i] :
( ~ ( in @ SY3638 @ ( powerset @ SV154 ) )
| ! [SY3639: $i] :
( ~ ( in @ SY3639 @ SV154 )
| ~ ( in @ SY3639 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3639 @ ( binunion @ SV427 @ SY3638 ) ) ) ) )
= $true )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2421]) ).
thf(2657,plain,
! [SV428: $i > $o,SV155: $i,SV816: $i] :
( ( ( ~ ( ~ ( in @ SV816 @ SV155 )
| ~ ( SV428 @ SV816 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2422]) ).
thf(2658,plain,
! [SV429: $i,SV156: $i,SV740: $i] :
( ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( ! [SY3640: $i] :
( ~ ( in @ SY3640 @ SV156 )
| ~ ( in @ SY3640 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SY3640 @ ( binintersect @ SV429 @ SV740 ) ) ) )
= $true )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2423]) ).
thf(2659,plain,
! [SV158: $i,SV618: $i,SV431: $i] :
( ( ( subset @ SV431 @ SV618 )
= $false )
| ( ( subset @ SV158 @ SV618 )
= $true )
| ( ( subset @ SV158 @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2660,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2425]) ).
thf(2661,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
| ~ ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
| ~ ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
| ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2426]) ).
thf(2662,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( ~ ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) ) )
= $false )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2663,plain,
! [SV160: $i,SV619: $i,SV433: $i > $o] :
( ( ( ~ ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) ) )
= $false )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2427]) ).
thf(2664,plain,
! [SV161: $i,SV620: $i,SV434: $i > $o] :
( ( ( SV434 @ SV620 )
= $false )
| ( ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
!= emptyset )
= $true )
| ( ( in @ SV620 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2428]) ).
thf(2665,plain,
! [SV165: $i,SV623: $i,SV437: $i,SV817: $i] :
( ( ( ~ ( in @ SV817 @ SV437 ) )
= $true )
| ( ( in @ ( kpair @ SV623 @ SV817 ) @ ( cartprod @ SV165 @ SV437 ) )
= $true )
| ( ( in @ SV623 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2430]) ).
thf(2666,plain,
! [SV438: $i,SV166: $i,SV741: $i] :
( ( ( in @ SV741 @ ( powerset @ SV166 ) )
= $false )
| ( ( in @ ( setminus @ SV166 @ SV438 ) @ ( powerset @ ( setminus @ SV166 @ ( binintersect @ SV438 @ SV741 ) ) ) )
= $true )
| ( ( in @ SV438 @ ( powerset @ SV166 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2431]) ).
thf(2667,plain,
! [SV167: $i,SV624: $i,SV439: $i,SV818: $i] :
( ( ( ~ ( in @ SV818 @ SV439 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV624 @ SV818 ) )
= SV624 )
= $true )
| ( ( in @ SV624 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2432]) ).
thf(2668,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK24_SY3199 @ SV440 @ SV168 ) @ SV168 )
| ~ ( SV440 @ ( sK24_SY3199 @ SV440 @ SV168 ) ) ) )
= $true )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2433]) ).
thf(2669,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( ~ ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) ) )
= $true )
| ( ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2670,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( ~ ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) ) )
= $true )
| ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2435]) ).
thf(2671,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2672,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ! [SY3642: $i] :
~ ~ ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3642 )
| ~ ! [SY3643: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3643 )
| ( SY3642 = SY3643 ) ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2437]) ).
thf(2673,plain,
! [SV443: $i,SV171: $i,SV626: $i] :
( ( ( in @ SV626 @ SV171 )
= $false )
| ( ( in @ SV443 @ ( setunion @ SV171 ) )
= $true )
| ( ( in @ SV443 @ SV626 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2674,plain,
! [SV819: $i > $o,SV627: $i,SV445: $i,SV173: $i] :
( ( ( ~ ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV173 )
| ! [SY3711: $i] :
( ~ ( in @ SY3711 @ SV445 )
| ~ ( in @ ( kpair @ SY3710 @ SY3711 ) @ SV627 )
| ( SV819 @ ( kpair @ SY3710 @ SY3711 ) ) ) ) )
= $true )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2439]) ).
thf(2675,plain,
! [SV177: $i,SV449: $i] :
( ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true )
| ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) )
| ( SV177 = SV449 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2676,plain,
! [SV177: $i,SV449: $i] :
( ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) ) )
= $true )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2677,plain,
! [SV179: $i,SV451: $i,SV692: $i,SV630: $i] :
( ( ( SV630 != SV692 )
= $true )
| ( ( SV451 = SV692 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SV692 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2678,plain,
! [SV631: $i,SV452: $i,SV180: $i,SV820: $i] :
( ( ( ~ ( in @ SV820 @ SV180 ) )
= $true )
| ( ( ! [SY3713: $i] :
( ~ ( in @ SY3713 @ SV452 )
| ~ ( in @ ( kpair @ SV820 @ SY3713 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SY3713 ) ) )
= $true )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2679,plain,
! [SV454: $i,SV183: $i,SV742: $i] :
( ( ( in @ SV742 @ ( powerset @ SV183 ) )
= $false )
| ( ( in @ ( setminus @ SV183 @ ( binunion @ SV454 @ SV742 ) ) @ ( powerset @ ( setminus @ SV183 @ SV454 ) ) )
= $true )
| ( ( in @ SV454 @ ( powerset @ SV183 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2680,plain,
! [SV455: $i,SV743: $i,SV185: $i] :
( ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SV185 )
| ! [SY3645: $i] :
( ~ ( in @ SY3645 @ SV185 )
| ~ ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV455 )
| ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV743 ) ) )
| ( subset @ SV455 @ SV743 ) )
= $true )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2681,plain,
! [SV186: $i,SV456: $i,SV633: $i] :
( ( ( in @ SV633 @ SV456 )
= $false )
| ( ( in @ SV633 @ ( binintersect @ SV186 @ SV456 ) )
= $true )
| ( ( in @ SV633 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2682,plain,
! [SV457: $i,SV187: $i,SV744: $i] :
( ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( ! [SY3646: $i] :
( ~ ( in @ SY3646 @ ( powerset @ SV187 ) )
| ! [SY3647: $i] :
( ~ ( in @ SY3647 @ SV187 )
| ~ ( in @ SY3647 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3647 @ ( binintersect @ ( binunion @ SV457 @ SY3646 ) @ ( binunion @ SV744 @ SY3646 ) ) ) ) ) )
= $true )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2683,plain,
! [SV458: $i,SV188: $i,SV745: $i] :
( ( ( in @ SV745 @ SV188 )
= $false )
| ( ( ! [SY3648: $i] :
( ~ ( in @ SY3648 @ SV188 )
| ~ ( in @ ( kpair @ SY3648 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SY3648 ) @ SV458 ) ) )
= $true )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2684,plain,
! [SV746: $o,SV189: $i,SV459: $i] :
( ( ( ! [SY3649: $i] :
( ~ ( in @ SV459 @ SY3649 )
| ~ ( in @ SY3649 @ SV189 )
| SV746 ) )
= $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2450]) ).
thf(2685,plain,
! [SV189: $i,SV459: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2451]) ).
thf(2686,plain,
! [SV189: $i,SV459: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV459 @ SX0 )
| ~ ( in @ SX0 @ SV189 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2687,plain,
! [SV462: $i,SV192: $i,SV747: $i] :
( ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( ! [SY3650: $i] :
( ~ ( in @ SY3650 @ SV192 )
| ~ ~ ( in @ SY3650 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SY3650 @ SV462 ) ) )
= $true )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2453]) ).
thf(2688,plain,
! [SV463: $i,SV193: $i,SV748: $i] :
( ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( ! [SY3651: $i] :
( ~ ( in @ SY3651 @ SV193 )
| ~ ( in @ SY3651 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SY3651 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) ) )
= $true )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2454]) ).
thf(2689,plain,
! [SV464: $i,SV194: $i,SV749: $i] :
( ( ( in @ SV749 @ ( powerset @ SV194 ) )
= $false )
| ( ( ! [SY3652: $i] :
( ~ ( in @ SY3652 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SY3652 ) @ ( binunion @ SV749 @ SY3652 ) ) ) ) ) )
= $true )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2455]) ).
thf(2690,plain,
! [SV465: $i,SV821: $o,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| SV821 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2456]) ).
thf(2691,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2457]) ).
thf(2692,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ~ ( ( SV635 != SV195 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2693,plain,
! [SV197: $i,SV467: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV467 ) ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2459]) ).
thf(2694,plain,
! [SV469: $i,SV199: $i,SV750: $i] :
( ( ( in @ SV750 @ ( powerset @ SV199 ) )
= $false )
| ( ( in @ ( setminus @ SV469 @ SV750 ) @ ( powerset @ SV199 ) )
= $true )
| ( ( in @ SV469 @ ( powerset @ SV199 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2695,plain,
! [SV200: $i,SV637: $i > $i,SV470: $i] :
( ( ( ~ ( in @ ( sK25_SY3515 @ SV470 @ SV637 @ SV200 ) @ SV200 ) )
= $false )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2696,plain,
! [SV200: $i,SV470: $i,SV637: $i > $i] :
( ( ( in @ ( SV637 @ ( sK25_SY3515 @ SV470 @ SV637 @ SV200 ) ) @ SV470 )
= $false )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2461]) ).
thf(2697,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ( ~ ( in @ ( sK26_SY3253 @ SV471 @ SV201 ) @ SV201 )
| ~ ( in @ SV471 @ ( sK26_SY3253 @ SV471 @ SV201 ) ) ) )
= $true )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2462]) ).
thf(2698,plain,
! [SV473: $i,SV203: $i,SV751: $i] :
( ( ( in @ SV751 @ ( powerset @ SV203 ) )
= $false )
| ( ( in @ ( binintersect @ SV473 @ SV751 ) @ ( powerset @ SV203 ) )
= $true )
| ( ( in @ SV473 @ ( powerset @ SV203 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2699,plain,
! [SV474: $i,SV204: $i,SV752: $i] :
( ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( ! [SY3653: $i] :
( ~ ( in @ SY3653 @ ( powerset @ SV204 ) )
| ! [SY3654: $i] :
( ~ ( in @ SY3654 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SY3653 @ SY3654 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SY3653 ) @ ( setminus @ SV204 @ SY3654 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2464]) ).
thf(2700,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV753 )
| ~ ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2701,plain,
! [SV211: $i,SV639: $i,SV479: $i,SV822: $i] :
( ( ( ~ ( in @ SV822 @ SV479 ) )
= $true )
| ( ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SV822 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) )
= $true )
| ( ( in @ SV639 @ SV211 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2468]) ).
thf(2702,plain,
! [SV480: $i,SV754: $i,SV212: $i] :
( ( ( breln1 @ SV212 @ SV754 )
= $false )
| ( ( breln1 @ SV212 @ ( binunion @ SV480 @ SV754 ) )
= $true )
| ( ( breln1 @ SV212 @ SV480 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2469]) ).
thf(2703,plain,
! [SV641: $i,SV482: $o,SV214: $i,SV823: $i] :
( ( ( ~ ( in @ SV823 @ SV214 ) )
= $true )
| ( ( ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SV823 )
= SV641 ) )
= $true )
| ( ( in @ SV641 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2704,plain,
! [SV642: $i,SV214: $i,SV824: $i] :
( ( ( ~ ( in @ SV824 @ SV214 ) )
= $true )
| ( ( ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SV824 )
= SV642 ) )
= $true )
| ( ( in @ SV642 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2471]) ).
thf(2705,plain,
! [SV643: $i,SV214: $i,SV825: $i] :
( ( ( ~ ( in @ SV825 @ SV214 ) )
= $true )
| ( ( ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SV825 )
= SV643 ) )
= $true )
| ( ( in @ SV643 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2706,plain,
! [SV483: $i,SV755: $i,SV215: $i] :
( ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( ! [SY3656: $i] :
( ~ ( in @ SY3656 @ SV215 )
| ! [SY3657: $i] :
( ~ ( in @ SY3657 @ SV215 )
| ~ ( in @ ( kpair @ SY3656 @ SY3657 ) @ SV483 )
| ( in @ ( kpair @ SY3656 @ SY3657 ) @ ( binunion @ SV483 @ SV755 ) ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2707,plain,
! [SV484: $i,SV216: $i,SV756: $i] :
( ( ( in @ SV756 @ ( powerset @ SV216 ) )
= $false )
| ( ( ~ ( subset @ SV484 @ ( setminus @ SV216 @ SV756 ) )
| ( subset @ SV756 @ ( setminus @ SV216 @ SV484 ) ) )
= $true )
| ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2708,plain,
! [SV644: $i > $i > $o,SV485: $i,SV217: $i,SV757: $i,SV693: $i] :
( ( ( in @ ( kpair @ SV693 @ SV757 )
@ ( dpsetconstr @ SV217 @ SV485
@ ^ [SY3523: $i,SY3524: $i] : ( SV644 @ SY3523 @ SY3524 ) ) )
= $false )
| ( ( in @ SV757 @ SV485 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2709,plain,
! [SV486: $i,SV218: $i,SV758: $i] :
( ( ( in @ SV758 @ ( powerset @ SV218 ) )
= $false )
| ( ( ( setminus @ SV218 @ ( binunion @ SV486 @ SV758 ) )
= ( binintersect @ ( setminus @ SV218 @ SV486 ) @ ( setminus @ SV218 @ SV758 ) ) )
= $true )
| ( ( in @ SV486 @ ( powerset @ SV218 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2710,plain,
! [SV219: $i,SV487: $i,SV645: $i] :
( ( ( ~ ~ ( in @ SV645 @ SV487 ) )
= $true )
| ( ( ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true )
| ( ( in @ SV645 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2711,plain,
! [SV488: $i,SV220: $i,SV759: $i] :
( ( ( in @ SV759 @ SV220 )
= $false )
| ( ( ~ ( in @ SV759 @ SV488 )
| ~ ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) ) )
= $true )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2712,plain,
! [SV489: $i > $o,SV221: $i,SV826: $i] :
( ( ( ~ ( in @ SV826 @ SV221 ) )
= $true )
| ( ( SV489 @ SV826 )
= $true )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2479]) ).
thf(2713,plain,
! [SV491: $i,SV223: $i,SV760: $i] :
( ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( ! [SY3660: $i] :
( ~ ( in @ SY3660 @ SV223 )
| ~ ( in @ SY3660 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SY3660 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) ) )
= $true )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2480]) ).
thf(2714,plain,
! [SV225: $i,SV493: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV493 ) )
= $false )
| ( ( ~ ( subset @ SV225 @ SV493 ) )
= $true )
| ( ( in @ SV647 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2715,plain,
! [SV648: $i,SV827: $i,SV494: $i,SV226: $i] :
( ( ( ~ ( breln @ SV226 @ SV494 @ SV827 ) )
= $true )
| ( ( ~ ! [SY3714: $i] :
( ~ ( in @ SY3714 @ SV226 )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV494 )
| ~ ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV648 )
| ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV827 ) ) )
| ( subset @ SV648 @ SV827 ) )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2483]) ).
thf(2716,plain,
! [SV495: $i,SV227: $i,SV761: $i] :
( ( ( in @ SV761 @ ( powerset @ SV227 ) )
= $false )
| ( ( in @ ( binunion @ SV495 @ SV761 ) @ ( powerset @ SV227 ) )
= $true )
| ( ( in @ SV495 @ ( powerset @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2717,plain,
! [SV228: $i,SV496: $i,SV649: $i] :
( ( ( in @ SV649 @ SV496 )
= $false )
| ( ( in @ SV649 @ SV228 )
= $true )
| ( ( in @ SV496 @ ( powerset @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2718,plain,
! [SV231: $i,SV650: $i,SV499: $i,SV828: $i] :
( ( ( ~ ( in @ SV828 @ SV499 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SV828 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) )
= $true )
| ( ( in @ SV650 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2486]) ).
thf(2719,plain,
! [SV500: $i,SV232: $i,SV762: $i] :
( ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( ~ ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV232 )
| ~ ( in @ SY3661 @ SV500 )
| ( in @ SY3661 @ SV762 ) )
| ( subset @ SV500 @ SV762 ) )
= $true )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2487]) ).
thf(2720,plain,
! [SV501: $i,SV233: $i,SV763: $i] :
( ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV233 )
| ~ ( in @ SY3662 @ SV501 )
| ( in @ SY3662 @ SV763 ) )
| ( in @ SV501 @ ( powerset @ SV763 ) ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2721,plain,
! [SV503: $i,SV235: $i,SV764: $i] :
( ( ( in @ SV764 @ SV235 )
= $false )
| ( ( ~ ( in @ SV764 @ SV503 )
| ( in @ SV764 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) ) )
= $true )
| ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2722,plain,
! [SV652: $i,SV505: $o,SV237: $i,SV829: $i] :
( ( ( ~ ( in @ SV829 @ SV237 ) )
= $true )
| ( ( in @ ( if @ SV237 @ SV505 @ SV652 @ SV829 ) @ SV237 )
= $true )
| ( ( in @ SV652 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2492]) ).
thf(2723,plain,
! [SV653: $i,SV237: $i,SV830: $i] :
( ( ( ~ ( in @ SV830 @ SV237 ) )
= $true )
| ( ( in @ ( if @ SV237 @ $true @ SV653 @ SV830 ) @ SV237 )
= $true )
| ( ( in @ SV653 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2493]) ).
thf(2724,plain,
! [SV654: $i,SV237: $i,SV831: $i] :
( ( ( ~ ( in @ SV831 @ SV237 ) )
= $true )
| ( ( in @ ( if @ SV237 @ $false @ SV654 @ SV831 ) @ SV237 )
= $true )
| ( ( in @ SV654 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2494]) ).
thf(2725,plain,
! [SV506: $i,SV238: $i,SV765: $i] :
( ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( ! [SY3663: $i] :
( ~ ( in @ SY3663 @ ( powerset @ SV238 ) )
| ! [SY3664: $i] :
( ~ ( in @ SY3664 @ SV238 )
| ~ ( in @ SY3664 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3664 @ ( binunion @ SV765 @ SY3663 ) ) ) ) )
= $true )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2726,plain,
! [SV508: $i,SV766: $i,SV240: $i] :
( ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( ! [SY3665: $i] :
( ~ ( in @ SY3665 @ SV240 )
| ! [SY3666: $i] :
( ~ ( in @ SY3666 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3666 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3667: $o] :
( ~ ! [SY3668: $i] :
( ~ ( in @ SY3668 @ SV240 )
| ~ ( in @ ( kpair @ SY3665 @ SY3668 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3668 @ SY3666 ) @ SV766 )
| SY3667 )
| SY3667 ) ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2727,plain,
! [SV767: $i > $o,SV509: $i,SV241: $i] :
( ( ( ! [SY3669: $i] :
( ~ ( in @ SY3669 @ SV241 )
| ! [SY3670: $i] :
( ~ ( in @ SY3670 @ SV241 )
| ~ ( in @ ( kpair @ SY3669 @ SY3670 ) @ SV509 )
| ( SV767 @ ( kpair @ SY3669 @ SY3670 ) ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2497]) ).
thf(2728,plain,
! [SV510: $i,SV242: $i,SV768: $i] :
( ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( ! [SY3672: $i] :
( ~ ( in @ SY3672 @ SV242 )
| ~ ( in @ SY3672 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SY3672 @ SV510 ) ) )
= $true )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2498]) ).
thf(2729,plain,
! [SV511: $i,SV243: $i,SV769: $i] :
( ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( ! [SY3673: $i] :
( ~ ( in @ SY3673 @ SV243 )
| ~ ( in @ SY3673 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SY3673 @ ( setminus @ SV243 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2499]) ).
thf(2730,plain,
! [SV657: $i > $i > $o,SV249: $i,SV694: $i,SV517: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ SV517 )
| ~ ( in @ ( kpair @ SV694 @ SV847 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SV847 ) )
= $true )
| ( ( in @ SV694 @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2500]) ).
thf(2731,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
| ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 ) )
| ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) ) )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2501]) ).
thf(2732,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ( breln @ SV251 @ SV518 @ SV832 ) )
= $true )
| ( ( ~ ! [SY3716: $i] :
( ~ ( in @ SY3716 @ SV251 )
| ! [SY3717: $i] :
( ~ ( in @ SY3717 @ SV518 )
| ~ ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV658 )
| ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV832 ) ) )
| ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2502]) ).
thf(2733,plain,
! [SV519: $i,SV252: $i,SV771: $i] :
( ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( ! [SY3675: $i] :
( ~ ( in @ SY3675 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SY3675 @ SV771 )
| ~ ( in @ SY3675 @ SV519 ) ) )
= $true )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2734,plain,
! [SV772: $i,SV254: $i] :
( ( ( SV254 = emptyset )
= $false )
| ( ( in @ SV772 @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2735,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
| ~ ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) ) ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2505]) ).
thf(2736,plain,
! [SV524: $i,SV773: $i,SV258: $i] :
( ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( ! [SY3676: $i] :
( ~ ( in @ SY3676 @ SV258 )
| ! [SY3677: $i] :
( ~ ( in @ SY3677 @ SV258 )
| ! [SY3678: $i] :
( ~ ( in @ SY3678 @ SV258 )
| ~ ( in @ ( kpair @ SY3676 @ SY3678 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3678 @ SY3677 ) @ SV773 )
| ( in @ ( kpair @ SY3676 @ SY3677 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2737,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( ~ ! [SY3679: $i] :
( ~ ( in @ SY3679 @ SV259 )
| ! [SY3680: $i] :
( ~ ( in @ SY3680 @ SV259 )
| ~ ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV525 )
| ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV774 ) ) )
| ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2738,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2508]) ).
thf(2739,plain,
! [SV661: $i,SV528: $i,SV262: $i,SV833: $i] :
( ( ( ~ ( in @ SV833 @ SV262 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3720: $i] : ( in @ ( kpair @ SV833 @ SY3720 ) @ SV661 ) ) )
= $true )
| ( ( func @ SV262 @ SV528 @ SV661 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2740,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV775 )
| ~ ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2741,plain,
! [SV529: $i,SV264: $i,SV776: $i] :
( ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( ! [SY3684: $i] :
( ~ ( in @ SY3684 @ SV264 )
| ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SY3684 @ SV776 )
| ~ ( in @ SY3684 @ SV529 ) ) )
= $true )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2742,plain,
! [SV777: $i,SV265: $i] :
( ( ( ! [SY2861: $i] :
~ ~ ( ~ ( in @ SY2861 @ SV265 )
| ~ ~ ~ ! [SY2862: $i] :
~ ~ ( ~ ( in @ SY2862 @ SY2861 )
| ~ ( in @ SY2862 @ SV265 ) ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2743,plain,
! [SV530: $i,SV266: $i,SV662: $i] :
( ( ( in @ SV662 @ ( setminus @ SV266 @ SV530 ) )
= $false )
| ( ( in @ SV662 @ SV266 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2744,plain,
! [SV268: $i] :
( ( ( in @ ( sK27_SY2868 @ SV268 ) @ SV268 )
= $true )
| ( ( SV268 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2515]) ).
thf(2745,plain,
! [SV534: $i,SV272: $i,SV778: $i] :
( ( ( in @ SV778 @ ( powerset @ SV272 ) )
= $false )
| ( ( ~ ( subset @ SV534 @ SV778 )
| ( subset @ ( setminus @ SV272 @ SV778 ) @ ( setminus @ SV272 @ SV534 ) ) )
= $true )
| ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2516]) ).
thf(2746,plain,
! [SV273: $i,SV664: $i,SV535: $i,SV834: $i] :
( ( ( ~ ( in @ SV834 @ SV535 ) )
= $true )
| ( ( in @ ( kpair @ SV664 @ SV834 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) )
= $true )
| ( ( in @ SV664 @ SV273 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2747,plain,
! [SV665: $i,SV536: $i,SV274: $i,SV835: $i] :
( ( ( ~ ( in @ SV835 @ SV274 ) )
= $true )
| ( ( ( ap @ SV274 @ SV536 @ SV665 @ SV835 )
= ( ap @ SV274 @ SV536 @ SV665 @ SV835 ) )
= $true )
| ( ( func @ SV274 @ SV536 @ SV665 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2518]) ).
thf(2748,plain,
! [SV537: $i,SV275: $i,SV779: $i] :
( ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( ! [SY3685: $i] :
( ~ ( in @ SY3685 @ SV275 )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SY3685 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SY3685 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) ) )
= $true )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2749,plain,
! [SV666: $i,SV538: $i,SV276: $i,SV836: $i] :
( ( ( ~ ( in @ SV836 @ SV276 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3721: $i] : ( in @ ( kpair @ SV836 @ SY3721 ) @ SV666 ) ) )
@ SV538 )
= $true )
| ( ( func @ SV276 @ SV538 @ SV666 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2520]) ).
thf(2750,plain,
! [SV667: $i,SV539: $i,SV277: $i,SV837: $i] :
( ( ( ~ ( in @ SV837 @ SV277 ) )
= $true )
| ( ( in @ ( kpair @ SV837 @ ( ap @ SV277 @ SV539 @ SV667 @ SV837 ) ) @ SV667 )
= $true )
| ( ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2521]) ).
thf(2751,plain,
! [SV540: $i > $o,SV278: $i,SV838: $i] :
( ( ( ~ ( ~ ( in @ SV838 @ SV278 )
| ~ ~ ( SV540 @ SV838 ) ) )
= $false )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2752,plain,
! [SV541: $i,SV279: $i,SV780: $i] :
( ( ( in @ SV780 @ SV279 )
= $false )
| ( ( ! [SY3686: $i] :
( ~ ( in @ SY3686 @ SV279 )
| ~ ( in @ ( kpair @ SV780 @ SY3686 ) @ SV541 )
| ( in @ ( kpair @ SY3686 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) ) )
= $true )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2753,plain,
! [SV280: $i,SV668: $i > $i,SV542: $i] :
( ( ( ~ ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 ) )
= $false )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2754,plain,
! [SV280: $i,SV542: $i,SV668: $i > $i] :
( ( ( in @ ( SV668 @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) ) @ SV542 )
= $false )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2524]) ).
thf(2755,plain,
! [SV282: $i,SV670: $i > $i,SV544: $i] :
( ( ( ~ ( in @ ( sK29_SY3556 @ SV544 @ SV670 @ SV282 ) @ SV282 ) )
= $false )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2756,plain,
! [SV282: $i,SV544: $i,SV670: $i > $i] :
( ( ( in @ ( SV670 @ ( sK29_SY3556 @ SV544 @ SV670 @ SV282 ) ) @ SV544 )
= $false )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2526]) ).
thf(2757,plain,
! [SV545: $i,SV283: $i,SV781: $i] :
( ( ( in @ SV781 @ ( powerset @ SV283 ) )
= $false )
| ( ( in @ ( setminus @ SV283 @ SV545 ) @ ( powerset @ ( setminus @ SV283 @ ( binintersect @ SV545 @ SV781 ) ) ) )
= $true )
| ( ( in @ SV545 @ ( powerset @ SV283 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2527]) ).
thf(2758,plain,
! [SV284: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_SY2910 @ SV284 ) @ SV284 )
| ~ $true ) )
= $true )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2759,plain,
! [SV285: $i,SV546: $i,SV671: $i] :
( ( ( ~ ( in @ SV671 @ SV546 ) )
= $false )
| ( ( SV285 != SV546 )
= $true )
| ( ( in @ SV671 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2760,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ( ~ ( in @ SV672 @ SV286 ) )
= $true )
| ( ( in @ SV672 @ SV547 )
= $true )
| ( ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2761,plain,
! [SV673: $i,SV548: $i,SV287: $i,SV839: $i] :
( ( ( ~ ( in @ SV839 @ SV287 ) )
= $true )
| ( ( ! [SY3722: $i] :
( ~ ( in @ SY3722 @ SV548 )
| ~ ( in @ ( kpair @ SV839 @ SY3722 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SY3722 ) ) )
= $true )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2762,plain,
! [SV674: $i,SV549: $o,SV288: $i,SV840: $i] :
( ( ( ~ ( in @ SV840 @ SV288 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3723: $i] :
( ~ ( ~ SV549
| ( SY3723 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3723 != SV840 ) ) ) ) )
= $true )
| ( ( in @ SV674 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2532]) ).
thf(2763,plain,
! [SV675: $i,SV288: $i,SV841: $i] :
( ( ( ~ ( in @ SV841 @ SV288 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3724: $i] :
( ~ ( ~ $true
| ( SY3724 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3724 != SV841 ) ) ) ) )
= $true )
| ( ( in @ SV675 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2764,plain,
! [SV676: $i,SV288: $i,SV842: $i] :
( ( ( ~ ( in @ SV842 @ SV288 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3725: $i] :
( ~ ( ~ $false
| ( SY3725 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3725 != SV842 ) ) ) ) )
= $true )
| ( ( in @ SV676 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2534]) ).
thf(2765,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ SV782 )
| ~ ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2536]) ).
thf(2766,plain,
! [SV294: $i,SV554: $i,SV679: $i] :
( ( ( ~ ( in @ SV679 @ SV554 ) )
= $false )
| ( ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) )
= $true )
| ( ( in @ SV679 @ SV294 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2767,plain,
! [SV680: $i,SV555: $o,SV296: $i,SV843: $i] :
( ( ( ~ ( in @ SV843 @ SV296 ) )
= $true )
| ( ( ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3726: $i] :
( ~ ( ~ SV555
| ( SY3726 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3726 != SV843 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) )
= $true )
| ( ( in @ SV680 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2768,plain,
! [SV681: $i,SV296: $i,SV844: $i] :
( ( ( ~ ( in @ SV844 @ SV296 ) )
= $true )
| ( ( ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3727: $i] :
( ~ ( ~ $true
| ( SY3727 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3727 != SV844 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) )
= $true )
| ( ( in @ SV681 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2769,plain,
! [SV682: $i,SV296: $i,SV845: $i] :
( ( ( ~ ( in @ SV845 @ SV296 ) )
= $true )
| ( ( ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3728: $i] :
( ~ ( ~ $false
| ( SY3728 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3728 != SV845 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) )
= $true )
| ( ( in @ SV682 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2770,plain,
! [SV699: $i,SV322: $i,SV37: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ ( powerset @ SV37 ) )
| ! [SY3735: $i] :
( ~ ( in @ SY3735 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SY3735 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SY3735 ) ) ) )
= $true )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2542]) ).
thf(2771,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ( SV38 @ SV700 ) )
= $true )
| ( ( ~ ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2772,plain,
! [SV41: $i,SV325: $i,SV560: $i] :
( ( ( in @ SV560 @ SV325 )
= $true )
| ( ( ~ ( in @ SV560 @ SV41 ) )
= $true )
| ( ( subset @ SV41 @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2545]) ).
thf(2773,plain,
! [SV42: $i,SV561: $i,SV326: $i,SV783: $i] :
( ( ( in @ SV783 @ SV326 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV561 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV561 @ ( setadjoin @ SV783 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV42 @ SV326 ) ) )
= $true )
| ( ( in @ SV561 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2774,plain,
! [SV784: $i > $o,SV702: $i > $o,SV328: $i,SV44: $i] :
( ( ( ! [SY3688: $i] :
( ~ ( in @ SY3688 @ SV44 )
| ! [SY3689: $i] :
( ~ ( in @ SY3689 @ SV328 )
| ( SY3688 != SY3689 )
| ~ ( ~ ( ~ ( SV702 @ SY3688 )
| ( SV784 @ SY3689 ) )
| ~ ( ~ ( SV784 @ SY3689 )
| ( SV702 @ SY3688 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2775,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
| ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2776,plain,
! [SV45: $i,SV849: $i] :
( ( ~ ~ ( ~ ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) )
| ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
| ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2549]) ).
thf(2777,plain,
! [SV703: $i,SV329: $i > $o,SV46: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ SV46 )
| ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SV850 )
| ( SV703 = SV850 ) )
= $true )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2550]) ).
thf(2778,plain,
! [SV49: $i,SV563: $i > $i,SV331: $i] :
( ( ( in @ ( sK18_SY3418 @ SV331 @ SV563 @ SV49 ) @ SV49 )
= $true )
| ( ( func @ SV49 @ SV331
@ ( lam @ SV49 @ SV331
@ ^ [SY3419: $i] : ( SV563 @ SY3419 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2551]) ).
thf(2779,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
| ~ ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 ) )
| ( in @ ( setadjoin @ ( sK39_SY2254 @ SV52 ) @ ( sK39_SY2254 @ SV52 ) ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2554]) ).
thf(2780,plain,
! [SV53: $i,SV333: $i] :
( ( ( ! [SY2973: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2973 )
| ~ ( in @ SY2973 @ SV53 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2781,plain,
! [SV53: $i,SV333: $i] :
( ( ( ! [SY2974: $i] :
~ ~ ( ~ ( in @ SV333 @ SY2974 )
| ~ ( in @ SY2974 @ SV53 ) ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2782,plain,
! [SV564: $i,SV334: $i > $o,SV54: $i] :
( ( ( ~ ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) ) )
= $true )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2557]) ).
thf(2783,plain,
! [SV55: $i,SV565: $i > $i,SV335: $i] :
( ( ( in @ ( sK19_SY3422 @ SV335 @ SV565 @ SV55 ) @ SV55 )
= $true )
| ( ( func @ SV55 @ SV335
@ ( dpsetconstr @ SV55 @ SV335
@ ^ [SY3423: $i,SY3424: $i] :
( ( SV565 @ SY3423 )
= SY3424 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2558]) ).
thf(2784,plain,
! [SV566: $i,SV336: $i,SV56: $i,SV785: $i] :
( ( ( in @ SV785 @ SV56 )
= $false )
| ( ( ( ap @ SV56 @ SV336 @ SV566 @ SV785 )
= ( ap @ SV56 @ SV336 @ SV566 @ SV785 ) )
= $true )
| ( ( in @ SV566 @ ( funcSet @ SV56 @ SV336 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2785,plain,
! [SV704: $i,SV337: $i,SV57: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ SV57 )
| ~ ( in @ SV851 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SV851 @ ( setminus @ SV57 @ SV337 ) ) )
= $true )
| ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2561]) ).
thf(2786,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( ~ ~ ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) ) )
= $true )
| ( ( in @ SV705 @ SV339 )
= $true )
| ( ( in @ SV705 @ SV59 )
= $false )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2787,plain,
! [SV568: $i,SV341: $i,SV61: $i,SV786: $i] :
( ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( ~ ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3692 )
= ( ap @ SV61 @ SV341 @ SV786 @ SY3692 ) ) )
| ( SV568 = SV786 ) )
= $true )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2788,plain,
! [SV706: $i,SV62: $i,SV342: $i] :
( ( ( ~ ( subset @ SV342 @ ( setminus @ SV62 @ SV706 ) ) )
= $true )
| ( ( subset @ SV706 @ ( setminus @ SV62 @ SV342 ) )
= $true )
| ( ( in @ SV706 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2564]) ).
thf(2789,plain,
! [SV707: $i,SV343: $i,SV63: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ SV63 )
| ~ ~ ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2565]) ).
thf(2790,plain,
! [SV344: $i,SV708: $i,SV64: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( powerset @ SV64 ) )
| ~ ( subset @ SV708 @ SV853 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SV853 ) )
= $true )
| ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2566]) ).
thf(2791,plain,
! [SV345: $i,SV709: $i,SV65: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ SV65 )
| ~ ~ ( in @ SV854 @ SV709 )
| ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2567]) ).
thf(2792,plain,
! [SV346: $i,SV66: $i,SV710: $i] :
( ( ( ~ ( in @ SV710 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) ) )
= $true )
| ( ( in @ SV710 @ SV346 )
= $true )
| ( ( in @ SV710 @ SV66 )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2568]) ).
thf(2793,plain,
! [SV711: $i,SV348: $i,SV68: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV68 )
| ! [SY3743: $i] :
( ~ ( in @ SY3743 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3743 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3744: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3744 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3744 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3744 @ SY3743 ) @ SV711 ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2570]) ).
thf(2794,plain,
! [SV712: $i,SV349: $i,SV69: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV69 )
| ~ ( in @ SV856 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SV856 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) )
= $true )
| ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2571]) ).
thf(2795,plain,
! [SV70: $i,SV569: $i > $i,SV350: $i] :
( ( ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 )
= $true )
| ( ( ! [SY3430: $i] :
( ~ ( in @ SY3430 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SY3430 )
= ( SV569 @ SY3430 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2572]) ).
thf(2796,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV857 )
= ( SV569 @ SV857 ) ) )
= $true )
| ( ( in @ ( SV569 @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) ) @ SV350 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2573]) ).
thf(2797,plain,
! [SV71: $i,SV685: $i,SV570: $i > $i > $o,SV351: $i,SV846: $i] :
( ( ( ~ ( in @ SV846 @ SV351 ) )
= $true )
| ( ( ~ ( SV570 @ SV685 @ SV846 )
| ( in @ ( kpair @ SV685 @ SV846 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) )
= $true )
| ( ( in @ SV685 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2798,plain,
! [SV571: $i,SV352: $i,SV72: $i,SV787: $i] :
( ( ( in @ SV787 @ SV72 )
= $false )
| ( ( in @ ( ap @ SV72 @ SV352 @ SV571 @ SV787 ) @ SV352 )
= $true )
| ( ( in @ SV571 @ ( funcSet @ SV72 @ SV352 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2575]) ).
thf(2799,plain,
! [SV74: $i,SV354: $i,SV573: $i > $i > $o] :
( ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2577]) ).
thf(2800,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i] :
( ( ( ! [SY3693: $i] :
~ ~ ( ~ ( in @ SY3693 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SY3693 ) ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2801,plain,
! [SV574: $i,SV355: $i,SV75: $i,SV788: $i] :
( ( ( in @ SV788 @ SV75 )
= $false )
| ( ( in @ ( kpair @ SV788 @ ( ap @ SV75 @ SV355 @ SV574 @ SV788 ) ) @ SV574 )
= $true )
| ( ( func @ SV75 @ SV355 @ SV574 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2802,plain,
! [SV356: $i > $o,SV76: $i,SV789: $i] :
( ( ( in @ SV789 @ SV76 )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( ~ ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2580]) ).
thf(2803,plain,
( ( ~ ( in @ sK31_SY3607 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2804,plain,
( ( ! [SY3731: $i] :
( ~ ( in @ SY3731 @ sK1_SX0 )
| ~ ( in @ ( kpair @ sK31_SY3607 @ SY3731 ) @ sK8_SY3448 )
| ( in @ ( kpair @ sK31_SY3607 @ SY3731 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2583]) ).
thf(2805,plain,
! [SV358: $i,SV78: $i,SV790: $i,SV714: $i] :
( ( ( SV714 = SV790 )
= $false )
| ( ( ~ ( in @ SV714 @ SV78 )
| ( in @ SV790 @ SV358 ) )
= $true )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2806,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i] :
( ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( ~ ! [SY3694: $i] :
( ~ ( in @ SY3694 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3694 )
= ( ap @ SV81 @ SV361 @ SV791 @ SY3694 ) ) )
| ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2807,plain,
! [SV82: $i,SV362: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ SV362 )
| ( in @ SV858 @ SV82 ) )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2586]) ).
thf(2808,plain,
! [SV362: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK40_SY3049 @ SV82 @ SV362 ) @ SV362 )
| ( in @ ( sK40_SY3049 @ SV82 @ SV362 ) @ SV82 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2587]) ).
thf(2809,plain,
! [SV363: $i,SV83: $i,SV792: $i,SV715: $i] :
( ( ( SV715 = SV792 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) )
| ~ ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) ) ) )
= $true )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2588]) ).
thf(2810,plain,
! [SV859: $o,SV716: $i,SV365: $i,SV85: $i] :
( ( ( ! [SY3746: $i] :
( ~ ( in @ SY3746 @ SV85 )
| ~ ( in @ SY3746 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SY3746 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SY3746 @ SV716 )
| SV859 )
| SV859 ) )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2589]) ).
thf(2811,plain,
! [SV716: $i,SV365: $i,SV85: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV85 )
| ~ ( in @ SX0 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SX0 @ SV365 )
| $true )
| ~ ( ~ ( in @ SX0 @ SV716 )
| $true )
| $true ) )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2589]) ).
thf(2812,plain,
! [SV716: $i,SV365: $i,SV85: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV85 )
| ~ ( in @ SX0 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SX0 @ SV365 )
| $false )
| ~ ( ~ ( in @ SX0 @ SV716 )
| $false )
| $false ) )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2589]) ).
thf(2813,plain,
! [SV366: $i,SV688: $o,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 )
| SV688 )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2814,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2815,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2816,plain,
! [SV367: $i,SV87: $i,SV579: $i] :
( ( ( in @ SV579 @ ( symdiff @ SV87 @ SV367 ) )
= $false )
| ( ( in @ SV579 @ SV367 )
= $false )
| ( ( in @ SV579 @ SV87 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2817,plain,
! [SV89: $i,SV581: $i,SV369: $i,SV793: $i] :
( ( ( in @ SV793 @ SV369 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV581 @ SV793 ) )
= SV793 )
= $true )
| ( ( in @ SV581 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2818,plain,
! [SV92: $i,SV583: $i,SV372: $i,SV794: $i] :
( ( ( in @ SV794 @ SV372 )
= $false )
| ( ( ( kpair @ SV583 @ SV794 )
= ( kpair @ SV583 @ SV794 ) )
= $true )
| ( ( in @ SV583 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2595]) ).
thf(2819,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2596]) ).
thf(2820,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2821,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 )
| ~ ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2598]) ).
thf(2822,plain,
! [SV94: $i,SV374: $i,SV585: $i] :
( ( ( in @ SV585 @ SV374 )
= $true )
| ( ( in @ SV585 @ ( symdiff @ SV94 @ SV374 ) )
= $true )
| ( ( in @ SV585 @ SV94 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2599]) ).
thf(2823,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY2389: $i,SY2390: $i] :
( ~ ( SV95 @ SY2389 )
| ~ ( SV95 @ SY2390 )
| ( SY2389 = SY2390 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2824,plain,
! [SV375: $i,SV96: $i,SV796: $i,SV718: $i] :
( ( ( SV718 = SV796 )
= $false )
| ( ( ( setadjoin @ SV96 @ SV718 )
= ( setadjoin @ SV375 @ SV796 ) )
= $true )
| ( ( SV96 = SV375 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2825,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2602]) ).
thf(2826,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
| ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2827,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2604]) ).
thf(2828,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2829,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
| ~ ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
| ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2605]) ).
thf(2830,plain,
! [SV100: $i,SV586: $i,SV381: $i,SV797: $i] :
( ( ( in @ SV797 @ SV381 )
= $false )
| ( ( subset @ ( setadjoin @ SV586 @ ( setadjoin @ SV797 @ emptyset ) ) @ ( binunion @ SV100 @ SV381 ) )
= $true )
| ( ( in @ SV586 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2831,plain,
! [SV383: $i,SV720: $i,SV102: $i] :
( ( ( ~ ( subset @ ( setminus @ SV102 @ SV720 ) @ ( setminus @ SV102 @ SV383 ) ) )
= $true )
| ( ( subset @ SV383 @ SV720 )
= $true )
| ( ( in @ SV720 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2608]) ).
thf(2832,plain,
! [SV721: $i,SV385: $i,SV104: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ ( powerset @ SV104 ) )
| ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SV860 ) @ ( binunion @ SV721 @ SV860 ) ) ) ) )
= $true )
| ( ( in @ SV721 @ ( powerset @ SV104 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2609]) ).
thf(2833,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV722 ) )
= $true )
| ( ( ~ ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2610]) ).
thf(2834,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
| ~ ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) ) ) )
= $true )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2835,plain,
! [SV723: $i,SV387: $i,SV107: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV107 )
| ~ ~ ( in @ SV861 @ SV387 )
| ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2612]) ).
thf(2836,plain,
! [SV588: $i,SV388: $o,SV108: $i,SV798: $i] :
( ( ( in @ SV798 @ SV108 )
= $false )
| ( ( in @ ( if @ SV108 @ SV388 @ SV588 @ SV798 ) @ ( setadjoin @ SV588 @ ( setadjoin @ SV798 @ emptyset ) ) )
= $true )
| ( ( in @ SV588 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2837,plain,
! [SV589: $i,SV108: $i,SV799: $i] :
( ( ( in @ SV799 @ SV108 )
= $false )
| ( ( in @ ( if @ SV108 @ $true @ SV589 @ SV799 ) @ ( setadjoin @ SV589 @ ( setadjoin @ SV799 @ emptyset ) ) )
= $true )
| ( ( in @ SV589 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2838,plain,
! [SV590: $i,SV108: $i,SV800: $i] :
( ( ( in @ SV800 @ SV108 )
= $false )
| ( ( in @ ( if @ SV108 @ $false @ SV590 @ SV800 ) @ ( setadjoin @ SV590 @ ( setadjoin @ SV800 @ emptyset ) ) )
= $true )
| ( ( in @ SV590 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2615]) ).
thf(2839,plain,
! [SV724: $i,SV391: $i,SV111: $i] :
( ( ( ~ ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV111 )
| ~ ( in @ SY3619 @ SV391 )
| ( in @ SY3619 @ SV724 ) ) )
= $true )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2840,plain,
! [SV725: $i,SV392: $i,SV112: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV112 )
| ~ ~ ( in @ SV862 @ SV392 )
| ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2841,plain,
! [SV114: $i,SV394: $i,SV592: $i] :
( ( ( ~ ( in @ SV592 @ SV394 ) )
= $false )
| ( ( ~ ( in @ SV592 @ SV114 ) )
= $true )
| ( ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2619]) ).
thf(2842,plain,
! [SV593: $i,SV396: $o,SV117: $i,SV801: $i] :
( ( ( in @ SV801 @ SV117 )
= $false )
| ( ( ~ ~ SV396
| ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) ) )
= $true )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2620]) ).
thf(2843,plain,
! [SV594: $i,SV117: $i,SV802: $i] :
( ( ( in @ SV802 @ SV117 )
= $false )
| ( ( ~ ~ $true
| ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) ) )
= $true )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2621]) ).
thf(2844,plain,
! [SV595: $i,SV117: $i,SV803: $i] :
( ( ( in @ SV803 @ SV117 )
= $false )
| ( ( ~ ~ $false
| ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) ) )
= $true )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2845,plain,
! [SV118: $i,SV726: $i,SV397: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ ( binintersect @ SV397 @ SV726 ) )
| ( in @ SV863 @ SV118 ) )
= $true )
| ( ( in @ SV726 @ ( powerset @ SV118 ) )
= $false )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2623]) ).
thf(2846,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $false )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2624]) ).
thf(2847,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ~ ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $false )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2625]) ).
thf(2848,plain,
! [SV727: $i,SV401: $i,SV122: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV122 )
| ~ ( in @ SV864 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SV864 @ ( setminus @ SV122 @ SV401 ) ) )
= $true )
| ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2626]) ).
thf(2849,plain,
! [SV600: $i,SV404: $i,SV125: $i,SV804: $i] :
( ( ( in @ SV804 @ SV125 )
= $false )
| ( ( in @ ( ap @ SV125 @ SV404 @ SV600 @ SV804 ) @ SV404 )
= $true )
| ( ( func @ SV125 @ SV404 @ SV600 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2850,plain,
! [SV805: $i > $o,SV601: $i,SV405: $i,SV126: $i] :
( ( ( ! [SY3700: $i] :
( ~ ( in @ SY3700 @ SV126 )
| ! [SY3701: $i] :
( ~ ( in @ SY3701 @ SV405 )
| ~ ( in @ ( kpair @ SY3700 @ SY3701 ) @ SV601 )
| ( SV805 @ ( kpair @ SY3700 @ SY3701 ) ) ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2851,plain,
! [SV729: $i,SV406: $i,SV127: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ SV127 )
| ~ ( in @ SV865 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SV865 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2630]) ).
thf(2852,plain,
! [SV128: $i,SV407: $i,SV602: $i] :
( ( ( in @ SV602 @ SV407 )
= $false )
| ( ( in @ SV602 @ ( symdiff @ SV128 @ SV407 ) )
= $true )
| ( ( in @ SV602 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2631]) ).
thf(2853,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV730 ) )
= $true )
| ( ( ~ ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2632]) ).
thf(2854,plain,
! [SV731: $i,SV409: $i,SV132: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV132 )
| ~ ( in @ SV866 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SV866 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) )
= $true )
| ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2633]) ).
thf(2855,plain,
! [SV732: $i,SV411: $i,SV134: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV134 )
| ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SV867 @ SV411 )
| ( in @ SV867 @ SV732 ) )
= $true )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2634]) ).
thf(2856,plain,
! [SV605: $i,SV806: $i,SV413: $i,SV137: $i] :
( ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( ~ ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3703 )
= ( ap @ SV137 @ SV413 @ SV806 @ SY3703 ) ) )
| ( SV605 = SV806 ) )
= $true )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2857,plain,
! [SV606: $i,SV414: $o,SV138: $i,SV807: $i] :
( ( ( in @ SV807 @ SV138 )
= $false )
| ( ( ~ SV414
| ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3704: $i] :
( ~ ( ~ SV414
| ( SY3704 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3704 != SV807 ) ) ) ) ) )
= $true )
| ( ( in @ SV606 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2858,plain,
! [SV607: $i,SV138: $i,SV808: $i] :
( ( ( in @ SV808 @ SV138 )
= $false )
| ( ( ~ $true
| ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3705: $i] :
( ~ ( ~ $true
| ( SY3705 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3705 != SV808 ) ) ) ) ) )
= $true )
| ( ( in @ SV607 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2637]) ).
thf(2859,plain,
! [SV608: $i,SV138: $i,SV809: $i] :
( ( ( in @ SV809 @ SV138 )
= $false )
| ( ( ~ $false
| ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3706: $i] :
( ~ ( ~ $false
| ( SY3706 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3706 != SV809 ) ) ) ) ) )
= $true )
| ( ( in @ SV608 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2638]) ).
thf(2860,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV733 ) )
= $true )
| ( ( ~ ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2639]) ).
thf(2861,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2641]) ).
thf(2862,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
| ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2642]) ).
thf(2863,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SV142 )
| ~ ~ ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) ) )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2643]) ).
thf(2864,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( ~ ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 )
| ! [SY3747: $i] :
( ~ ( in @ SY3747 @ SV144 )
| ~ ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SY3747 ) @ SV419 )
| ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SY3747 ) ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2645]) ).
thf(2865,plain,
! [SV736: $i,SV420: $i,SV145: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ ( powerset @ SV145 ) )
| ~ ( subset @ SV420 @ SV868 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SV868 ) )
= $true )
| ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2646]) ).
thf(2866,plain,
! [SV611: $i,SV422: $o,SV147: $i,SV810: $i] :
( ( ( in @ SV810 @ SV147 )
= $false )
| ( ( ~ ~ SV422
| ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) ) )
= $true )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2867,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( ( in @ SV811 @ SV147 )
= $false )
| ( ( ~ ~ $true
| ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) ) )
= $true )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2868,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( ( in @ SV812 @ SV147 )
= $false )
| ( ( ~ ~ $false
| ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) ) )
= $true )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2869,plain,
! [SV614: $i,SV423: $o,SV149: $i,SV813: $i] :
( ( ( in @ SV813 @ SV149 )
= $false )
| ( ( ~ ~ SV423
| ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 ) )
= $true )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2650]) ).
thf(2870,plain,
! [SV615: $i,SV149: $i,SV814: $i] :
( ( ( in @ SV814 @ SV149 )
= $false )
| ( ( ~ ~ $true
| ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 ) )
= $true )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2871,plain,
! [SV616: $i,SV149: $i,SV815: $i] :
( ( ( in @ SV815 @ SV149 )
= $false )
| ( ( ~ ~ $false
| ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 ) )
= $true )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2872,plain,
! [SV737: $i,SV151: $i,SV425: $i] :
( ( ( ~ ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) ) )
= $true )
| ( ( ! [SY3636: $i] :
( ~ ( in @ SY3636 @ SV151 )
| ~ ( in @ SY3636 @ SV737 )
| ( in @ SY3636 @ ( setminus @ SV151 @ SV425 ) ) ) )
= $true )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2873,plain,
! [SV738: $i,SV426: $i,SV152: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( powerset @ SV152 ) )
| ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SV869 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) ) )
= $true )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2655]) ).
thf(2874,plain,
! [SV739: $i,SV427: $i,SV154: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ ( powerset @ SV154 ) )
| ! [SY3748: $i] :
( ~ ( in @ SY3748 @ SV154 )
| ~ ( in @ SY3748 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3748 @ ( binunion @ SV427 @ SV870 ) ) ) )
= $true )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2656]) ).
thf(2875,plain,
! [SV428: $i > $o,SV155: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ SV155 )
| ~ ( SV428 @ SV816 ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2657]) ).
thf(2876,plain,
! [SV740: $i,SV429: $i,SV156: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV156 )
| ~ ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) ) )
= $true )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2658]) ).
thf(2877,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2878,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2879,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
| ~ ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
| ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2661]) ).
thf(2880,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
| ( SV433 @ SV619 ) )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2662]) ).
thf(2881,plain,
! [SV160: $i,SV619: $i,SV433: $i > $o] :
( ( ( ~ ( SV433 @ SV619 )
| ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) ) )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2663]) ).
thf(2882,plain,
! [SV620: $i,SV434: $i > $o,SV161: $i] :
( ( ( ( dsetconstr @ SV161
@ ^ [SY3189: $i] : ( SV434 @ SY3189 ) )
= emptyset )
= $false )
| ( ( SV434 @ SV620 )
= $false )
| ( ( in @ SV620 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2883,plain,
! [SV165: $i,SV623: $i,SV437: $i,SV817: $i] :
( ( ( in @ SV817 @ SV437 )
= $false )
| ( ( in @ ( kpair @ SV623 @ SV817 ) @ ( cartprod @ SV165 @ SV437 ) )
= $true )
| ( ( in @ SV623 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2884,plain,
! [SV167: $i,SV624: $i,SV439: $i,SV818: $i] :
( ( ( in @ SV818 @ SV439 )
= $false )
| ( ( ( kfst @ ( kpair @ SV624 @ SV818 ) )
= SV624 )
= $true )
| ( ( in @ SV624 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2885,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( ~ ( in @ ( sK24_SY3199 @ SV440 @ SV168 ) @ SV168 )
| ~ ( SV440 @ ( sK24_SY3199 @ SV440 @ SV168 ) ) )
= $false )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2668]) ).
thf(2886,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $false )
| ( ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2887,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( ( SV625 = SV169 )
| ( in @ SV625 @ SV441 ) )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2670]) ).
thf(2888,plain,
! [SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2671]) ).
thf(2889,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
| ~ ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2672]) ).
thf(2890,plain,
! [SV819: $i > $o,SV627: $i,SV445: $i,SV173: $i] :
( ( ( ! [SY3710: $i] :
( ~ ( in @ SY3710 @ SV173 )
| ! [SY3711: $i] :
( ~ ( in @ SY3711 @ SV445 )
| ~ ( in @ ( kpair @ SY3710 @ SY3711 ) @ SV627 )
| ( SV819 @ ( kpair @ SY3710 @ SY3711 ) ) ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2891,plain,
! [SV177: $i,SV449: $i] :
( ( ( ~ ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) ) )
= $true )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2675]) ).
thf(2892,plain,
! [SV177: $i,SV449: $i] :
( ( ( ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2893,plain,
! [SV179: $i,SV451: $i,SV692: $i,SV630: $i] :
( ( ( SV630 = SV692 )
= $false )
| ( ( SV451 = SV692 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV179 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV179 @ ( setadjoin @ SV451 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV630 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV630 @ ( setadjoin @ SV692 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2677]) ).
thf(2894,plain,
! [SV631: $i,SV452: $i,SV180: $i,SV820: $i] :
( ( ( in @ SV820 @ SV180 )
= $false )
| ( ( ! [SY3713: $i] :
( ~ ( in @ SY3713 @ SV452 )
| ~ ( in @ ( kpair @ SV820 @ SY3713 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SY3713 ) ) )
= $true )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2895,plain,
! [SV743: $i,SV455: $i,SV185: $i] :
( ( ( ~ ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SV185 )
| ! [SY3645: $i] :
( ~ ( in @ SY3645 @ SV185 )
| ~ ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV455 )
| ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV743 ) ) ) )
= $true )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2680]) ).
thf(2896,plain,
! [SV744: $i,SV457: $i,SV187: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ ( powerset @ SV187 ) )
| ! [SY3750: $i] :
( ~ ( in @ SY3750 @ SV187 )
| ~ ( in @ SY3750 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3750 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) ) )
= $true )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2682]) ).
thf(2897,plain,
! [SV458: $i,SV745: $i,SV188: $i,SV874: $i] :
( ( ( ~ ( in @ SV874 @ SV188 )
| ~ ( in @ ( kpair @ SV874 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SV874 ) @ SV458 ) )
= $true )
| ( ( in @ SV745 @ SV188 )
= $false )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2683]) ).
thf(2898,plain,
! [SV189: $i,SV746: $o,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) )
| ~ ( in @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) @ SV189 )
| SV746 )
= $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2684]) ).
thf(2899,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK43_SX0 @ SV189 @ SV459 ) )
| ~ ( in @ ( sK43_SX0 @ SV189 @ SV459 ) @ SV189 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2685]) ).
thf(2900,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK44_SX0 @ SV189 @ SV459 ) )
| ~ ( in @ ( sK44_SX0 @ SV189 @ SV459 ) @ SV189 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2686]) ).
thf(2901,plain,
! [SV747: $i,SV462: $i,SV192: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ SV192 )
| ~ ~ ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2687]) ).
thf(2902,plain,
! [SV748: $i,SV463: $i,SV193: $i,SV876: $i] :
( ( ( ~ ( in @ SV876 @ SV193 )
| ~ ( in @ SV876 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SV876 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2688]) ).
thf(2903,plain,
! [SV749: $i,SV464: $i,SV194: $i,SV877: $i] :
( ( ( ~ ( in @ SV877 @ ( powerset @ SV194 ) )
| ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SV877 ) @ ( binunion @ SV749 @ SV877 ) ) ) ) )
= $true )
| ( ( in @ SV749 @ ( powerset @ SV194 ) )
= $false )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(2904,plain,
! [SV465: $i,SV821: $o,SV195: $i,SV635: $i] :
( ( ( ( SV635 != SV195 )
| SV821 )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2905,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ( SV635 != SV195 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2691]) ).
thf(2906,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( ( SV635 != SV195 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2907,plain,
! [SV197: $i,SV467: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV467 ) ) )
= $true )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2908,plain,
! [SV200: $i,SV637: $i > $i,SV470: $i] :
( ( ( in @ ( sK25_SY3515 @ SV470 @ SV637 @ SV200 ) @ SV200 )
= $true )
| ( ( in
@ ( lam @ SV200 @ SV470
@ ^ [SY3516: $i] : ( SV637 @ SY3516 ) )
@ ( funcSet @ SV200 @ SV470 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2909,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ( in @ ( sK26_SY3253 @ SV471 @ SV201 ) @ SV201 )
| ~ ( in @ SV471 @ ( sK26_SY3253 @ SV471 @ SV201 ) ) )
= $false )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2697]) ).
thf(2910,plain,
! [SV752: $i,SV474: $i,SV204: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ ( powerset @ SV204 ) )
| ! [SY3751: $i] :
( ~ ( in @ SY3751 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SY3751 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SY3751 ) ) ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2699]) ).
thf(2911,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV753 ) )
= $true )
| ( ( ~ ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2700]) ).
thf(2912,plain,
! [SV211: $i,SV639: $i,SV479: $i,SV822: $i] :
( ( ( in @ SV822 @ SV479 )
= $false )
| ( ( in @ ( setadjoin @ SV639 @ ( setadjoin @ SV822 @ emptyset ) ) @ ( powerset @ ( binunion @ SV211 @ SV479 ) ) )
= $true )
| ( ( in @ SV639 @ SV211 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2701]) ).
thf(2913,plain,
! [SV641: $i,SV482: $o,SV214: $i,SV823: $i] :
( ( ( in @ SV823 @ SV214 )
= $false )
| ( ( ~ SV482
| ( ( if @ SV214 @ SV482 @ SV641 @ SV823 )
= SV641 ) )
= $true )
| ( ( in @ SV641 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2914,plain,
! [SV642: $i,SV214: $i,SV824: $i] :
( ( ( in @ SV824 @ SV214 )
= $false )
| ( ( ~ $true
| ( ( if @ SV214 @ $true @ SV642 @ SV824 )
= SV642 ) )
= $true )
| ( ( in @ SV642 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2915,plain,
! [SV643: $i,SV214: $i,SV825: $i] :
( ( ( in @ SV825 @ SV214 )
= $false )
| ( ( ~ $false
| ( ( if @ SV214 @ $false @ SV643 @ SV825 )
= SV643 ) )
= $true )
| ( ( in @ SV643 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2705]) ).
thf(2916,plain,
! [SV755: $i,SV483: $i,SV215: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV215 )
| ! [SY3752: $i] :
( ~ ( in @ SY3752 @ SV215 )
| ~ ( in @ ( kpair @ SV879 @ SY3752 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SY3752 ) @ ( binunion @ SV483 @ SV755 ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2706]) ).
thf(2917,plain,
! [SV756: $i,SV216: $i,SV484: $i] :
( ( ( ~ ( subset @ SV484 @ ( setminus @ SV216 @ SV756 ) ) )
= $true )
| ( ( subset @ SV756 @ ( setminus @ SV216 @ SV484 ) )
= $true )
| ( ( in @ SV756 @ ( powerset @ SV216 ) )
= $false )
| ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2707]) ).
thf(2918,plain,
! [SV219: $i,SV487: $i,SV645: $i] :
( ( ( ~ ( in @ SV645 @ SV487 ) )
= $false )
| ( ( ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true )
| ( ( in @ SV645 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2919,plain,
! [SV220: $i,SV488: $i,SV759: $i] :
( ( ( ~ ( in @ SV759 @ SV488 ) )
= $true )
| ( ( ~ ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) ) )
= $true )
| ( ( in @ SV759 @ SV220 )
= $false )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2711]) ).
thf(2920,plain,
! [SV489: $i > $o,SV221: $i,SV826: $i] :
( ( ( in @ SV826 @ SV221 )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( ~ ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2712]) ).
thf(2921,plain,
! [SV760: $i,SV491: $i,SV223: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV223 )
| ~ ( in @ SV880 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SV880 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) )
= $true )
| ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2713]) ).
thf(2922,plain,
! [SV225: $i,SV493: $i,SV647: $i] :
( ( ( in @ SV647 @ SV493 )
= $true )
| ( ( ~ ( subset @ SV225 @ SV493 ) )
= $true )
| ( ( in @ SV647 @ SV225 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2923,plain,
! [SV648: $i,SV827: $i,SV494: $i,SV226: $i] :
( ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( ~ ! [SY3714: $i] :
( ~ ( in @ SY3714 @ SV226 )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV494 )
| ~ ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV648 )
| ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV827 ) ) )
| ( subset @ SV648 @ SV827 ) )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2924,plain,
! [SV231: $i,SV650: $i,SV499: $i,SV828: $i] :
( ( ( in @ SV828 @ SV499 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV650 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV650 @ ( setadjoin @ SV828 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV231 @ SV499 ) ) ) )
= $true )
| ( ( in @ SV650 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2925,plain,
! [SV762: $i,SV500: $i,SV232: $i] :
( ( ( ~ ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV232 )
| ~ ( in @ SY3661 @ SV500 )
| ( in @ SY3661 @ SV762 ) ) )
= $true )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2719]) ).
thf(2926,plain,
! [SV763: $i,SV501: $i,SV233: $i] :
( ( ( ~ ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV233 )
| ~ ( in @ SY3662 @ SV501 )
| ( in @ SY3662 @ SV763 ) ) )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2720]) ).
thf(2927,plain,
! [SV235: $i,SV503: $i,SV764: $i] :
( ( ( ~ ( in @ SV764 @ SV503 ) )
= $true )
| ( ( in @ SV764 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) )
= $true )
| ( ( in @ SV764 @ SV235 )
= $false )
| ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(2928,plain,
! [SV652: $i,SV505: $o,SV237: $i,SV829: $i] :
( ( ( in @ SV829 @ SV237 )
= $false )
| ( ( in @ ( if @ SV237 @ SV505 @ SV652 @ SV829 ) @ SV237 )
= $true )
| ( ( in @ SV652 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2929,plain,
! [SV653: $i,SV237: $i,SV830: $i] :
( ( ( in @ SV830 @ SV237 )
= $false )
| ( ( in @ ( if @ SV237 @ $true @ SV653 @ SV830 ) @ SV237 )
= $true )
| ( ( in @ SV653 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2930,plain,
! [SV654: $i,SV237: $i,SV831: $i] :
( ( ( in @ SV831 @ SV237 )
= $false )
| ( ( in @ ( if @ SV237 @ $false @ SV654 @ SV831 ) @ SV237 )
= $true )
| ( ( in @ SV654 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2931,plain,
! [SV765: $i,SV506: $i,SV238: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ ( powerset @ SV238 ) )
| ! [SY3753: $i] :
( ~ ( in @ SY3753 @ SV238 )
| ~ ( in @ SY3753 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3753 @ ( binunion @ SV765 @ SV881 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2725]) ).
thf(2932,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV240 )
| ! [SY3754: $i] :
( ~ ( in @ SY3754 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3754 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3755: $o] :
( ~ ! [SY3756: $i] :
( ~ ( in @ SY3756 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3756 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3756 @ SY3754 ) @ SV766 )
| SY3755 )
| SY3755 ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2726]) ).
thf(2933,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( ~ ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 )
| ! [SY3757: $i] :
( ~ ( in @ SY3757 @ SV241 )
| ~ ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SY3757 ) @ SV509 )
| ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SY3757 ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2727]) ).
thf(2934,plain,
! [SV768: $i,SV510: $i,SV242: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV242 )
| ~ ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SV883 @ SV510 ) )
= $true )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2728]) ).
thf(2935,plain,
! [SV769: $i,SV511: $i,SV243: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV243 )
| ~ ( in @ SV884 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SV884 @ ( setminus @ SV243 @ SV769 ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2729]) ).
thf(2936,plain,
! [SV657: $i > $i > $o,SV249: $i,SV694: $i,SV517: $i,SV847: $i] :
( ( ( ~ ( in @ SV847 @ SV517 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV694 @ SV847 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SV847 ) )
= $true )
| ( ( in @ SV694 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2730]) ).
thf(2937,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
| ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 ) )
| ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2731]) ).
thf(2938,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( ~ ! [SY3716: $i] :
( ~ ( in @ SY3716 @ SV251 )
| ! [SY3717: $i] :
( ~ ( in @ SY3717 @ SV518 )
| ~ ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV658 )
| ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV832 ) ) )
| ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2939,plain,
! [SV771: $i,SV519: $i,SV252: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ SV252 )
| ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SV885 @ SV771 )
| ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2733]) ).
thf(2940,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
| ~ ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) ) ) )
= $true )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2735]) ).
thf(2941,plain,
! [SV773: $i,SV524: $i,SV258: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV258 )
| ! [SY3758: $i] :
( ~ ( in @ SY3758 @ SV258 )
| ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3759 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3759 @ SY3758 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SY3758 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2736]) ).
thf(2942,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ~ ! [SY3679: $i] :
( ~ ( in @ SY3679 @ SV259 )
| ! [SY3680: $i] :
( ~ ( in @ SY3680 @ SV259 )
| ~ ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV525 )
| ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV774 ) ) ) )
= $true )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2943,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2738]) ).
thf(2944,plain,
! [SV661: $i,SV528: $i,SV262: $i,SV833: $i] :
( ( ( in @ SV833 @ SV262 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV528
@ ^ [SY3720: $i] : ( in @ ( kpair @ SV833 @ SY3720 ) @ SV661 ) ) )
= $true )
| ( ( func @ SV262 @ SV528 @ SV661 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2945,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV775 ) )
= $true )
| ( ( ~ ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2946,plain,
! [SV776: $i,SV529: $i,SV264: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ SV264 )
| ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SV887 @ SV776 )
| ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2741]) ).
thf(2947,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK46_SY2861 @ SV777 @ SV265 ) @ SV265 )
| ~ ~ ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2742]) ).
thf(2948,plain,
! [SV272: $i,SV778: $i,SV534: $i] :
( ( ( ~ ( subset @ SV534 @ SV778 ) )
= $true )
| ( ( subset @ ( setminus @ SV272 @ SV778 ) @ ( setminus @ SV272 @ SV534 ) )
= $true )
| ( ( in @ SV778 @ ( powerset @ SV272 ) )
= $false )
| ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2745]) ).
thf(2949,plain,
! [SV273: $i,SV664: $i,SV535: $i,SV834: $i] :
( ( ( in @ SV834 @ SV535 )
= $false )
| ( ( in @ ( kpair @ SV664 @ SV834 ) @ ( powerset @ ( powerset @ ( binunion @ SV273 @ SV535 ) ) ) )
= $true )
| ( ( in @ SV664 @ SV273 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2746]) ).
thf(2950,plain,
! [SV665: $i,SV536: $i,SV274: $i,SV835: $i] :
( ( ( in @ SV835 @ SV274 )
= $false )
| ( ( ( ap @ SV274 @ SV536 @ SV665 @ SV835 )
= ( ap @ SV274 @ SV536 @ SV665 @ SV835 ) )
= $true )
| ( ( func @ SV274 @ SV536 @ SV665 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2951,plain,
! [SV779: $i,SV537: $i,SV275: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ SV275 )
| ~ ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2748]) ).
thf(2952,plain,
! [SV666: $i,SV538: $i,SV276: $i,SV836: $i] :
( ( ( in @ SV836 @ SV276 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV538
@ ^ [SY3721: $i] : ( in @ ( kpair @ SV836 @ SY3721 ) @ SV666 ) ) )
@ SV538 )
= $true )
| ( ( func @ SV276 @ SV538 @ SV666 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2953,plain,
! [SV667: $i,SV539: $i,SV277: $i,SV837: $i] :
( ( ( in @ SV837 @ SV277 )
= $false )
| ( ( in @ ( kpair @ SV837 @ ( ap @ SV277 @ SV539 @ SV667 @ SV837 ) ) @ SV667 )
= $true )
| ( ( in @ SV667 @ ( funcSet @ SV277 @ SV539 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2954,plain,
! [SV540: $i > $o,SV278: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ SV278 )
| ~ ~ ( SV540 @ SV838 ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2751]) ).
thf(2955,plain,
! [SV541: $i,SV780: $i,SV279: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ SV279 )
| ~ ( in @ ( kpair @ SV780 @ SV889 ) @ SV541 )
| ( in @ ( kpair @ SV889 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) )
= $true )
| ( ( in @ SV780 @ SV279 )
= $false )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2752]) ).
thf(2956,plain,
! [SV280: $i,SV668: $i > $i,SV542: $i] :
( ( ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 )
= $true )
| ( ( ! [SY3553: $i] :
( ~ ( in @ SY3553 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SY3553 )
= ( SV668 @ SY3553 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2753]) ).
thf(2957,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV890 )
= ( SV668 @ SV890 ) ) )
= $true )
| ( ( in @ ( SV668 @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) ) @ SV542 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2754]) ).
thf(2958,plain,
! [SV282: $i,SV670: $i > $i,SV544: $i] :
( ( ( in @ ( sK29_SY3556 @ SV544 @ SV670 @ SV282 ) @ SV282 )
= $true )
| ( ( ( lam @ SV282 @ SV544
@ ^ [SY3557: $i] : ( SV670 @ SY3557 ) )
= ( lam @ SV282 @ SV544
@ ^ [SY3558: $i] : ( SV670 @ SY3558 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2959,plain,
! [SV284: $i] :
( ( ( ~ ( in @ ( sK30_SY2910 @ SV284 ) @ SV284 )
| ~ $true )
= $false )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2758]) ).
thf(2960,plain,
! [SV285: $i,SV546: $i,SV671: $i] :
( ( ( in @ SV671 @ SV546 )
= $true )
| ( ( SV285 != SV546 )
= $true )
| ( ( in @ SV671 @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2961,plain,
! [SV547: $i,SV286: $i,SV672: $i] :
( ( ( in @ SV672 @ SV286 )
= $false )
| ( ( in @ SV672 @ SV547 )
= $true )
| ( ( in @ SV672 @ ( setminus @ SV286 @ SV547 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2962,plain,
! [SV673: $i,SV548: $i,SV287: $i,SV839: $i] :
( ( ( in @ SV839 @ SV287 )
= $false )
| ( ( ! [SY3722: $i] :
( ~ ( in @ SY3722 @ SV548 )
| ~ ( in @ ( kpair @ SV839 @ SY3722 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SY3722 ) ) )
= $true )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2963,plain,
! [SV674: $i,SV549: $o,SV288: $i,SV840: $i] :
( ( ( in @ SV840 @ SV288 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3723: $i] :
( ~ ( ~ SV549
| ( SY3723 != SV674 ) )
| ~ ( ~ ~ SV549
| ( SY3723 != SV840 ) ) ) ) )
= $true )
| ( ( in @ SV674 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2762]) ).
thf(2964,plain,
! [SV675: $i,SV288: $i,SV841: $i] :
( ( ( in @ SV841 @ SV288 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3724: $i] :
( ~ ( ~ $true
| ( SY3724 != SV675 ) )
| ~ ( ~ ~ $true
| ( SY3724 != SV841 ) ) ) ) )
= $true )
| ( ( in @ SV675 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2965,plain,
! [SV676: $i,SV288: $i,SV842: $i] :
( ( ( in @ SV842 @ SV288 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV288
@ ^ [SY3725: $i] :
( ~ ( ~ $false
| ( SY3725 != SV676 ) )
| ~ ( ~ ~ $false
| ( SY3725 != SV842 ) ) ) ) )
= $true )
| ( ( in @ SV676 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2966,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ SV782 ) )
= $true )
| ( ( ~ ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2765]) ).
thf(2967,plain,
! [SV294: $i,SV554: $i,SV679: $i] :
( ( ( in @ SV679 @ SV554 )
= $true )
| ( ( in @ SV679 @ ( setminus @ SV294 @ SV554 ) )
= $true )
| ( ( in @ SV679 @ SV294 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2968,plain,
! [SV680: $i,SV555: $o,SV296: $i,SV843: $i] :
( ( ( in @ SV843 @ SV296 )
= $false )
| ( ( ~ SV555
| ( ( dsetconstr @ SV296
@ ^ [SY3726: $i] :
( ~ ( ~ SV555
| ( SY3726 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3726 != SV843 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) ) )
= $true )
| ( ( in @ SV680 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2767]) ).
thf(2969,plain,
! [SV681: $i,SV296: $i,SV844: $i] :
( ( ( in @ SV844 @ SV296 )
= $false )
| ( ( ~ $true
| ( ( dsetconstr @ SV296
@ ^ [SY3727: $i] :
( ~ ( ~ $true
| ( SY3727 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3727 != SV844 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) ) )
= $true )
| ( ( in @ SV681 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2970,plain,
! [SV682: $i,SV296: $i,SV845: $i] :
( ( ( in @ SV845 @ SV296 )
= $false )
| ( ( ~ $false
| ( ( dsetconstr @ SV296
@ ^ [SY3728: $i] :
( ~ ( ~ $false
| ( SY3728 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3728 != SV845 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) ) )
= $true )
| ( ( in @ SV682 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2769]) ).
thf(2971,plain,
! [SV699: $i,SV322: $i,SV37: $i,SV848: $i] :
( ( ( ~ ( in @ SV848 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ! [SY3735: $i] :
( ~ ( in @ SY3735 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SY3735 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SY3735 ) ) ) )
= $true )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2972,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( SV38 @ SV700 )
= $false )
| ( ( ~ ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) )
= $true )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2771]) ).
thf(2973,plain,
! [SV325: $i,SV41: $i,SV560: $i] :
( ( ( in @ SV560 @ SV41 )
= $false )
| ( ( in @ SV560 @ SV325 )
= $true )
| ( ( subset @ SV41 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2974,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) @ SV44 )
| ! [SY3762: $i] :
( ~ ( in @ SY3762 @ SV328 )
| ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
!= SY3762 )
| ~ ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ SY3762 ) )
| ~ ( ~ ( SV784 @ SY3762 )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2774]) ).
thf(2975,plain,
! [SV45: $i] :
( ( ~ ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2976,plain,
! [SV45: $i] :
( ( ~ ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2775]) ).
thf(2977,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ~ ( ~ ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) )
| ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2776]) ).
thf(2978,plain,
! [SV703: $i,SV329: $i > $o,SV46: $i,SV850: $i] :
( ( ( ~ ( in @ SV850 @ SV46 ) )
= $true )
| ( ( ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SV850 )
| ( SV703 = SV850 ) )
= $true )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2777]) ).
thf(2979,plain,
! [SV52: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
| ~ ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 ) ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2980,plain,
! [SV52: $i] :
( ( ( in @ ( setadjoin @ ( sK39_SY2254 @ SV52 ) @ ( sK39_SY2254 @ SV52 ) ) @ SV52 )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2779]) ).
thf(2981,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ( in @ SV333 @ ( sK48_SY2973 @ SV53 @ SV333 ) )
| ~ ( in @ ( sK48_SY2973 @ SV53 @ SV333 ) @ SV53 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2780]) ).
thf(2982,plain,
! [SV53: $i,SV891: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ( in @ SV333 @ SV891 )
| ~ ( in @ SV891 @ SV53 ) ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(2983,plain,
! [SV564: $i,SV334: $i > $o,SV54: $i] :
( ( ( ! [SY3420: $i] :
( ~ ( in @ SY3420 @ SV54 )
| ~ ( SV334 @ SY3420 )
| ( SY3420 = SV564 ) ) )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2984,plain,
! [SV704: $i,SV337: $i,SV57: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ SV57 ) )
= $true )
| ( ( ~ ( in @ SV851 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SV851 @ ( setminus @ SV57 @ SV337 ) ) )
= $true )
| ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2785]) ).
thf(2985,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( ~ ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) ) )
= $false )
| ( ( in @ SV705 @ SV339 )
= $true )
| ( ( in @ SV705 @ SV59 )
= $false )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2986,plain,
! [SV786: $i,SV568: $i,SV341: $i,SV61: $i] :
( ( ( ~ ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3692 )
= ( ap @ SV61 @ SV341 @ SV786 @ SY3692 ) ) ) )
= $true )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2787]) ).
thf(2987,plain,
! [SV706: $i,SV62: $i,SV342: $i] :
( ( ( subset @ SV342 @ ( setminus @ SV62 @ SV706 ) )
= $false )
| ( ( subset @ SV706 @ ( setminus @ SV62 @ SV342 ) )
= $true )
| ( ( in @ SV706 @ ( powerset @ SV62 ) )
= $false )
| ( ( in @ SV342 @ ( powerset @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2788]) ).
thf(2988,plain,
! [SV707: $i,SV343: $i,SV63: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ SV63 ) )
= $true )
| ( ( ~ ~ ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2789]) ).
thf(2989,plain,
! [SV344: $i,SV708: $i,SV64: $i,SV853: $i] :
( ( ( ~ ( in @ SV853 @ ( powerset @ SV64 ) ) )
= $true )
| ( ( ~ ( subset @ SV708 @ SV853 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SV853 ) )
= $true )
| ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2790]) ).
thf(2990,plain,
! [SV345: $i,SV709: $i,SV65: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ SV65 ) )
= $true )
| ( ( ~ ~ ( in @ SV854 @ SV709 )
| ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2791]) ).
thf(2991,plain,
! [SV346: $i,SV66: $i,SV710: $i] :
( ( ( in @ SV710 @ ( setminus @ SV66 @ ( setminus @ SV66 @ SV346 ) ) )
= $false )
| ( ( in @ SV710 @ SV346 )
= $true )
| ( ( in @ SV710 @ SV66 )
= $false )
| ( ( in @ SV346 @ ( powerset @ SV66 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2792]) ).
thf(2992,plain,
! [SV711: $i,SV348: $i,SV68: $i,SV855: $i] :
( ( ( ~ ( in @ SV855 @ SV68 ) )
= $true )
| ( ( ! [SY3743: $i] :
( ~ ( in @ SY3743 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3743 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3744: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3744 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3744 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3744 @ SY3743 ) @ SV711 ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2793]) ).
thf(2993,plain,
! [SV712: $i,SV349: $i,SV69: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ SV69 ) )
= $true )
| ( ( ~ ( in @ SV856 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SV856 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) )
= $true )
| ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2794]) ).
thf(2994,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV892: $i] :
( ( ( ~ ( in @ SV892 @ SV70 )
| ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV892 )
= ( SV569 @ SV892 ) ) )
= $true )
| ( ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2795]) ).
thf(2995,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV857: $i] :
( ( ( ~ ( in @ SV857 @ SV70 ) )
= $true )
| ( ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV857 )
= ( SV569 @ SV857 ) )
= $true )
| ( ( in @ ( SV569 @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) ) @ SV350 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2796]) ).
thf(2996,plain,
! [SV71: $i,SV685: $i,SV570: $i > $i > $o,SV351: $i,SV846: $i] :
( ( ( in @ SV846 @ SV351 )
= $false )
| ( ( ~ ( SV570 @ SV685 @ SV846 )
| ( in @ ( kpair @ SV685 @ SV846 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) ) )
= $true )
| ( ( in @ SV685 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2797]) ).
thf(2997,plain,
! [SV573: $i > $i > $o,SV74: $i,SV354: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SV893 )
| ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3765: $i] :
~ ( ~ ( SV573 @ SY3764 @ SY3765 )
| ~ ! [SY3766: $i] :
( ~ ( in @ SY3766 @ SV354 )
| ~ ( SV573 @ SY3764 @ SY3766 )
| ( in @ ( kpair @ SY3765 @ SY3766 ) @ SV893 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2799]) ).
thf(2998,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i,SV894: $i] :
( ( ( ~ ~ ( ~ ( in @ SV894 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 ) ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2800]) ).
thf(2999,plain,
! [SV789: $i,SV356: $i > $o,SV76: $i] :
( ( ( ! [SY3033: $i] :
~ ~ ( ~ ( in @ SY3033 @ SV76 )
| ~ ~ ( SV356 @ SY3033 ) ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(3000,plain,
( ( in @ sK31_SY3607 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2803]) ).
thf(3001,plain,
( ( ~ ( in @ sK49_SY3731 @ sK1_SX0 )
| ~ ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ sK8_SY3448 )
| ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[2804]) ).
thf(3002,plain,
! [SV358: $i,SV790: $i,SV78: $i,SV714: $i] :
( ( ( ~ ( in @ SV714 @ SV78 ) )
= $true )
| ( ( in @ SV790 @ SV358 )
= $true )
| ( ( SV714 = SV790 )
= $false )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2805]) ).
thf(3003,plain,
! [SV791: $i,SV577: $i,SV361: $i,SV81: $i] :
( ( ( ~ ! [SY3694: $i] :
( ~ ( in @ SY3694 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3694 )
= ( ap @ SV81 @ SV361 @ SV791 @ SY3694 ) ) ) )
= $true )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(3004,plain,
! [SV82: $i,SV362: $i,SV858: $i] :
( ( ( ~ ( in @ SV858 @ SV362 ) )
= $true )
| ( ( in @ SV858 @ SV82 )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(3005,plain,
! [SV362: $i,SV82: $i] :
( ( ( ~ ( in @ ( sK40_SY3049 @ SV82 @ SV362 ) @ SV362 ) )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(3006,plain,
! [SV362: $i,SV82: $i] :
( ( ( in @ ( sK40_SY3049 @ SV82 @ SV362 ) @ SV82 )
= $false )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2808]) ).
thf(3007,plain,
! [SV363: $i,SV792: $i,SV83: $i,SV715: $i] :
( ( ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) )
| ~ ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) ) )
= $false )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2809]) ).
thf(3008,plain,
! [SV859: $o,SV716: $i,SV365: $i,SV85: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV85 )
| ~ ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2810]) ).
thf(3009,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV85 )
| ~ ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV896 @ SV365 )
| $true )
| ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2811]) ).
thf(3010,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV85 )
| ~ ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV897 @ SV365 )
| $false )
| ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2812]) ).
thf(3011,plain,
! [SV688: $o,SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2813]) ).
thf(3012,plain,
! [SV86: $i,SV366: $i,SV578: $i,SV688: $o] :
( ( SV688 = $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2813]) ).
thf(3013,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(3014,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2814]) ).
thf(3015,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV86 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(3016,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(3017,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2819]) ).
thf(3018,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2819]) ).
thf(3019,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(3020,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(3021,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(3022,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2821]) ).
thf(3023,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY3767: $i] :
( ~ ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
| ~ ( SV95 @ SY3767 )
| ( ( sK50_SY2389 @ SV717 @ SV95 )
= SY3767 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2823]) ).
thf(3024,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2825]) ).
thf(3025,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2826]) ).
thf(3026,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(3027,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2828]) ).
thf(3028,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(3029,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
| ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2829]) ).
thf(3030,plain,
! [SV383: $i,SV720: $i,SV102: $i] :
( ( ( subset @ ( setminus @ SV102 @ SV720 ) @ ( setminus @ SV102 @ SV383 ) )
= $false )
| ( ( subset @ SV383 @ SV720 )
= $true )
| ( ( in @ SV720 @ ( powerset @ SV102 ) )
= $false )
| ( ( in @ SV383 @ ( powerset @ SV102 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2831]) ).
thf(3031,plain,
! [SV721: $i,SV385: $i,SV104: $i,SV860: $i] :
( ( ( ~ ( in @ SV860 @ ( powerset @ SV104 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SV860 ) @ ( binunion @ SV721 @ SV860 ) ) ) )
= $true )
| ( ( in @ SV721 @ ( powerset @ SV104 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(3032,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( SV105 @ SV722 )
= $false )
| ( ( ~ ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) )
= $true )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2833]) ).
thf(3033,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
| ~ ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2834]) ).
thf(3034,plain,
! [SV723: $i,SV387: $i,SV107: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV107 ) )
= $true )
| ( ( ~ ~ ( in @ SV861 @ SV387 )
| ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2835]) ).
thf(3035,plain,
! [SV724: $i,SV391: $i,SV111: $i] :
( ( ( ! [SY3619: $i] :
( ~ ( in @ SY3619 @ SV111 )
| ~ ( in @ SY3619 @ SV391 )
| ( in @ SY3619 @ SV724 ) ) )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(3036,plain,
! [SV725: $i,SV392: $i,SV112: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV112 ) )
= $true )
| ( ( ~ ~ ( in @ SV862 @ SV392 )
| ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(3037,plain,
! [SV114: $i,SV394: $i,SV592: $i] :
( ( ( in @ SV592 @ SV394 )
= $true )
| ( ( ~ ( in @ SV592 @ SV114 ) )
= $true )
| ( ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2841]) ).
thf(3038,plain,
! [SV801: $i,SV593: $i,SV117: $i,SV396: $o] :
( ( ( ~ ~ SV396 )
= $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) )
= $true )
| ( ( in @ SV801 @ SV117 )
= $false )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(3039,plain,
! [SV802: $i,SV594: $i,SV117: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) )
= $true )
| ( ( in @ SV802 @ SV117 )
= $false )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(3040,plain,
! [SV803: $i,SV595: $i,SV117: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) )
= $true )
| ( ( in @ SV803 @ SV117 )
= $false )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(3041,plain,
! [SV118: $i,SV726: $i,SV397: $i,SV863: $i] :
( ( ( ~ ( in @ SV863 @ ( binintersect @ SV397 @ SV726 ) ) )
= $true )
| ( ( in @ SV863 @ SV118 )
= $true )
| ( ( in @ SV726 @ ( powerset @ SV118 ) )
= $false )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(3042,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2846]) ).
thf(3043,plain,
! [SV400: $i > $o,SV121: $i] :
( ( ( ! [SY3110: $i] :
~ ~ ( ~ ( in @ SY3110 @ SV121 )
| ~ ( SV400 @ SY3110 ) ) )
= $true )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(3044,plain,
! [SV727: $i,SV401: $i,SV122: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ SV122 ) )
= $true )
| ( ( ~ ( in @ SV864 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SV864 @ ( setminus @ SV122 @ SV401 ) ) )
= $true )
| ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(3045,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( ~ ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 )
| ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV405 )
| ~ ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SY3768 ) @ SV601 )
| ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SY3768 ) ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2850]) ).
thf(3046,plain,
! [SV729: $i,SV406: $i,SV127: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ SV127 ) )
= $true )
| ( ( ~ ( in @ SV865 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SV865 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(3047,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) )
= $true )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(3048,plain,
! [SV731: $i,SV409: $i,SV132: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ SV132 ) )
= $true )
| ( ( ~ ( in @ SV866 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SV866 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) )
= $true )
| ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(3049,plain,
! [SV732: $i,SV411: $i,SV134: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV134 ) )
= $true )
| ( ( ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SV867 @ SV411 )
| ( in @ SV867 @ SV732 ) )
= $true )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(3050,plain,
! [SV806: $i,SV605: $i,SV413: $i,SV137: $i] :
( ( ( ~ ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3703 )
= ( ap @ SV137 @ SV413 @ SV806 @ SY3703 ) ) ) )
= $true )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2856]) ).
thf(3051,plain,
! [SV807: $i,SV138: $i,SV606: $i,SV414: $o] :
( ( ( ~ SV414 ) = $true )
| ( ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3704: $i] :
( ~ ( ~ SV414
| ( SY3704 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3704 != SV807 ) ) ) ) )
= $true )
| ( ( in @ SV807 @ SV138 )
= $false )
| ( ( in @ SV606 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3052,plain,
! [SV808: $i,SV138: $i,SV607: $i] :
( ( ( ~ $true ) = $true )
| ( ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3705: $i] :
( ~ ( ~ $true
| ( SY3705 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3705 != SV808 ) ) ) ) )
= $true )
| ( ( in @ SV808 @ SV138 )
= $false )
| ( ( in @ SV607 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3053,plain,
! [SV809: $i,SV138: $i,SV608: $i] :
( ( ( ~ $false ) = $true )
| ( ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3706: $i] :
( ~ ( ~ $false
| ( SY3706 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3706 != SV809 ) ) ) ) )
= $true )
| ( ( in @ SV809 @ SV138 )
= $false )
| ( ( in @ SV608 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(3054,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( SV139 @ SV733 )
= $false )
| ( ( ~ ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) )
= $true )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2860]) ).
thf(3055,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2861]) ).
thf(3056,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2862]) ).
thf(3057,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( ~ ( in @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SV142 )
| ~ ~ ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2863]) ).
thf(3058,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( ~ ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2864]) ).
thf(3059,plain,
! [SV419: $i,SV735: $i > $o,SV144: $i] :
( ( ( ! [SY3747: $i] :
( ~ ( in @ SY3747 @ SV144 )
| ~ ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SY3747 ) @ SV419 )
| ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SY3747 ) ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2864]) ).
thf(3060,plain,
! [SV736: $i,SV420: $i,SV145: $i,SV868: $i] :
( ( ( ~ ( in @ SV868 @ ( powerset @ SV145 ) ) )
= $true )
| ( ( ~ ( subset @ SV420 @ SV868 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SV868 ) )
= $true )
| ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2865]) ).
thf(3061,plain,
! [SV611: $i,SV147: $i,SV810: $i,SV422: $o] :
( ( ( ~ ~ SV422 )
= $true )
| ( ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) )
= $true )
| ( ( in @ SV810 @ SV147 )
= $false )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2866]) ).
thf(3062,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) )
= $true )
| ( ( in @ SV811 @ SV147 )
= $false )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(3063,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) )
= $true )
| ( ( in @ SV812 @ SV147 )
= $false )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3064,plain,
! [SV813: $i,SV614: $i,SV149: $i,SV423: $o] :
( ( ( ~ ~ SV423 )
= $true )
| ( ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 )
= $true )
| ( ( in @ SV813 @ SV149 )
= $false )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3065,plain,
! [SV814: $i,SV615: $i,SV149: $i] :
( ( ( ~ ~ $true )
= $true )
| ( ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 )
= $true )
| ( ( in @ SV814 @ SV149 )
= $false )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2870]) ).
thf(3066,plain,
! [SV815: $i,SV616: $i,SV149: $i] :
( ( ( ~ ~ $false )
= $true )
| ( ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 )
= $true )
| ( ( in @ SV815 @ SV149 )
= $false )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3067,plain,
! [SV737: $i,SV151: $i,SV425: $i] :
( ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( ! [SY3636: $i] :
( ~ ( in @ SY3636 @ SV151 )
| ~ ( in @ SY3636 @ SV737 )
| ( in @ SY3636 @ ( setminus @ SV151 @ SV425 ) ) ) )
= $true )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2872]) ).
thf(3068,plain,
! [SV738: $i,SV426: $i,SV152: $i,SV869: $i] :
( ( ( ~ ( in @ SV869 @ ( powerset @ SV152 ) ) )
= $true )
| ( ( ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SV869 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) ) )
= $true )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2873]) ).
thf(3069,plain,
! [SV739: $i,SV427: $i,SV154: $i,SV870: $i] :
( ( ( ~ ( in @ SV870 @ ( powerset @ SV154 ) ) )
= $true )
| ( ( ! [SY3748: $i] :
( ~ ( in @ SY3748 @ SV154 )
| ~ ( in @ SY3748 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3748 @ ( binunion @ SV427 @ SV870 ) ) ) )
= $true )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3070,plain,
! [SV428: $i > $o,SV155: $i,SV816: $i] :
( ( ( ~ ( in @ SV816 @ SV155 ) )
= $true )
| ( ( ~ ( SV428 @ SV816 ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3071,plain,
! [SV740: $i,SV429: $i,SV156: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ SV156 ) )
= $true )
| ( ( ~ ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) ) )
= $true )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3072,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2877]) ).
thf(3073,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2878]) ).
thf(3074,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(3075,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
| ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2879]) ).
thf(3076,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( ~ ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) ) )
= $true )
| ( ( SV433 @ SV619 )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3077,plain,
! [SV160: $i,SV619: $i,SV433: $i > $o] :
( ( ( ~ ( SV433 @ SV619 ) )
= $true )
| ( ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3078,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( ~ ( in @ ( sK24_SY3199 @ SV440 @ SV168 ) @ SV168 ) )
= $false )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3079,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( ~ ( SV440 @ ( sK24_SY3199 @ SV440 @ SV168 ) ) )
= $false )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2885]) ).
thf(3080,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( SV625 = SV169 )
= $true )
| ( ( in @ SV625 @ SV441 )
= $true )
| ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3081,plain,
! [SV441: $i,SV169: $i,SV625: $i] :
( ( ( SV625 = SV169 )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(3082,plain,
! [SV169: $i,SV441: $i,SV625: $i] :
( ( ( in @ SV625 @ SV441 )
= $false )
| ( ( in @ SV625 @ ( setadjoin @ SV169 @ SV441 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2887]) ).
thf(3083,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ! [SY3769: $i] :
~ ( ~ ( ~ ( in @ SY3769 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3769 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3769 ) )
| ( in @ SY3769 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) ) ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2888]) ).
thf(3084,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
| ~ ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) ) )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2889]) ).
thf(3085,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( ~ ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 )
| ! [SY3772: $i] :
( ~ ( in @ SY3772 @ SV445 )
| ~ ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SY3772 ) @ SV627 )
| ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SY3772 ) ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2890]) ).
thf(3086,plain,
! [SV177: $i,SV449: $i] :
( ( ( ! [SY3217: $i] :
( ~ ( in @ SY3217 @ SV449 )
| ( in @ SY3217 @ SV177 ) ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2891]) ).
thf(3087,plain,
! [SV449: $i,SV177: $i] :
( ( ( ~ ( in @ ( sK54_SY3217 @ SV177 @ SV449 ) @ SV449 )
| ( in @ ( sK54_SY3217 @ SV177 @ SV449 ) @ SV177 ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2892]) ).
thf(3088,plain,
! [SV180: $i,SV631: $i,SV820: $i,SV452: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV452 )
| ~ ( in @ ( kpair @ SV820 @ SV898 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SV898 ) )
= $true )
| ( ( in @ SV820 @ SV180 )
= $false )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2894]) ).
thf(3089,plain,
! [SV743: $i,SV455: $i,SV185: $i] :
( ( ( ! [SY3644: $i] :
( ~ ( in @ SY3644 @ SV185 )
| ! [SY3645: $i] :
( ~ ( in @ SY3645 @ SV185 )
| ~ ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV455 )
| ( in @ ( kpair @ SY3644 @ SY3645 ) @ SV743 ) ) ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3090,plain,
! [SV744: $i,SV457: $i,SV187: $i,SV873: $i] :
( ( ( ~ ( in @ SV873 @ ( powerset @ SV187 ) ) )
= $true )
| ( ( ! [SY3750: $i] :
( ~ ( in @ SY3750 @ SV187 )
| ~ ( in @ SY3750 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3750 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) ) )
= $true )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3091,plain,
! [SV458: $i,SV745: $i,SV188: $i,SV874: $i] :
( ( ( ~ ( in @ SV874 @ SV188 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV874 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SV874 ) @ SV458 ) )
= $true )
| ( ( in @ SV745 @ SV188 )
= $false )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3092,plain,
! [SV189: $i,SV746: $o,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) ) )
= $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(3093,plain,
! [SV459: $i,SV189: $i,SV746: $o] :
( ( ( ~ ( in @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) @ SV189 )
| SV746 )
= $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(3094,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK43_SX0 @ SV189 @ SV459 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3095,plain,
! [SV459: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK43_SX0 @ SV189 @ SV459 ) @ SV189 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2899]) ).
thf(3096,plain,
! [SV189: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK44_SX0 @ SV189 @ SV459 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(3097,plain,
! [SV459: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK44_SX0 @ SV189 @ SV459 ) @ SV189 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2900]) ).
thf(3098,plain,
! [SV747: $i,SV462: $i,SV192: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ SV192 ) )
= $true )
| ( ( ~ ~ ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(3099,plain,
! [SV748: $i,SV463: $i,SV193: $i,SV876: $i] :
( ( ( ~ ( in @ SV876 @ SV193 ) )
= $true )
| ( ( ~ ( in @ SV876 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SV876 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(3100,plain,
! [SV749: $i,SV464: $i,SV194: $i,SV877: $i] :
( ( ( ~ ( in @ SV877 @ ( powerset @ SV194 ) ) )
= $true )
| ( ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SV877 ) @ ( binunion @ SV749 @ SV877 ) ) ) )
= $true )
| ( ( in @ SV749 @ ( powerset @ SV194 ) )
= $false )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2903]) ).
thf(3101,plain,
! [SV821: $o,SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 != SV195 )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3102,plain,
! [SV195: $i,SV465: $i,SV635: $i,SV821: $o] :
( ( SV821 = $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2904]) ).
thf(3103,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 != SV195 )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3104,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2905]) ).
thf(3105,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 != SV195 )
= $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3106,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2906]) ).
thf(3107,plain,
! [SV197: $i,SV467: $i] :
( ( ( ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV197 )
| ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV467 ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2907]) ).
thf(3108,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ( in @ ( sK26_SY3253 @ SV471 @ SV201 ) @ SV201 ) )
= $false )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3109,plain,
! [SV201: $i,SV471: $i] :
( ( ( ~ ( in @ SV471 @ ( sK26_SY3253 @ SV471 @ SV201 ) ) )
= $false )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2909]) ).
thf(3110,plain,
! [SV752: $i,SV474: $i,SV204: $i,SV878: $i] :
( ( ( ~ ( in @ SV878 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( ! [SY3751: $i] :
( ~ ( in @ SY3751 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SY3751 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SY3751 ) ) ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3111,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) )
= $true )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(3112,plain,
! [SV823: $i,SV641: $i,SV214: $i,SV482: $o] :
( ( ( ~ SV482 ) = $true )
| ( ( ( if @ SV214 @ SV482 @ SV641 @ SV823 )
= SV641 )
= $true )
| ( ( in @ SV823 @ SV214 )
= $false )
| ( ( in @ SV641 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2913]) ).
thf(3113,plain,
! [SV824: $i,SV642: $i,SV214: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( if @ SV214 @ $true @ SV642 @ SV824 )
= SV642 )
= $true )
| ( ( in @ SV824 @ SV214 )
= $false )
| ( ( in @ SV642 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3114,plain,
! [SV825: $i,SV643: $i,SV214: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( if @ SV214 @ $false @ SV643 @ SV825 )
= SV643 )
= $true )
| ( ( in @ SV825 @ SV214 )
= $false )
| ( ( in @ SV643 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2915]) ).
thf(3115,plain,
! [SV755: $i,SV483: $i,SV215: $i,SV879: $i] :
( ( ( ~ ( in @ SV879 @ SV215 ) )
= $true )
| ( ( ! [SY3752: $i] :
( ~ ( in @ SY3752 @ SV215 )
| ~ ( in @ ( kpair @ SV879 @ SY3752 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SY3752 ) @ ( binunion @ SV483 @ SV755 ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3116,plain,
! [SV756: $i,SV216: $i,SV484: $i] :
( ( ( subset @ SV484 @ ( setminus @ SV216 @ SV756 ) )
= $false )
| ( ( subset @ SV756 @ ( setminus @ SV216 @ SV484 ) )
= $true )
| ( ( in @ SV756 @ ( powerset @ SV216 ) )
= $false )
| ( ( in @ SV484 @ ( powerset @ SV216 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2917]) ).
thf(3117,plain,
! [SV219: $i,SV487: $i,SV645: $i] :
( ( ( in @ SV645 @ SV487 )
= $true )
| ( ( ~ ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) ) )
= $true )
| ( ( in @ SV645 @ SV219 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(3118,plain,
! [SV220: $i,SV488: $i,SV759: $i] :
( ( ( in @ SV759 @ SV488 )
= $false )
| ( ( ~ ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) ) )
= $true )
| ( ( in @ SV759 @ SV220 )
= $false )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2919]) ).
thf(3119,plain,
! [SV826: $i,SV489: $i > $o,SV221: $i] :
( ( ( ! [SY3278: $i] :
~ ~ ( ~ ( in @ SY3278 @ SV221 )
| ~ ~ ( SV489 @ SY3278 ) ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3120,plain,
! [SV760: $i,SV491: $i,SV223: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ SV223 ) )
= $true )
| ( ( ~ ( in @ SV880 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SV880 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) )
= $true )
| ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2921]) ).
thf(3121,plain,
! [SV647: $i,SV493: $i,SV225: $i] :
( ( ( subset @ SV225 @ SV493 )
= $false )
| ( ( in @ SV647 @ SV493 )
= $true )
| ( ( in @ SV647 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3122,plain,
! [SV827: $i,SV648: $i,SV494: $i,SV226: $i] :
( ( ( ~ ! [SY3714: $i] :
( ~ ( in @ SY3714 @ SV226 )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV494 )
| ~ ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV648 )
| ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV827 ) ) ) )
= $true )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2923]) ).
thf(3123,plain,
! [SV762: $i,SV500: $i,SV232: $i] :
( ( ( ! [SY3661: $i] :
( ~ ( in @ SY3661 @ SV232 )
| ~ ( in @ SY3661 @ SV500 )
| ( in @ SY3661 @ SV762 ) ) )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3124,plain,
! [SV763: $i,SV501: $i,SV233: $i] :
( ( ( ! [SY3662: $i] :
( ~ ( in @ SY3662 @ SV233 )
| ~ ( in @ SY3662 @ SV501 )
| ( in @ SY3662 @ SV763 ) ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3125,plain,
! [SV235: $i,SV503: $i,SV764: $i] :
( ( ( in @ SV764 @ SV503 )
= $false )
| ( ( in @ SV764 @ ( setminus @ SV235 @ ( setminus @ SV235 @ SV503 ) ) )
= $true )
| ( ( in @ SV764 @ SV235 )
= $false )
| ( ( in @ SV503 @ ( powerset @ SV235 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2927]) ).
thf(3126,plain,
! [SV765: $i,SV506: $i,SV238: $i,SV881: $i] :
( ( ( ~ ( in @ SV881 @ ( powerset @ SV238 ) ) )
= $true )
| ( ( ! [SY3753: $i] :
( ~ ( in @ SY3753 @ SV238 )
| ~ ( in @ SY3753 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3753 @ ( binunion @ SV765 @ SV881 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2931]) ).
thf(3127,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV882: $i] :
( ( ( ~ ( in @ SV882 @ SV240 ) )
= $true )
| ( ( ! [SY3754: $i] :
( ~ ( in @ SY3754 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3754 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3755: $o] :
( ~ ! [SY3756: $i] :
( ~ ( in @ SY3756 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3756 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3756 @ SY3754 ) @ SV766 )
| SY3755 )
| SY3755 ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2932]) ).
thf(3128,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( ~ ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3129,plain,
! [SV509: $i,SV767: $i > $o,SV241: $i] :
( ( ( ! [SY3757: $i] :
( ~ ( in @ SY3757 @ SV241 )
| ~ ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SY3757 ) @ SV509 )
| ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SY3757 ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3130,plain,
! [SV768: $i,SV510: $i,SV242: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ SV242 ) )
= $true )
| ( ( ~ ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SV883 @ SV510 ) )
= $true )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3131,plain,
! [SV769: $i,SV511: $i,SV243: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ SV243 ) )
= $true )
| ( ( ~ ( in @ SV884 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SV884 @ ( setminus @ SV243 @ SV769 ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3132,plain,
! [SV657: $i > $i > $o,SV249: $i,SV694: $i,SV517: $i,SV847: $i] :
( ( ( in @ SV847 @ SV517 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV694 @ SV847 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
| ( SV657 @ SV694 @ SV847 ) )
= $true )
| ( ( in @ SV694 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2936]) ).
thf(3133,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
| ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 ) ) )
= $true )
| ( ( ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3134,plain,
! [SV832: $i,SV658: $i,SV518: $i,SV251: $i] :
( ( ( ~ ! [SY3716: $i] :
( ~ ( in @ SY3716 @ SV251 )
| ! [SY3717: $i] :
( ~ ( in @ SY3717 @ SV518 )
| ~ ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV658 )
| ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV832 ) ) ) )
= $true )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3135,plain,
! [SV771: $i,SV519: $i,SV252: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ SV252 ) )
= $true )
| ( ( ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SV885 @ SV771 )
| ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3136,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
| ~ ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2940]) ).
thf(3137,plain,
! [SV773: $i,SV524: $i,SV258: $i,SV886: $i] :
( ( ( ~ ( in @ SV886 @ SV258 ) )
= $true )
| ( ( ! [SY3758: $i] :
( ~ ( in @ SY3758 @ SV258 )
| ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3759 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3759 @ SY3758 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SY3758 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2941]) ).
thf(3138,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ! [SY3679: $i] :
( ~ ( in @ SY3679 @ SV259 )
| ! [SY3680: $i] :
( ~ ( in @ SY3680 @ SV259 )
| ~ ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV525 )
| ( in @ ( kpair @ SY3679 @ SY3680 ) @ SV774 ) ) ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2942]) ).
thf(3139,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3140,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2943]) ).
thf(3141,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) )
= $true )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3142,plain,
! [SV776: $i,SV529: $i,SV264: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ SV264 ) )
= $true )
| ( ( ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SV887 @ SV776 )
| ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2946]) ).
thf(3143,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ( ~ ( in @ ( sK46_SY2861 @ SV777 @ SV265 ) @ SV265 )
| ~ ~ ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(3144,plain,
! [SV272: $i,SV778: $i,SV534: $i] :
( ( ( subset @ SV534 @ SV778 )
= $false )
| ( ( subset @ ( setminus @ SV272 @ SV778 ) @ ( setminus @ SV272 @ SV534 ) )
= $true )
| ( ( in @ SV778 @ ( powerset @ SV272 ) )
= $false )
| ( ( in @ SV534 @ ( powerset @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3145,plain,
! [SV779: $i,SV537: $i,SV275: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ SV275 ) )
= $true )
| ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2951]) ).
thf(3146,plain,
! [SV540: $i > $o,SV278: $i,SV838: $i] :
( ( ( ~ ( in @ SV838 @ SV278 ) )
= $true )
| ( ( ~ ~ ( SV540 @ SV838 ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2954]) ).
thf(3147,plain,
! [SV541: $i,SV780: $i,SV279: $i,SV889: $i] :
( ( ( ~ ( in @ SV889 @ SV279 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV780 @ SV889 ) @ SV541 )
| ( in @ ( kpair @ SV889 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) )
= $true )
| ( ( in @ SV780 @ SV279 )
= $false )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2955]) ).
thf(3148,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV280 )
| ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV899 )
= ( SV668 @ SV899 ) ) )
= $true )
| ( ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2956]) ).
thf(3149,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV890: $i] :
( ( ( ~ ( in @ SV890 @ SV280 ) )
= $true )
| ( ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV890 )
= ( SV668 @ SV890 ) )
= $true )
| ( ( in @ ( SV668 @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) ) @ SV542 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2957]) ).
thf(3150,plain,
! [SV284: $i] :
( ( ( ~ ( in @ ( sK30_SY2910 @ SV284 ) @ SV284 ) )
= $false )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2959]) ).
thf(3151,plain,
! [SV284: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2959]) ).
thf(3152,plain,
! [SV671: $i,SV546: $i,SV285: $i] :
( ( ( SV285 = SV546 )
= $false )
| ( ( in @ SV671 @ SV546 )
= $true )
| ( ( in @ SV671 @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2960]) ).
thf(3153,plain,
! [SV287: $i,SV673: $i,SV839: $i,SV548: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV548 )
| ~ ( in @ ( kpair @ SV839 @ SV900 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SV900 ) )
= $true )
| ( ( in @ SV839 @ SV287 )
= $false )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2962]) ).
thf(3154,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) )
= $true )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2966]) ).
thf(3155,plain,
! [SV843: $i,SV680: $i,SV296: $i,SV555: $o] :
( ( ( ~ SV555 ) = $true )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3726: $i] :
( ~ ( ~ SV555
| ( SY3726 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3726 != SV843 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) )
= $true )
| ( ( in @ SV843 @ SV296 )
= $false )
| ( ( in @ SV680 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2968]) ).
thf(3156,plain,
! [SV844: $i,SV681: $i,SV296: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3727: $i] :
( ~ ( ~ $true
| ( SY3727 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3727 != SV844 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) )
= $true )
| ( ( in @ SV844 @ SV296 )
= $false )
| ( ( in @ SV681 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2969]) ).
thf(3157,plain,
! [SV845: $i,SV682: $i,SV296: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3728: $i] :
( ~ ( ~ $false
| ( SY3728 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3728 != SV845 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) )
= $true )
| ( ( in @ SV845 @ SV296 )
= $false )
| ( ( in @ SV682 @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2970]) ).
thf(3158,plain,
! [SV699: $i,SV322: $i,SV37: $i,SV848: $i] :
( ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( ! [SY3735: $i] :
( ~ ( in @ SY3735 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SY3735 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SY3735 ) ) ) )
= $true )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3159,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ! [SY3590: $i] :
( ~ ( SV38 @ SY3590 )
| ( SV700 = SY3590 ) ) )
= $false )
| ( ( SV38 @ SV700 )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2972]) ).
thf(3160,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) @ SV44 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2974]) ).
thf(3161,plain,
! [SV44: $i,SV702: $i > $o,SV784: $i > $o,SV328: $i] :
( ( ( ! [SY3762: $i] :
( ~ ( in @ SY3762 @ SV328 )
| ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
!= SY3762 )
| ~ ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ SY3762 ) )
| ~ ( ~ ( SV784 @ SY3762 )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2974]) ).
thf(3162,plain,
! [SV45: $i] :
( ( ~ ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2975]) ).
thf(3163,plain,
! [SV45: $i] :
( ( ! [SY3406: $i,SY3407: $i] :
( ~ ~ ( ~ ( in @ SY3406 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3407 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3406 )
| ( in @ SX4 @ SY3407 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY3407 )
| ( in @ SX4 @ SY3406 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2976]) ).
thf(3164,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ( ~ ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) )
| ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) ) )
= $false )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3165,plain,
! [SV703: $i,SV329: $i > $o,SV46: $i,SV850: $i] :
( ( ( in @ SV850 @ SV46 )
= $false )
| ( ( ~ ( SV329 @ SV703 )
| ~ ( SV329 @ SV850 )
| ( SV703 = SV850 ) )
= $true )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3166,plain,
! [SV52: $i] :
( ( ( ~ ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
| ~ ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 ) ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2979]) ).
thf(3167,plain,
! [SV52: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ omega )
| ( in @ SV901 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK39_SY2254 @ SV52 ) @ ( sK39_SY2254 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2980]) ).
thf(3168,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ( ~ ( in @ SV333 @ ( sK48_SY2973 @ SV53 @ SV333 ) )
| ~ ( in @ ( sK48_SY2973 @ SV53 @ SV333 ) @ SV53 ) ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3169,plain,
! [SV53: $i,SV891: $i,SV333: $i] :
( ( ( ~ ( ~ ( in @ SV333 @ SV891 )
| ~ ( in @ SV891 @ SV53 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2982]) ).
thf(3170,plain,
! [SV54: $i,SV334: $i > $o,SV564: $i] :
( ( ( ~ ( in @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) @ SV54 )
| ~ ( SV334 @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) )
| ( ( sK55_SY3420 @ SV564 @ SV334 @ SV54 )
= SV564 ) )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2983]) ).
thf(3171,plain,
! [SV704: $i,SV337: $i,SV57: $i,SV851: $i] :
( ( ( in @ SV851 @ SV57 )
= $false )
| ( ( ~ ( in @ SV851 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
| ( in @ SV851 @ ( setminus @ SV57 @ SV337 ) ) )
= $true )
| ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3172,plain,
! [SV339: $i,SV59: $i,SV705: $i] :
( ( ( in @ SV705 @ ( setminus @ SV59 @ SV339 ) )
= $true )
| ( ( in @ SV705 @ SV339 )
= $true )
| ( ( in @ SV705 @ SV59 )
= $false )
| ( ( in @ SV339 @ ( powerset @ SV59 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2985]) ).
thf(3173,plain,
! [SV786: $i,SV568: $i,SV341: $i,SV61: $i] :
( ( ( ! [SY3692: $i] :
( ~ ( in @ SY3692 @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ SY3692 )
= ( ap @ SV61 @ SV341 @ SV786 @ SY3692 ) ) ) )
= $false )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3174,plain,
! [SV707: $i,SV343: $i,SV63: $i,SV852: $i] :
( ( ( in @ SV852 @ SV63 )
= $false )
| ( ( ~ ~ ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) )
| ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3175,plain,
! [SV344: $i,SV708: $i,SV64: $i,SV853: $i] :
( ( ( in @ SV853 @ ( powerset @ SV64 ) )
= $false )
| ( ( ~ ( subset @ SV708 @ SV853 )
| ( subset @ ( binintersect @ SV344 @ SV708 ) @ SV853 ) )
= $true )
| ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3176,plain,
! [SV345: $i,SV709: $i,SV65: $i,SV854: $i] :
( ( ( in @ SV854 @ SV65 )
= $false )
| ( ( ~ ~ ( in @ SV854 @ SV709 )
| ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3177,plain,
! [SV711: $i,SV348: $i,SV68: $i,SV855: $i] :
( ( ( in @ SV855 @ SV68 )
= $false )
| ( ( ! [SY3743: $i] :
( ~ ( in @ SY3743 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3743 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3744: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3744 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3744 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3744 @ SY3743 ) @ SV711 ) ) ) )
= $true )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2992]) ).
thf(3178,plain,
! [SV712: $i,SV349: $i,SV69: $i,SV856: $i] :
( ( ( in @ SV856 @ SV69 )
= $false )
| ( ( ~ ( in @ SV856 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
| ( in @ SV856 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) ) )
= $true )
| ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2993]) ).
thf(3179,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV892: $i] :
( ( ( ~ ( in @ SV892 @ SV70 ) )
= $true )
| ( ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV892 )
= ( SV569 @ SV892 ) )
= $true )
| ( ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2994]) ).
thf(3180,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV857: $i] :
( ( ( in @ SV857 @ SV70 )
= $false )
| ( ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV857 )
= ( SV569 @ SV857 ) )
= $true )
| ( ( in @ ( SV569 @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) ) @ SV350 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3181,plain,
! [SV351: $i,SV71: $i,SV846: $i,SV685: $i,SV570: $i > $i > $o] :
( ( ( ~ ( SV570 @ SV685 @ SV846 ) )
= $true )
| ( ( in @ ( kpair @ SV685 @ SV846 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) )
= $true )
| ( ( in @ SV846 @ SV351 )
= $false )
| ( ( in @ SV685 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2996]) ).
thf(3182,plain,
! [SV573: $i > $i > $o,SV74: $i,SV354: $i,SV893: $i] :
( ( ( ~ ( in @ SV893 @ ( breln1Set @ SV354 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV354 @ SV893 )
| ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3765: $i] :
~ ( ~ ( SV573 @ SY3764 @ SY3765 )
| ~ ! [SY3766: $i] :
( ~ ( in @ SY3766 @ SV354 )
| ~ ( SV573 @ SY3764 @ SY3766 )
| ( in @ ( kpair @ SY3765 @ SY3766 ) @ SV893 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2997]) ).
thf(3183,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i,SV894: $i] :
( ( ( ~ ( ~ ( in @ SV894 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 ) ) )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3184,plain,
! [SV76: $i,SV356: $i > $o,SV789: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) @ SV76 )
| ~ ~ ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) ) ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2999]) ).
thf(3185,plain,
( ( ~ ( in @ sK49_SY3731 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3186,plain,
( ( ~ ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ sK8_SY3448 )
| ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3001]) ).
thf(3187,plain,
! [SV358: $i,SV790: $i,SV78: $i,SV714: $i] :
( ( ( in @ SV714 @ SV78 )
= $false )
| ( ( in @ SV790 @ SV358 )
= $true )
| ( ( SV714 = SV790 )
= $false )
| ( ( SV78 = SV358 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3188,plain,
! [SV791: $i,SV577: $i,SV361: $i,SV81: $i] :
( ( ( ! [SY3694: $i] :
( ~ ( in @ SY3694 @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ SY3694 )
= ( ap @ SV81 @ SV361 @ SV791 @ SY3694 ) ) ) )
= $false )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3189,plain,
! [SV82: $i,SV362: $i,SV858: $i] :
( ( ( in @ SV858 @ SV362 )
= $false )
| ( ( in @ SV858 @ SV82 )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3004]) ).
thf(3190,plain,
! [SV362: $i,SV82: $i] :
( ( ( in @ ( sK40_SY3049 @ SV82 @ SV362 ) @ SV362 )
= $true )
| ( ( in @ SV362 @ ( powerset @ SV82 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3191,plain,
! [SV363: $i,SV792: $i,SV83: $i,SV715: $i] :
( ( ( ~ ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) ) )
= $false )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3192,plain,
! [SV83: $i,SV715: $i,SV363: $i,SV792: $i] :
( ( ( ~ ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) ) )
= $false )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3007]) ).
thf(3193,plain,
! [SV859: $o,SV716: $i,SV365: $i,SV85: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3194,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV896 @ SV365 )
| $true )
| ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3009]) ).
thf(3195,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV85 ) )
= $true )
| ( ( ~ ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV897 @ SV365 )
| $false )
| ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3010]) ).
thf(3196,plain,
! [SV688: $o,SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ SV86 )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 )
| SV688 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3011]) ).
thf(3197,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 ) )
= $true )
| ( SV688 = $true )
| ( SV688 = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3012]) ).
thf(3198,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ SV86 )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true )
| $true )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3013]) ).
thf(3199,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3014]) ).
thf(3200,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( ( in @ SV578 @ SV86 )
= $true )
| ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false )
| $false )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3015]) ).
thf(3201,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3016]) ).
thf(3202,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3017]) ).
thf(3203,plain,
! [SV795: $o,SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3204,plain,
! [SV373: $i,SV93: $i,SV584: $i,SV795: $o] :
( ( SV795 = $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3018]) ).
thf(3205,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3019]) ).
thf(3206,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3020]) ).
thf(3207,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3020]) ).
thf(3208,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3021]) ).
thf(3209,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3210,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3022]) ).
thf(3211,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
| ~ ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
| ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3023]) ).
thf(3212,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3213,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
| ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
= $false )
| ( ( ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3025]) ).
thf(3214,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3026]) ).
thf(3215,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3027]) ).
thf(3216,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3028]) ).
thf(3217,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ~ ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3218,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3029]) ).
thf(3219,plain,
! [SV721: $i,SV385: $i,SV104: $i,SV860: $i] :
( ( ( in @ SV860 @ ( powerset @ SV104 ) )
= $false )
| ( ( in @ ( binintersect @ SV385 @ SV721 ) @ ( powerset @ ( binintersect @ ( binunion @ SV385 @ SV860 ) @ ( binunion @ SV721 @ SV860 ) ) ) )
= $true )
| ( ( in @ SV721 @ ( powerset @ SV104 ) )
= $false )
| ( ( in @ SV385 @ ( powerset @ SV104 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3220,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ! [SY3617: $i] :
( ~ ( SV105 @ SY3617 )
| ( SV722 = SY3617 ) ) )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3221,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3222,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( ~ ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) ) )
= $false )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3033]) ).
thf(3223,plain,
! [SV723: $i,SV387: $i,SV107: $i,SV861: $i] :
( ( ( in @ SV861 @ SV107 )
= $false )
| ( ( ~ ~ ( in @ SV861 @ SV387 )
| ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3224,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
| ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 ) )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3035]) ).
thf(3225,plain,
! [SV725: $i,SV392: $i,SV112: $i,SV862: $i] :
( ( ( in @ SV862 @ SV112 )
= $false )
| ( ( ~ ~ ( in @ SV862 @ SV392 )
| ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3226,plain,
! [SV394: $i,SV114: $i,SV592: $i] :
( ( ( in @ SV592 @ SV114 )
= $false )
| ( ( in @ SV592 @ SV394 )
= $true )
| ( ( in @ SV592 @ ( setminus @ SV114 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3227,plain,
! [SV801: $i,SV593: $i,SV117: $i,SV396: $o] :
( ( ( ~ SV396 ) = $false )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) )
= $true )
| ( ( in @ SV801 @ SV117 )
= $false )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3038]) ).
thf(3228,plain,
! [SV802: $i,SV594: $i,SV117: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) )
= $true )
| ( ( in @ SV802 @ SV117 )
= $false )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3039]) ).
thf(3229,plain,
! [SV803: $i,SV595: $i,SV117: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) )
= $true )
| ( ( in @ SV803 @ SV117 )
= $false )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3040]) ).
thf(3230,plain,
! [SV118: $i,SV726: $i,SV397: $i,SV863: $i] :
( ( ( in @ SV863 @ ( binintersect @ SV397 @ SV726 ) )
= $false )
| ( ( in @ SV863 @ SV118 )
= $true )
| ( ( in @ SV726 @ ( powerset @ SV118 ) )
= $false )
| ( ( in @ SV397 @ ( powerset @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3041]) ).
thf(3231,plain,
! [SV400: $i > $o,SV121: $i,SV902: $i] :
( ( ( ~ ~ ( ~ ( in @ SV902 @ SV121 )
| ~ ( SV400 @ SV902 ) ) )
= $true )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3042]) ).
thf(3232,plain,
! [SV400: $i > $o,SV121: $i,SV903: $i] :
( ( ( ~ ~ ( ~ ( in @ SV903 @ SV121 )
| ~ ( SV400 @ SV903 ) ) )
= $true )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3043]) ).
thf(3233,plain,
! [SV727: $i,SV401: $i,SV122: $i,SV864: $i] :
( ( ( in @ SV864 @ SV122 )
= $false )
| ( ( ~ ( in @ SV864 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
| ( in @ SV864 @ ( setminus @ SV122 @ SV401 ) ) )
= $true )
| ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3044]) ).
thf(3234,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( ~ ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3235,plain,
! [SV126: $i,SV601: $i,SV805: $i > $o,SV405: $i] :
( ( ( ! [SY3768: $i] :
( ~ ( in @ SY3768 @ SV405 )
| ~ ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SY3768 ) @ SV601 )
| ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SY3768 ) ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3045]) ).
thf(3236,plain,
! [SV729: $i,SV406: $i,SV127: $i,SV865: $i] :
( ( ( in @ SV865 @ SV127 )
= $false )
| ( ( ~ ( in @ SV865 @ ( setminus @ SV127 @ SV406 ) )
| ( in @ SV865 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) ) )
= $true )
| ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3237,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ! [SY3627: $i] :
( ~ ( SV129 @ SY3627 )
| ( SV730 = SY3627 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3238,plain,
! [SV731: $i,SV409: $i,SV132: $i,SV866: $i] :
( ( ( in @ SV866 @ SV132 )
= $false )
| ( ( ~ ( in @ SV866 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
| ( in @ SV866 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) ) )
= $true )
| ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3239,plain,
! [SV732: $i,SV411: $i,SV134: $i,SV867: $i] :
( ( ( in @ SV867 @ SV134 )
= $false )
| ( ( ~ ( in @ SV411 @ ( powerset @ SV732 ) )
| ~ ( in @ SV867 @ SV411 )
| ( in @ SV867 @ SV732 ) )
= $true )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3240,plain,
! [SV806: $i,SV605: $i,SV413: $i,SV137: $i] :
( ( ( ! [SY3703: $i] :
( ~ ( in @ SY3703 @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ SY3703 )
= ( ap @ SV137 @ SV413 @ SV806 @ SY3703 ) ) ) )
= $false )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3241,plain,
! [SV807: $i,SV138: $i,SV606: $i,SV414: $o] :
( ( SV414 = $false )
| ( ( in @ SV606
@ ( dsetconstr @ SV138
@ ^ [SY3704: $i] :
( ~ ( ~ SV414
| ( SY3704 != SV606 ) )
| ~ ( ~ ~ SV414
| ( SY3704 != SV807 ) ) ) ) )
= $true )
| ( ( in @ SV807 @ SV138 )
= $false )
| ( ( in @ SV606 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3051]) ).
thf(3242,plain,
! [SV808: $i,SV138: $i,SV607: $i] :
( ( $true = $false )
| ( ( in @ SV607
@ ( dsetconstr @ SV138
@ ^ [SY3705: $i] :
( ~ ( ~ $true
| ( SY3705 != SV607 ) )
| ~ ( ~ ~ $true
| ( SY3705 != SV808 ) ) ) ) )
= $true )
| ( ( in @ SV808 @ SV138 )
= $false )
| ( ( in @ SV607 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3243,plain,
! [SV809: $i,SV138: $i,SV608: $i] :
( ( $false = $false )
| ( ( in @ SV608
@ ( dsetconstr @ SV138
@ ^ [SY3706: $i] :
( ~ ( ~ $false
| ( SY3706 != SV608 ) )
| ~ ( ~ ~ $false
| ( SY3706 != SV809 ) ) ) ) )
= $true )
| ( ( in @ SV809 @ SV138 )
= $false )
| ( ( in @ SV608 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3244,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ! [SY3630: $i] :
( ~ ( SV139 @ SY3630 )
| ( SV733 = SY3630 ) ) )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3245,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3246,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3055]) ).
thf(3247,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
| ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
= $false )
| ( ( ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3056]) ).
thf(3248,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( ~ ( in @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SV142 ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3249,plain,
! [SV142: $i,SV610: $i,SV417: $i] :
( ( ( ~ ~ ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3057]) ).
thf(3250,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 )
= $true )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3058]) ).
thf(3251,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i] :
( ( ( ~ ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 )
| ~ ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
| ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3059]) ).
thf(3252,plain,
! [SV736: $i,SV420: $i,SV145: $i,SV868: $i] :
( ( ( in @ SV868 @ ( powerset @ SV145 ) )
= $false )
| ( ( ~ ( subset @ SV420 @ SV868 )
| ( subset @ ( binintersect @ SV420 @ SV736 ) @ SV868 ) )
= $true )
| ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3253,plain,
! [SV611: $i,SV147: $i,SV810: $i,SV422: $o] :
( ( ( ~ SV422 ) = $false )
| ( ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) )
= $true )
| ( ( in @ SV810 @ SV147 )
= $false )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3254,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( ( ~ $true ) = $false )
| ( ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) )
= $true )
| ( ( in @ SV811 @ SV147 )
= $false )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3255,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( ( ~ $false ) = $false )
| ( ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) )
= $true )
| ( ( in @ SV812 @ SV147 )
= $false )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3256,plain,
! [SV813: $i,SV614: $i,SV149: $i,SV423: $o] :
( ( ( ~ SV423 ) = $false )
| ( ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 )
= $true )
| ( ( in @ SV813 @ SV149 )
= $false )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3257,plain,
! [SV814: $i,SV615: $i,SV149: $i] :
( ( ( ~ $true ) = $false )
| ( ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 )
= $true )
| ( ( in @ SV814 @ SV149 )
= $false )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3258,plain,
! [SV815: $i,SV616: $i,SV149: $i] :
( ( ( ~ $false ) = $false )
| ( ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 )
= $true )
| ( ( in @ SV815 @ SV149 )
= $false )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3259,plain,
! [SV425: $i,SV737: $i,SV151: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV151 )
| ~ ( in @ SV904 @ SV737 )
| ( in @ SV904 @ ( setminus @ SV151 @ SV425 ) ) )
= $true )
| ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3260,plain,
! [SV738: $i,SV426: $i,SV152: $i,SV869: $i] :
( ( ( in @ SV869 @ ( powerset @ SV152 ) )
= $false )
| ( ( ~ ( subset @ SV426 @ SV738 )
| ~ ( subset @ SV426 @ SV869 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) ) )
= $true )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3068]) ).
thf(3261,plain,
! [SV739: $i,SV427: $i,SV154: $i,SV870: $i] :
( ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( ! [SY3748: $i] :
( ~ ( in @ SY3748 @ SV154 )
| ~ ( in @ SY3748 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SY3748 @ ( binunion @ SV427 @ SV870 ) ) ) )
= $true )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3069]) ).
thf(3262,plain,
! [SV428: $i > $o,SV155: $i,SV816: $i] :
( ( ( in @ SV816 @ SV155 )
= $false )
| ( ( ~ ( SV428 @ SV816 ) )
= $true )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3070]) ).
thf(3263,plain,
! [SV740: $i,SV429: $i,SV156: $i,SV871: $i] :
( ( ( in @ SV871 @ SV156 )
= $false )
| ( ( ~ ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) )
| ~ ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) ) )
= $true )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3264,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3072]) ).
thf(3265,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3073]) ).
thf(3266,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3074]) ).
thf(3267,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ~ ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3268,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3075]) ).
thf(3269,plain,
! [SV433: $i > $o,SV160: $i,SV619: $i] :
( ( ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3186: $i] : ( SV433 @ SY3186 ) ) )
= $false )
| ( ( SV433 @ SV619 )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3270,plain,
! [SV160: $i,SV619: $i,SV433: $i > $o] :
( ( ( SV433 @ SV619 )
= $false )
| ( ( in @ SV619
@ ( dsetconstr @ SV160
@ ^ [SY3187: $i] : ( SV433 @ SY3187 ) ) )
= $true )
| ( ( in @ SV619 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3271,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( in @ ( sK24_SY3199 @ SV440 @ SV168 ) @ SV168 )
= $true )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3078]) ).
thf(3272,plain,
! [SV168: $i,SV440: $i > $o] :
( ( ( SV440 @ ( sK24_SY3199 @ SV440 @ SV168 ) )
= $true )
| ( ( ex1 @ SV168
@ ^ [SY3198: $i] : ( SV440 @ SY3198 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3079]) ).
thf(3273,plain,
! [SV442: $i,SV170: $i > $i > $o] :
( ( ( ! [SY3769: $i] :
~ ( ~ ( ~ ( in @ SY3769 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3769 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3769 ) )
| ( in @ SY3769 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3083]) ).
thf(3274,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
| ~ ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3084]) ).
thf(3275,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( ~ ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3276,plain,
! [SV173: $i,SV627: $i,SV819: $i > $o,SV445: $i] :
( ( ( ! [SY3772: $i] :
( ~ ( in @ SY3772 @ SV445 )
| ~ ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SY3772 ) @ SV627 )
| ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SY3772 ) ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3085]) ).
thf(3277,plain,
! [SV449: $i,SV177: $i] :
( ( ( ~ ( in @ ( sK60_SY3217 @ SV177 @ SV449 ) @ SV449 )
| ( in @ ( sK60_SY3217 @ SV177 @ SV449 ) @ SV177 ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3086]) ).
thf(3278,plain,
! [SV449: $i,SV177: $i] :
( ( ( ~ ( in @ ( sK54_SY3217 @ SV177 @ SV449 ) @ SV449 ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3279,plain,
! [SV449: $i,SV177: $i] :
( ( ( in @ ( sK54_SY3217 @ SV177 @ SV449 ) @ SV177 )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3087]) ).
thf(3280,plain,
! [SV180: $i,SV631: $i,SV820: $i,SV452: $i,SV898: $i] :
( ( ( ~ ( in @ SV898 @ SV452 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV820 @ SV898 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SV898 ) )
= $true )
| ( ( in @ SV820 @ SV180 )
= $false )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3281,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( ~ ( in @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SV185 )
| ! [SY3774: $i] :
( ~ ( in @ SY3774 @ SV185 )
| ~ ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SY3774 ) @ SV455 )
| ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SY3774 ) @ SV743 ) ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3089]) ).
thf(3282,plain,
! [SV744: $i,SV457: $i,SV187: $i,SV873: $i] :
( ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( ! [SY3750: $i] :
( ~ ( in @ SY3750 @ SV187 )
| ~ ( in @ SY3750 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SY3750 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) ) )
= $true )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3283,plain,
! [SV458: $i,SV745: $i,SV188: $i,SV874: $i] :
( ( ( in @ SV874 @ SV188 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV874 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
| ( in @ ( kpair @ SV745 @ SV874 ) @ SV458 ) )
= $true )
| ( ( in @ SV745 @ SV188 )
= $false )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3091]) ).
thf(3284,plain,
! [SV189: $i,SV746: $o,SV459: $i] :
( ( ( in @ SV459 @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) )
= $true )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3285,plain,
! [SV459: $i,SV189: $i,SV746: $o] :
( ( ( ~ ( in @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) @ SV189 ) )
= $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3286,plain,
! [SV189: $i,SV459: $i,SV746: $o] :
( ( SV746 = $false )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3287,plain,
! [SV189: $i,SV459: $i] :
( ( ( in @ SV459 @ ( sK43_SX0 @ SV189 @ SV459 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3094]) ).
thf(3288,plain,
! [SV459: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK43_SX0 @ SV189 @ SV459 ) @ SV189 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3095]) ).
thf(3289,plain,
! [SV189: $i,SV459: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3095]) ).
thf(3290,plain,
! [SV189: $i,SV459: $i] :
( ( ( in @ SV459 @ ( sK44_SX0 @ SV189 @ SV459 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3096]) ).
thf(3291,plain,
! [SV459: $i,SV189: $i] :
( ( ( ~ ( in @ ( sK44_SX0 @ SV189 @ SV459 ) @ SV189 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3292,plain,
! [SV189: $i,SV459: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3293,plain,
! [SV747: $i,SV462: $i,SV192: $i,SV875: $i] :
( ( ( in @ SV875 @ SV192 )
= $false )
| ( ( ~ ~ ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) )
| ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3294,plain,
! [SV748: $i,SV463: $i,SV193: $i,SV876: $i] :
( ( ( in @ SV876 @ SV193 )
= $false )
| ( ( ~ ( in @ SV876 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
| ( in @ SV876 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3099]) ).
thf(3295,plain,
! [SV749: $i,SV464: $i,SV194: $i,SV877: $i] :
( ( ( in @ SV877 @ ( powerset @ SV194 ) )
= $false )
| ( ( in @ ( binintersect @ SV464 @ SV749 ) @ ( powerset @ ( binintersect @ ( binunion @ SV464 @ SV877 ) @ ( binunion @ SV749 @ SV877 ) ) ) )
= $true )
| ( ( in @ SV749 @ ( powerset @ SV194 ) )
= $false )
| ( ( in @ SV464 @ ( powerset @ SV194 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3296,plain,
! [SV821: $o,SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 = SV195 )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 )
| SV821 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3101]) ).
thf(3297,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 ) )
= $true )
| ( SV821 = $true )
| ( SV821 = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3102]) ).
thf(3298,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 = SV195 )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true )
| $true )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3299,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3104]) ).
thf(3300,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( ( SV635 = SV195 )
= $true )
| ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false )
| $false )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3105]) ).
thf(3301,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3106]) ).
thf(3302,plain,
! [SV197: $i,SV467: $i] :
( ( ( ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV197 ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3303,plain,
! [SV197: $i,SV467: $i] :
( ( ( ~ ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV467 ) )
= $false )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3107]) ).
thf(3304,plain,
! [SV201: $i,SV471: $i] :
( ( ( in @ ( sK26_SY3253 @ SV471 @ SV201 ) @ SV201 )
= $true )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3108]) ).
thf(3305,plain,
! [SV201: $i,SV471: $i] :
( ( ( in @ SV471 @ ( sK26_SY3253 @ SV471 @ SV201 ) )
= $true )
| ( ( in @ SV471 @ ( setunion @ SV201 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3109]) ).
thf(3306,plain,
! [SV752: $i,SV474: $i,SV204: $i,SV878: $i] :
( ( ( in @ SV878 @ ( powerset @ SV204 ) )
= $false )
| ( ( ! [SY3751: $i] :
( ~ ( in @ SY3751 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SY3751 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SY3751 ) ) ) ) ) )
= $true )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3307,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ! [SY3655: $i] :
( ~ ( SV207 @ SY3655 )
| ( SV753 = SY3655 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3308,plain,
! [SV823: $i,SV641: $i,SV214: $i,SV482: $o] :
( ( SV482 = $false )
| ( ( ( if @ SV214 @ SV482 @ SV641 @ SV823 )
= SV641 )
= $true )
| ( ( in @ SV823 @ SV214 )
= $false )
| ( ( in @ SV641 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3112]) ).
thf(3309,plain,
! [SV824: $i,SV642: $i,SV214: $i] :
( ( $true = $false )
| ( ( ( if @ SV214 @ $true @ SV642 @ SV824 )
= SV642 )
= $true )
| ( ( in @ SV824 @ SV214 )
= $false )
| ( ( in @ SV642 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3113]) ).
thf(3310,plain,
! [SV825: $i,SV643: $i,SV214: $i] :
( ( $false = $false )
| ( ( ( if @ SV214 @ $false @ SV643 @ SV825 )
= SV643 )
= $true )
| ( ( in @ SV825 @ SV214 )
= $false )
| ( ( in @ SV643 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3114]) ).
thf(3311,plain,
! [SV755: $i,SV483: $i,SV215: $i,SV879: $i] :
( ( ( in @ SV879 @ SV215 )
= $false )
| ( ( ! [SY3752: $i] :
( ~ ( in @ SY3752 @ SV215 )
| ~ ( in @ ( kpair @ SV879 @ SY3752 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SY3752 ) @ ( binunion @ SV483 @ SV755 ) ) ) )
= $true )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3115]) ).
thf(3312,plain,
! [SV487: $i,SV219: $i,SV645: $i] :
( ( ( in @ SV645 @ ( symdiff @ SV219 @ SV487 ) )
= $false )
| ( ( in @ SV645 @ SV487 )
= $true )
| ( ( in @ SV645 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3117]) ).
thf(3313,plain,
! [SV488: $i,SV220: $i,SV759: $i] :
( ( ( in @ SV759 @ ( setminus @ SV220 @ SV488 ) )
= $false )
| ( ( in @ SV759 @ SV488 )
= $false )
| ( ( in @ SV759 @ SV220 )
= $false )
| ( ( in @ SV488 @ ( powerset @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3118]) ).
thf(3314,plain,
! [SV221: $i,SV489: $i > $o,SV826: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) @ SV221 )
| ~ ~ ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) ) ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3119]) ).
thf(3315,plain,
! [SV760: $i,SV491: $i,SV223: $i,SV880: $i] :
( ( ( in @ SV880 @ SV223 )
= $false )
| ( ( ~ ( in @ SV880 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
| ( in @ SV880 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) ) )
= $true )
| ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3120]) ).
thf(3316,plain,
! [SV827: $i,SV648: $i,SV494: $i,SV226: $i] :
( ( ( ! [SY3714: $i] :
( ~ ( in @ SY3714 @ SV226 )
| ! [SY3715: $i] :
( ~ ( in @ SY3715 @ SV494 )
| ~ ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV648 )
| ( in @ ( kpair @ SY3714 @ SY3715 ) @ SV827 ) ) ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3122]) ).
thf(3317,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( ~ ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV232 )
| ~ ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV500 )
| ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV762 ) )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3123]) ).
thf(3318,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( ~ ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV233 )
| ~ ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV501 )
| ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV763 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3124]) ).
thf(3319,plain,
! [SV765: $i,SV506: $i,SV238: $i,SV881: $i] :
( ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( ! [SY3753: $i] :
( ~ ( in @ SY3753 @ SV238 )
| ~ ( in @ SY3753 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SY3753 @ ( binunion @ SV765 @ SV881 ) ) ) )
= $true )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3126]) ).
thf(3320,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV882: $i] :
( ( ( in @ SV882 @ SV240 )
= $false )
| ( ( ! [SY3754: $i] :
( ~ ( in @ SY3754 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3754 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3755: $o] :
( ~ ! [SY3756: $i] :
( ~ ( in @ SY3756 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3756 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3756 @ SY3754 ) @ SV766 )
| SY3755 )
| SY3755 ) ) )
= $true )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3321,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3322,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i] :
( ( ( ~ ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 )
| ~ ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
| ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3129]) ).
thf(3323,plain,
! [SV768: $i,SV510: $i,SV242: $i,SV883: $i] :
( ( ( in @ SV883 @ SV242 )
= $false )
| ( ( ~ ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
| ~ ( in @ SV883 @ SV510 ) )
= $true )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3130]) ).
thf(3324,plain,
! [SV769: $i,SV511: $i,SV243: $i,SV884: $i] :
( ( ( in @ SV884 @ SV243 )
= $false )
| ( ( ~ ( in @ SV884 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
| ( in @ SV884 @ ( setminus @ SV243 @ SV769 ) ) )
= $true )
| ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3131]) ).
thf(3325,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i,SV847: $i,SV694: $i] :
( ( ( ~ ( in @ ( kpair @ SV694 @ SV847 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) ) )
= $true )
| ( ( SV657 @ SV694 @ SV847 )
= $true )
| ( ( in @ SV847 @ SV517 )
= $false )
| ( ( in @ SV694 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3326,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
| ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 ) )
= $false )
| ( ( ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3133]) ).
thf(3327,plain,
! [SV832: $i,SV658: $i,SV518: $i,SV251: $i] :
( ( ( ! [SY3716: $i] :
( ~ ( in @ SY3716 @ SV251 )
| ! [SY3717: $i] :
( ~ ( in @ SY3717 @ SV518 )
| ~ ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV658 )
| ( in @ ( kpair @ SY3716 @ SY3717 ) @ SV832 ) ) ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3328,plain,
! [SV771: $i,SV519: $i,SV252: $i,SV885: $i] :
( ( ( in @ SV885 @ SV252 )
= $false )
| ( ( ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
| ~ ( in @ SV885 @ SV771 )
| ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3329,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( ~ ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3136]) ).
thf(3330,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( ~ ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) ) )
= $false )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3136]) ).
thf(3331,plain,
! [SV773: $i,SV524: $i,SV258: $i,SV886: $i] :
( ( ( in @ SV886 @ SV258 )
= $false )
| ( ( ! [SY3758: $i] :
( ~ ( in @ SY3758 @ SV258 )
| ! [SY3759: $i] :
( ~ ( in @ SY3759 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3759 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3759 @ SY3758 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SY3758 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) ) )
= $true )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3332,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
| ! [SY3775: $i] :
( ~ ( in @ SY3775 @ SV259 )
| ~ ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SY3775 ) @ SV525 )
| ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SY3775 ) @ SV774 ) ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3138]) ).
thf(3333,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) ) )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3139]) ).
thf(3334,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3335,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ! [SY3683: $i] :
( ~ ( SV263 @ SY3683 )
| ( SV775 = SY3683 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3336,plain,
! [SV776: $i,SV529: $i,SV264: $i,SV887: $i] :
( ( ( in @ SV887 @ SV264 )
= $false )
| ( ( ~ ( subset @ SV529 @ SV776 )
| ~ ~ ( in @ SV887 @ SV776 )
| ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3142]) ).
thf(3337,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ( in @ ( sK46_SY2861 @ SV777 @ SV265 ) @ SV265 )
| ~ ~ ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3338,plain,
! [SV779: $i,SV537: $i,SV275: $i,SV888: $i] :
( ( ( in @ SV888 @ SV275 )
= $false )
| ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
| ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) )
= $true )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3145]) ).
thf(3339,plain,
! [SV540: $i > $o,SV278: $i,SV838: $i] :
( ( ( in @ SV838 @ SV278 )
= $false )
| ( ( ~ ~ ( SV540 @ SV838 ) )
= $true )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3146]) ).
thf(3340,plain,
! [SV541: $i,SV780: $i,SV279: $i,SV889: $i] :
( ( ( in @ SV889 @ SV279 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV780 @ SV889 ) @ SV541 )
| ( in @ ( kpair @ SV889 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) ) )
= $true )
| ( ( in @ SV780 @ SV279 )
= $false )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3147]) ).
thf(3341,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV899: $i] :
( ( ( ~ ( in @ SV899 @ SV280 ) )
= $true )
| ( ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV899 )
= ( SV668 @ SV899 ) )
= $true )
| ( ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3148]) ).
thf(3342,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV890: $i] :
( ( ( in @ SV890 @ SV280 )
= $false )
| ( ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV890 )
= ( SV668 @ SV890 ) )
= $true )
| ( ( in @ ( SV668 @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) ) @ SV542 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3343,plain,
! [SV284: $i] :
( ( ( in @ ( sK30_SY2910 @ SV284 ) @ SV284 )
= $true )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3150]) ).
thf(3344,plain,
! [SV284: $i] :
( ( $true = $true )
| ( ( SV284 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3151]) ).
thf(3345,plain,
! [SV287: $i,SV673: $i,SV839: $i,SV548: $i,SV900: $i] :
( ( ( ~ ( in @ SV900 @ SV548 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV839 @ SV900 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SV900 ) )
= $true )
| ( ( in @ SV839 @ SV287 )
= $false )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3153]) ).
thf(3346,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ! [SY3687: $i] :
( ~ ( SV291 @ SY3687 )
| ( SV782 = SY3687 ) ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3154]) ).
thf(3347,plain,
! [SV843: $i,SV680: $i,SV296: $i,SV555: $o] :
( ( SV555 = $false )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3726: $i] :
( ~ ( ~ SV555
| ( SY3726 != SV680 ) )
| ~ ( ~ ~ SV555
| ( SY3726 != SV843 ) ) ) )
= ( setadjoin @ SV680 @ emptyset ) )
= $true )
| ( ( in @ SV843 @ SV296 )
= $false )
| ( ( in @ SV680 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3348,plain,
! [SV844: $i,SV681: $i,SV296: $i] :
( ( $true = $false )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3727: $i] :
( ~ ( ~ $true
| ( SY3727 != SV681 ) )
| ~ ( ~ ~ $true
| ( SY3727 != SV844 ) ) ) )
= ( setadjoin @ SV681 @ emptyset ) )
= $true )
| ( ( in @ SV844 @ SV296 )
= $false )
| ( ( in @ SV681 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3349,plain,
! [SV845: $i,SV682: $i,SV296: $i] :
( ( $false = $false )
| ( ( ( dsetconstr @ SV296
@ ^ [SY3728: $i] :
( ~ ( ~ $false
| ( SY3728 != SV682 ) )
| ~ ( ~ ~ $false
| ( SY3728 != SV845 ) ) ) )
= ( setadjoin @ SV682 @ emptyset ) )
= $true )
| ( ( in @ SV845 @ SV296 )
= $false )
| ( ( in @ SV682 @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3157]) ).
thf(3350,plain,
! [SV699: $i,SV848: $i,SV322: $i,SV37: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ ( powerset @ SV37 ) )
| ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SV905 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3158]) ).
thf(3351,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ( SV38 @ ( sK67_SY3590 @ SV700 @ SV38 ) )
| ( SV700
= ( sK67_SY3590 @ SV700 @ SV38 ) ) )
= $false )
| ( ( SV38 @ SV700 )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3159]) ).
thf(3352,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( in @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) @ SV44 )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3160]) ).
thf(3353,plain,
! [SV328: $i,SV784: $i > $o,SV702: $i > $o,SV44: $i] :
( ( ( ~ ( in @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) @ SV328 )
| ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
!= ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ~ ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
| ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3161]) ).
thf(3354,plain,
! [SV45: $i] :
( ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) )
| ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[3162]) ).
thf(3355,plain,
! [SV45: $i,SV906: $i] :
( ( ! [SY3776: $i] :
( ~ ~ ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3776 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SY3777: $i] :
( ~ ( in @ SY3777 @ SV906 )
| ( in @ SY3777 @ SY3776 ) )
| ! [SY3778: $i] :
( ~ ( in @ SY3778 @ SY3776 )
| ( in @ SY3778 @ SV906 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3163]) ).
thf(3356,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) )
| ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3357,plain,
! [SV46: $i,SV850: $i,SV703: $i,SV329: $i > $o] :
( ( ( ~ ( SV329 @ SV703 ) )
= $true )
| ( ( ~ ( SV329 @ SV850 )
| ( SV703 = SV850 ) )
= $true )
| ( ( in @ SV850 @ SV46 )
= $false )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3358,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
| ~ ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3359,plain,
! [SV52: $i,SV901: $i] :
( ( ( ~ ( in @ SV901 @ omega ) )
= $true )
| ( ( in @ SV901 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK39_SY2254 @ SV52 ) @ ( sK39_SY2254 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3360,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( sK48_SY2973 @ SV53 @ SV333 ) )
| ~ ( in @ ( sK48_SY2973 @ SV53 @ SV333 ) @ SV53 ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3168]) ).
thf(3361,plain,
! [SV53: $i,SV891: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV891 )
| ~ ( in @ SV891 @ SV53 ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3362,plain,
! [SV54: $i,SV334: $i > $o,SV564: $i] :
( ( ( ~ ( in @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) @ SV54 ) )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3363,plain,
! [SV54: $i,SV564: $i,SV334: $i > $o] :
( ( ( ~ ( SV334 @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) )
| ( ( sK55_SY3420 @ SV564 @ SV334 @ SV54 )
= SV564 ) )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3170]) ).
thf(3364,plain,
! [SV704: $i,SV337: $i,SV57: $i,SV851: $i] :
( ( ( ~ ( in @ SV851 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) ) )
= $true )
| ( ( in @ SV851 @ ( setminus @ SV57 @ SV337 ) )
= $true )
| ( ( in @ SV851 @ SV57 )
= $false )
| ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3171]) ).
thf(3365,plain,
! [SV61: $i,SV341: $i,SV568: $i,SV786: $i] :
( ( ( ~ ( in @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) @ SV61 )
| ( ( ap @ SV61 @ SV341 @ SV568 @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) )
= ( ap @ SV61 @ SV341 @ SV786 @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) ) ) )
= $false )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3173]) ).
thf(3366,plain,
! [SV63: $i,SV707: $i,SV343: $i,SV852: $i] :
( ( ( ~ ~ ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) ) )
= $true )
| ( ( ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV852 @ SV63 )
= $false )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3174]) ).
thf(3367,plain,
! [SV64: $i,SV344: $i,SV853: $i,SV708: $i] :
( ( ( ~ ( subset @ SV708 @ SV853 ) )
= $true )
| ( ( subset @ ( binintersect @ SV344 @ SV708 ) @ SV853 )
= $true )
| ( ( in @ SV853 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3175]) ).
thf(3368,plain,
! [SV65: $i,SV345: $i,SV709: $i,SV854: $i] :
( ( ( ~ ~ ( in @ SV854 @ SV709 ) )
= $true )
| ( ( ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV854 @ SV65 )
= $false )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3176]) ).
thf(3369,plain,
! [SV711: $i,SV348: $i,SV855: $i,SV68: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3177]) ).
thf(3370,plain,
! [SV712: $i,SV349: $i,SV69: $i,SV856: $i] :
( ( ( ~ ( in @ SV856 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) ) )
= $true )
| ( ( in @ SV856 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) )
= $true )
| ( ( in @ SV856 @ SV69 )
= $false )
| ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3178]) ).
thf(3371,plain,
! [SV569: $i > $i,SV350: $i,SV70: $i,SV892: $i] :
( ( ( in @ SV892 @ SV70 )
= $false )
| ( ( ( ap @ SV70 @ SV350
@ ( lam @ SV70 @ SV350
@ ^ [SY3431: $i] : ( SV569 @ SY3431 ) )
@ SV892 )
= ( SV569 @ SV892 ) )
= $true )
| ( ( in @ ( sK20_SY3429 @ SV350 @ SV569 @ SV70 ) @ SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3179]) ).
thf(3372,plain,
! [SV351: $i,SV71: $i,SV846: $i,SV685: $i,SV570: $i > $i > $o] :
( ( ( SV570 @ SV685 @ SV846 )
= $false )
| ( ( in @ ( kpair @ SV685 @ SV846 )
@ ( dpsetconstr @ SV71 @ SV351
@ ^ [SY3434: $i,SY3435: $i] : ( SV570 @ SY3434 @ SY3435 ) ) )
= $true )
| ( ( in @ SV846 @ SV351 )
= $false )
| ( ( in @ SV685 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3181]) ).
thf(3373,plain,
! [SV573: $i > $i > $o,SV74: $i,SV354: $i,SV893: $i] :
( ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV354 @ SV893 )
| ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3765: $i] :
~ ( ~ ( SV573 @ SY3764 @ SY3765 )
| ~ ! [SY3766: $i] :
( ~ ( in @ SY3766 @ SV354 )
| ~ ( SV573 @ SY3764 @ SY3766 )
| ( in @ ( kpair @ SY3765 @ SY3766 ) @ SV893 ) ) ) ) ) ) )
= $true )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3182]) ).
thf(3374,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV354 )
| ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3183]) ).
thf(3375,plain,
! [SV76: $i,SV356: $i > $o,SV789: $i] :
( ( ( ~ ( ~ ( in @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) @ SV76 )
| ~ ~ ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) ) ) )
= $true )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3184]) ).
thf(3376,plain,
( ( in @ sK49_SY3731 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3185]) ).
thf(3377,plain,
( ( ~ ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ sK8_SY3448 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3378,plain,
( ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ ( binunion @ sK3_SY3035 @ sK8_SY3448 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3186]) ).
thf(3379,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i] :
( ( ( ~ ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
| ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) ) )
= $false )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3188]) ).
thf(3380,plain,
! [SV363: $i,SV792: $i,SV83: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV83 )
| ( in @ SV792 @ SV363 ) )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3191]) ).
thf(3381,plain,
! [SV83: $i,SV715: $i,SV363: $i,SV792: $i] :
( ( ( ~ ( in @ SV792 @ SV363 )
| ( in @ SV715 @ SV83 ) )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3192]) ).
thf(3382,plain,
! [SV859: $o,SV716: $i,SV365: $i,SV85: $i,SV895: $i] :
( ( ( in @ SV895 @ SV85 )
= $false )
| ( ( ~ ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3383,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV896: $i] :
( ( ( in @ SV896 @ SV85 )
= $false )
| ( ( ~ ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV896 @ SV365 )
| $true )
| ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3384,plain,
! [SV716: $i,SV365: $i,SV85: $i,SV897: $i] :
( ( ( in @ SV897 @ SV85 )
= $false )
| ( ( ~ ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
| ~ ( ~ ( in @ SV897 @ SV365 )
| $false )
| ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3385,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| SV688 ) )
= $true )
| ( SV688 = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3196]) ).
thf(3386,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| SV688 )
= $false )
| ( SV688 = $true )
| ( SV688 = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3387,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3198]) ).
thf(3388,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3389,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV366 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3200]) ).
thf(3390,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3201]) ).
thf(3391,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 ) )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3392,plain,
! [SV795: $o,SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3203]) ).
thf(3393,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 ) )
= $true )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3204]) ).
thf(3394,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3205]) ).
thf(3395,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3206]) ).
thf(3396,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3207]) ).
thf(3397,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3208]) ).
thf(3398,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3209]) ).
thf(3399,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3400,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3401,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
| ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3211]) ).
thf(3402,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3212]) ).
thf(3403,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) )
= $false )
| ( ( ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3404,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3213]) ).
thf(3405,plain,
! [SV377: $i > $o,SV98: $i,SV908: $i] :
( ( ( ~ ~ ( ~ ( in @ SV908 @ SV98 )
| ~ ( SV377 @ SV908 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3214]) ).
thf(3406,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3407,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3216]) ).
thf(3408,plain,
! [SV98: $i,SV377: $i > $o] :
( ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true )
| ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) )
| ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3409,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3218]) ).
thf(3410,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
| ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) ) )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3220]) ).
thf(3411,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
= $true )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3221]) ).
thf(3412,plain,
! [SV106: $i,SV386: $i > $o] :
( ( ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) )
= $true )
| ( ( ! [SY3089: $i] :
( ~ ( in @ SY3089 @ SV106 )
| ~ ( SV386 @ SY3089 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3222]) ).
thf(3413,plain,
! [SV107: $i,SV723: $i,SV387: $i,SV861: $i] :
( ( ( ~ ~ ( in @ SV861 @ SV387 ) )
= $true )
| ( ( ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV861 @ SV107 )
= $false )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3223]) ).
thf(3414,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 ) )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3415,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
| ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 ) )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3224]) ).
thf(3416,plain,
! [SV112: $i,SV725: $i,SV392: $i,SV862: $i] :
( ( ( ~ ~ ( in @ SV862 @ SV392 ) )
= $true )
| ( ( ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3417,plain,
! [SV801: $i,SV593: $i,SV117: $i,SV396: $o] :
( ( SV396 = $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3697: $i] :
( ~ ( ~ SV396
| ( SY3697 != SV593 ) )
| ~ ( ~ ~ SV396
| ( SY3697 != SV801 ) ) ) )
= ( setadjoin @ SV801 @ emptyset ) )
= $true )
| ( ( in @ SV801 @ SV117 )
= $false )
| ( ( in @ SV593 @ SV117 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3227]) ).
thf(3418,plain,
! [SV802: $i,SV594: $i,SV117: $i] :
( ( $true = $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3698: $i] :
( ~ ( ~ $true
| ( SY3698 != SV594 ) )
| ~ ( ~ ~ $true
| ( SY3698 != SV802 ) ) ) )
= ( setadjoin @ SV802 @ emptyset ) )
= $true )
| ( ( in @ SV802 @ SV117 )
= $false )
| ( ( in @ SV594 @ SV117 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3419,plain,
! [SV803: $i,SV595: $i,SV117: $i] :
( ( $false = $true )
| ( ( ( dsetconstr @ SV117
@ ^ [SY3699: $i] :
( ~ ( ~ $false
| ( SY3699 != SV595 ) )
| ~ ( ~ ~ $false
| ( SY3699 != SV803 ) ) ) )
= ( setadjoin @ SV803 @ emptyset ) )
= $true )
| ( ( in @ SV803 @ SV117 )
= $false )
| ( ( in @ SV595 @ SV117 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3229]) ).
thf(3420,plain,
! [SV400: $i > $o,SV121: $i,SV902: $i] :
( ( ( ~ ( ~ ( in @ SV902 @ SV121 )
| ~ ( SV400 @ SV902 ) ) )
= $false )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3231]) ).
thf(3421,plain,
! [SV400: $i > $o,SV121: $i,SV903: $i] :
( ( ( ~ ( ~ ( in @ SV903 @ SV121 )
| ~ ( SV400 @ SV903 ) ) )
= $false )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3232]) ).
thf(3422,plain,
! [SV727: $i,SV401: $i,SV122: $i,SV864: $i] :
( ( ( ~ ( in @ SV864 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) ) )
= $true )
| ( ( in @ SV864 @ ( setminus @ SV122 @ SV401 ) )
= $true )
| ( ( in @ SV864 @ SV122 )
= $false )
| ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3423,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 )
= $true )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3234]) ).
thf(3424,plain,
! [SV405: $i,SV805: $i > $o,SV601: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 )
| ~ ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
| ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3235]) ).
thf(3425,plain,
! [SV729: $i,SV406: $i,SV127: $i,SV865: $i] :
( ( ( ~ ( in @ SV865 @ ( setminus @ SV127 @ SV406 ) ) )
= $true )
| ( ( in @ SV865 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) )
= $true )
| ( ( in @ SV865 @ SV127 )
= $false )
| ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3236]) ).
thf(3426,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
| ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3237]) ).
thf(3427,plain,
! [SV731: $i,SV409: $i,SV132: $i,SV866: $i] :
( ( ( ~ ( in @ SV866 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) ) )
= $true )
| ( ( in @ SV866 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) )
= $true )
| ( ( in @ SV866 @ SV132 )
= $false )
| ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3238]) ).
thf(3428,plain,
! [SV134: $i,SV867: $i,SV732: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ ( powerset @ SV732 ) ) )
= $true )
| ( ( ~ ( in @ SV867 @ SV411 )
| ( in @ SV867 @ SV732 ) )
= $true )
| ( ( in @ SV867 @ SV134 )
= $false )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3239]) ).
thf(3429,plain,
! [SV137: $i,SV413: $i,SV605: $i,SV806: $i] :
( ( ( ~ ( in @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) @ SV137 )
| ( ( ap @ SV137 @ SV413 @ SV605 @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) )
= ( ap @ SV137 @ SV413 @ SV806 @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) ) ) )
= $false )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3240]) ).
thf(3430,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
| ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3244]) ).
thf(3431,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3245]) ).
thf(3432,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3246]) ).
thf(3433,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) )
= $false )
| ( ( ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3434,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3247]) ).
thf(3435,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( in @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SV142 )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3436,plain,
! [SV142: $i,SV610: $i,SV417: $i] :
( ( ( ~ ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3249]) ).
thf(3437,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV419 )
| ( SV735 @ SV909 ) )
= $true )
| ( ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3250]) ).
thf(3438,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i] :
( ( ( ~ ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3439,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
| ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3440,plain,
! [SV145: $i,SV736: $i,SV868: $i,SV420: $i] :
( ( ( ~ ( subset @ SV420 @ SV868 ) )
= $true )
| ( ( subset @ ( binintersect @ SV420 @ SV736 ) @ SV868 )
= $true )
| ( ( in @ SV868 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3252]) ).
thf(3441,plain,
! [SV611: $i,SV147: $i,SV810: $i,SV422: $o] :
( ( SV422 = $true )
| ( ( in @ SV810
@ ( dsetconstr @ SV147
@ ^ [SY3707: $i] :
( ~ ( ~ SV422
| ( SY3707 != SV611 ) )
| ~ ( ~ ~ SV422
| ( SY3707 != SV810 ) ) ) ) )
= $true )
| ( ( in @ SV810 @ SV147 )
= $false )
| ( ( in @ SV611 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3253]) ).
thf(3442,plain,
! [SV612: $i,SV147: $i,SV811: $i] :
( ( $true = $true )
| ( ( in @ SV811
@ ( dsetconstr @ SV147
@ ^ [SY3708: $i] :
( ~ ( ~ $true
| ( SY3708 != SV612 ) )
| ~ ( ~ ~ $true
| ( SY3708 != SV811 ) ) ) ) )
= $true )
| ( ( in @ SV811 @ SV147 )
= $false )
| ( ( in @ SV612 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3254]) ).
thf(3443,plain,
! [SV613: $i,SV147: $i,SV812: $i] :
( ( $false = $true )
| ( ( in @ SV812
@ ( dsetconstr @ SV147
@ ^ [SY3709: $i] :
( ~ ( ~ $false
| ( SY3709 != SV613 ) )
| ~ ( ~ ~ $false
| ( SY3709 != SV812 ) ) ) ) )
= $true )
| ( ( in @ SV812 @ SV147 )
= $false )
| ( ( in @ SV613 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3255]) ).
thf(3444,plain,
! [SV813: $i,SV614: $i,SV149: $i,SV423: $o] :
( ( SV423 = $true )
| ( ( ( if @ SV149 @ SV423 @ SV614 @ SV813 )
= SV813 )
= $true )
| ( ( in @ SV813 @ SV149 )
= $false )
| ( ( in @ SV614 @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3256]) ).
thf(3445,plain,
! [SV814: $i,SV615: $i,SV149: $i] :
( ( $true = $true )
| ( ( ( if @ SV149 @ $true @ SV615 @ SV814 )
= SV814 )
= $true )
| ( ( in @ SV814 @ SV149 )
= $false )
| ( ( in @ SV615 @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3257]) ).
thf(3446,plain,
! [SV815: $i,SV616: $i,SV149: $i] :
( ( $false = $true )
| ( ( ( if @ SV149 @ $false @ SV616 @ SV815 )
= SV815 )
= $true )
| ( ( in @ SV815 @ SV149 )
= $false )
| ( ( in @ SV616 @ SV149 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3258]) ).
thf(3447,plain,
! [SV425: $i,SV737: $i,SV151: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV151 ) )
= $true )
| ( ( ~ ( in @ SV904 @ SV737 )
| ( in @ SV904 @ ( setminus @ SV151 @ SV425 ) ) )
= $true )
| ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3259]) ).
thf(3448,plain,
! [SV152: $i,SV869: $i,SV738: $i,SV426: $i] :
( ( ( ~ ( subset @ SV426 @ SV738 ) )
= $true )
| ( ( ~ ( subset @ SV426 @ SV869 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) ) )
= $true )
| ( ( in @ SV869 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3260]) ).
thf(3449,plain,
! [SV870: $i,SV739: $i,SV427: $i,SV154: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV154 )
| ~ ( in @ SV910 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SV910 @ ( binunion @ SV427 @ SV870 ) ) )
= $true )
| ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3261]) ).
thf(3450,plain,
! [SV155: $i,SV816: $i,SV428: $i > $o] :
( ( ( SV428 @ SV816 )
= $false )
| ( ( in @ SV816 @ SV155 )
= $false )
| ( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3262]) ).
thf(3451,plain,
! [SV740: $i,SV429: $i,SV156: $i,SV871: $i] :
( ( ( ~ ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) ) )
= $true )
| ( ( ~ ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) ) )
= $true )
| ( ( in @ SV871 @ SV156 )
= $false )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3452,plain,
! [SV432: $i > $o,SV159: $i,SV911: $i] :
( ( ( ~ ~ ( ~ ( in @ SV911 @ SV159 )
| ~ ( SV432 @ SV911 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3264]) ).
thf(3453,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3265]) ).
thf(3454,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3455,plain,
! [SV159: $i,SV432: $i > $o] :
( ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true )
| ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) )
| ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3267]) ).
thf(3456,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3268]) ).
thf(3457,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
| ~ ( ~ ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) )
| ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3273]) ).
thf(3458,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 ) )
= $true )
| ( ( ~ ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3274]) ).
thf(3459,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 )
= $true )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3275]) ).
thf(3460,plain,
! [SV445: $i,SV819: $i > $o,SV627: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 )
| ~ ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
| ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3276]) ).
thf(3461,plain,
! [SV449: $i,SV177: $i] :
( ( ( ~ ( in @ ( sK60_SY3217 @ SV177 @ SV449 ) @ SV449 ) )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3462,plain,
! [SV449: $i,SV177: $i] :
( ( ( in @ ( sK60_SY3217 @ SV177 @ SV449 ) @ SV177 )
= $false )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3277]) ).
thf(3463,plain,
! [SV449: $i,SV177: $i] :
( ( ( in @ ( sK54_SY3217 @ SV177 @ SV449 ) @ SV449 )
= $true )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV449 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3278]) ).
thf(3464,plain,
! [SV180: $i,SV631: $i,SV820: $i,SV452: $i,SV898: $i] :
( ( ( in @ SV898 @ SV452 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV820 @ SV898 ) @ SV631 )
| ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SV898 ) )
= $true )
| ( ( in @ SV820 @ SV180 )
= $false )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3465,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( ~ ( in @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SV185 ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3466,plain,
! [SV455: $i,SV743: $i,SV185: $i] :
( ( ( ! [SY3774: $i] :
( ~ ( in @ SY3774 @ SV185 )
| ~ ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SY3774 ) @ SV455 )
| ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SY3774 ) @ SV743 ) ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3281]) ).
thf(3467,plain,
! [SV873: $i,SV744: $i,SV457: $i,SV187: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV187 )
| ~ ( in @ SV913 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SV913 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) )
= $true )
| ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3282]) ).
thf(3468,plain,
! [SV458: $i,SV188: $i,SV745: $i,SV874: $i] :
( ( ( ~ ( in @ ( kpair @ SV874 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) ) )
= $true )
| ( ( in @ ( kpair @ SV745 @ SV874 ) @ SV458 )
= $true )
| ( ( in @ SV874 @ SV188 )
= $false )
| ( ( in @ SV745 @ SV188 )
= $false )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3283]) ).
thf(3469,plain,
! [SV459: $i,SV189: $i,SV746: $o] :
( ( ( in @ ( sK42_SY3649 @ SV746 @ SV189 @ SV459 ) @ SV189 )
= $true )
| ( SV746 = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3285]) ).
thf(3470,plain,
! [SV459: $i,SV189: $i] :
( ( ( in @ ( sK43_SX0 @ SV189 @ SV459 ) @ SV189 )
= $true )
| ( $true = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3288]) ).
thf(3471,plain,
! [SV459: $i,SV189: $i] :
( ( ( in @ ( sK44_SX0 @ SV189 @ SV459 ) @ SV189 )
= $true )
| ( $false = $true )
| ( ( in @ SV459 @ ( setunion @ SV189 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3291]) ).
thf(3472,plain,
! [SV192: $i,SV747: $i,SV462: $i,SV875: $i] :
( ( ( ~ ~ ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) ) )
= $true )
| ( ( ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV875 @ SV192 )
= $false )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3293]) ).
thf(3473,plain,
! [SV748: $i,SV463: $i,SV193: $i,SV876: $i] :
( ( ( ~ ( in @ SV876 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) ) )
= $true )
| ( ( in @ SV876 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) )
= $true )
| ( ( in @ SV876 @ SV193 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3474,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| SV821 ) )
= $true )
| ( SV821 = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3296]) ).
thf(3475,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| SV821 )
= $false )
| ( SV821 = $true )
| ( SV821 = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3297]) ).
thf(3476,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3298]) ).
thf(3477,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3478,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( ~ ( in @ SV635 @ SV465 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3300]) ).
thf(3479,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3301]) ).
thf(3480,plain,
! [SV197: $i,SV467: $i] :
( ( ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV197 )
= $true )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3302]) ).
thf(3481,plain,
! [SV197: $i,SV467: $i] :
( ( ( in @ ( sK36_SY3248 @ SV467 @ SV197 ) @ SV467 )
= $true )
| ( ( ( binintersect @ SV197 @ SV467 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3303]) ).
thf(3482,plain,
! [SV878: $i,SV752: $i,SV474: $i,SV204: $i,SV914: $i] :
( ( ( ~ ( in @ SV914 @ ( powerset @ SV204 ) )
| ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SV914 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SV914 ) ) ) ) )
= $true )
| ( ( in @ SV878 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3306]) ).
thf(3483,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
| ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3307]) ).
thf(3484,plain,
! [SV755: $i,SV483: $i,SV879: $i,SV215: $i,SV915: $i] :
( ( ( ~ ( in @ SV915 @ SV215 )
| ~ ( in @ ( kpair @ SV879 @ SV915 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SV915 ) @ ( binunion @ SV483 @ SV755 ) ) )
= $true )
| ( ( in @ SV879 @ SV215 )
= $false )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3311]) ).
thf(3485,plain,
! [SV221: $i,SV489: $i > $o,SV826: $i] :
( ( ( ~ ( ~ ( in @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) @ SV221 )
| ~ ~ ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) ) ) )
= $true )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3314]) ).
thf(3486,plain,
! [SV760: $i,SV491: $i,SV223: $i,SV880: $i] :
( ( ( ~ ( in @ SV880 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) ) )
= $true )
| ( ( in @ SV880 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) )
= $true )
| ( ( in @ SV880 @ SV223 )
= $false )
| ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3315]) ).
thf(3487,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( ~ ( in @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SV226 )
| ! [SY3782: $i] :
( ~ ( in @ SY3782 @ SV494 )
| ~ ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SY3782 ) @ SV648 )
| ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SY3782 ) @ SV827 ) ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3316]) ).
thf(3488,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( ~ ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV232 ) )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3489,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( ~ ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV500 )
| ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV762 ) )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3317]) ).
thf(3490,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( ~ ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3318]) ).
thf(3491,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( ~ ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV501 )
| ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV763 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3318]) ).
thf(3492,plain,
! [SV881: $i,SV765: $i,SV506: $i,SV238: $i,SV916: $i] :
( ( ( ~ ( in @ SV916 @ SV238 )
| ~ ( in @ SV916 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SV916 @ ( binunion @ SV765 @ SV881 ) ) )
= $true )
| ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3319]) ).
thf(3493,plain,
! [SV766: $i,SV508: $i,SV882: $i,SV240: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3783: $o] :
( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3784 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3784 @ SV917 ) @ SV766 )
| SY3783 )
| SY3783 ) )
= $true )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3320]) ).
thf(3494,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV509 )
| ( SV767 @ SV918 ) )
= $true )
| ( ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3321]) ).
thf(3495,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i] :
( ( ( ~ ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3496,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
| ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3322]) ).
thf(3497,plain,
! [SV768: $i,SV510: $i,SV242: $i,SV883: $i] :
( ( ( ~ ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) ) )
= $true )
| ( ( ~ ( in @ SV883 @ SV510 ) )
= $true )
| ( ( in @ SV883 @ SV242 )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3323]) ).
thf(3498,plain,
! [SV769: $i,SV511: $i,SV243: $i,SV884: $i] :
( ( ( ~ ( in @ SV884 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) ) )
= $true )
| ( ( in @ SV884 @ ( setminus @ SV243 @ SV769 ) )
= $true )
| ( ( in @ SV884 @ SV243 )
= $false )
| ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3324]) ).
thf(3499,plain,
! [SV657: $i > $i > $o,SV517: $i,SV249: $i,SV847: $i,SV694: $i] :
( ( ( in @ ( kpair @ SV694 @ SV847 )
@ ( dpsetconstr @ SV249 @ SV517
@ ^ [SY3536: $i,SY3537: $i] : ( SV657 @ SY3536 @ SY3537 ) ) )
= $false )
| ( ( SV657 @ SV694 @ SV847 )
= $true )
| ( ( in @ SV847 @ SV517 )
= $false )
| ( ( in @ SV694 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3325]) ).
thf(3500,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) )
= $false )
| ( ( ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3501,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3326]) ).
thf(3502,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( ~ ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
| ! [SY3785: $i] :
( ~ ( in @ SY3785 @ SV518 )
| ~ ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SY3785 ) @ SV658 )
| ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SY3785 ) @ SV832 ) ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3327]) ).
thf(3503,plain,
! [SV885: $i,SV771: $i,SV252: $i,SV519: $i] :
( ( ( ~ ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) ) )
= $true )
| ( ( ~ ( in @ SV885 @ SV771 )
| ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( in @ SV885 @ SV252 )
= $false )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3504,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
= $true )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3505,plain,
! [SV256: $i,SV522: $i > $o] :
( ( ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) )
= $true )
| ( ( ! [SY3334: $i] :
( ~ ( in @ SY3334 @ SV256 )
| ~ ( SV522 @ SY3334 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3506,plain,
! [SV773: $i,SV524: $i,SV886: $i,SV258: $i,SV919: $i] :
( ( ( ~ ( in @ SV919 @ SV258 )
| ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3786 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3786 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3331]) ).
thf(3507,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3332]) ).
thf(3508,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ! [SY3775: $i] :
( ~ ( in @ SY3775 @ SV259 )
| ~ ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SY3775 ) @ SV525 )
| ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SY3775 ) @ SV774 ) ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3332]) ).
thf(3509,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
| ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 ) )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3510,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3334]) ).
thf(3511,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3334]) ).
thf(3512,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
| ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3335]) ).
thf(3513,plain,
! [SV264: $i,SV887: $i,SV776: $i,SV529: $i] :
( ( ( ~ ( subset @ SV529 @ SV776 ) )
= $true )
| ( ( ~ ~ ( in @ SV887 @ SV776 )
| ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3336]) ).
thf(3514,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ( in @ ( sK46_SY2861 @ SV777 @ SV265 ) @ SV265 ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3337]) ).
thf(3515,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ~ ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3337]) ).
thf(3516,plain,
! [SV779: $i,SV537: $i,SV275: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) ) )
= $true )
| ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) )
= $true )
| ( ( in @ SV888 @ SV275 )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3517,plain,
! [SV278: $i,SV838: $i,SV540: $i > $o] :
( ( ( ~ ( SV540 @ SV838 ) )
= $false )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3339]) ).
thf(3518,plain,
! [SV279: $i,SV541: $i,SV889: $i,SV780: $i] :
( ( ( ~ ( in @ ( kpair @ SV780 @ SV889 ) @ SV541 ) )
= $true )
| ( ( in @ ( kpair @ SV889 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) )
= $true )
| ( ( in @ SV889 @ SV279 )
= $false )
| ( ( in @ SV780 @ SV279 )
= $false )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3340]) ).
thf(3519,plain,
! [SV668: $i > $i,SV542: $i,SV280: $i,SV899: $i] :
( ( ( in @ SV899 @ SV280 )
= $false )
| ( ( ( ap @ SV280 @ SV542
@ ( lam @ SV280 @ SV542
@ ^ [SY3554: $i] : ( SV668 @ SY3554 ) )
@ SV899 )
= ( SV668 @ SV899 ) )
= $true )
| ( ( in @ ( sK28_SY3552 @ SV542 @ SV668 @ SV280 ) @ SV280 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3341]) ).
thf(3520,plain,
! [SV287: $i,SV673: $i,SV839: $i,SV548: $i,SV900: $i] :
( ( ( in @ SV900 @ SV548 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV839 @ SV900 ) @ SV673 )
| ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SV900 ) )
= $true )
| ( ( in @ SV839 @ SV287 )
= $false )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3345]) ).
thf(3521,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) )
| ( SV782
= ( sK81_SY3687 @ SV782 @ SV291 ) ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3346]) ).
thf(3522,plain,
! [SV699: $i,SV848: $i,SV322: $i,SV37: $i,SV905: $i] :
( ( ( ~ ( in @ SV905 @ ( powerset @ SV37 ) ) )
= $true )
| ( ( ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SV905 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3350]) ).
thf(3523,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( ~ ( SV38 @ ( sK67_SY3590 @ SV700 @ SV38 ) ) )
= $false )
| ( ( SV38 @ SV700 )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3351]) ).
thf(3524,plain,
! [SV38: $i > $o,SV700: $i] :
( ( ( SV700
= ( sK67_SY3590 @ SV700 @ SV38 ) )
= $false )
| ( ( SV38 @ SV700 )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3351]) ).
thf(3525,plain,
! [SV328: $i,SV784: $i > $o,SV702: $i > $o,SV44: $i] :
( ( ( ~ ( in @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3526,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
!= ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ~ ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
| ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3353]) ).
thf(3527,plain,
! [SV45: $i] :
( ( ~ ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3354]) ).
thf(3528,plain,
! [SV45: $i] :
( ( ~ ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[3354]) ).
thf(3529,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ~ ~ ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) )
| ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3355]) ).
thf(3530,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) ) )
= $true )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3356]) ).
thf(3531,plain,
! [SV46: $i,SV850: $i,SV703: $i,SV329: $i > $o] :
( ( ( SV329 @ SV703 )
= $false )
| ( ( ~ ( SV329 @ SV850 )
| ( SV703 = SV850 ) )
= $true )
| ( ( in @ SV850 @ SV46 )
= $false )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3357]) ).
thf(3532,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3358]) ).
thf(3533,plain,
! [SV52: $i] :
( ( ( ~ ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 ) )
= $false )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3358]) ).
thf(3534,plain,
! [SV52: $i,SV901: $i] :
( ( ( in @ SV901 @ omega )
= $false )
| ( ( in @ SV901 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( setadjoin @ ( sK39_SY2254 @ SV52 ) @ ( sK39_SY2254 @ SV52 ) ) @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3359]) ).
thf(3535,plain,
! [SV53: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( sK48_SY2973 @ SV53 @ SV333 ) ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3360]) ).
thf(3536,plain,
! [SV333: $i,SV53: $i] :
( ( ( ~ ( in @ ( sK48_SY2973 @ SV53 @ SV333 ) @ SV53 ) )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3360]) ).
thf(3537,plain,
! [SV53: $i,SV891: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ SV891 ) )
= $true )
| ( ( ~ ( in @ SV891 @ SV53 ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3361]) ).
thf(3538,plain,
! [SV54: $i,SV334: $i > $o,SV564: $i] :
( ( ( in @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) @ SV54 )
= $true )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3539,plain,
! [SV54: $i,SV564: $i,SV334: $i > $o] :
( ( ( ~ ( SV334 @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) ) )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3540,plain,
! [SV54: $i,SV334: $i > $o,SV564: $i] :
( ( ( ( sK55_SY3420 @ SV564 @ SV334 @ SV54 )
= SV564 )
= $false )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3363]) ).
thf(3541,plain,
! [SV704: $i,SV337: $i,SV57: $i,SV851: $i] :
( ( ( in @ SV851 @ ( setminus @ SV57 @ ( binunion @ SV337 @ SV704 ) ) )
= $false )
| ( ( in @ SV851 @ ( setminus @ SV57 @ SV337 ) )
= $true )
| ( ( in @ SV851 @ SV57 )
= $false )
| ( ( in @ SV704 @ ( powerset @ SV57 ) )
= $false )
| ( ( in @ SV337 @ ( powerset @ SV57 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3542,plain,
! [SV61: $i,SV341: $i,SV568: $i,SV786: $i] :
( ( ( ~ ( in @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) @ SV61 ) )
= $false )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3543,plain,
! [SV786: $i,SV568: $i,SV341: $i,SV61: $i] :
( ( ( ( ap @ SV61 @ SV341 @ SV568 @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) )
= ( ap @ SV61 @ SV341 @ SV786 @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) ) )
= $false )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3365]) ).
thf(3544,plain,
! [SV63: $i,SV707: $i,SV343: $i,SV852: $i] :
( ( ( ~ ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) ) )
= $false )
| ( ( ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV852 @ SV63 )
= $false )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3545,plain,
! [SV64: $i,SV344: $i,SV853: $i,SV708: $i] :
( ( ( subset @ SV708 @ SV853 )
= $false )
| ( ( subset @ ( binintersect @ SV344 @ SV708 ) @ SV853 )
= $true )
| ( ( in @ SV853 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV708 @ ( powerset @ SV64 ) )
= $false )
| ( ( in @ SV344 @ ( powerset @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3367]) ).
thf(3546,plain,
! [SV65: $i,SV345: $i,SV709: $i,SV854: $i] :
( ( ( ~ ( in @ SV854 @ SV709 ) )
= $false )
| ( ( ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV854 @ SV65 )
= $false )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3547,plain,
! [SV711: $i,SV348: $i,SV855: $i,SV68: $i,SV907: $i] :
( ( ( ~ ( in @ SV907 @ SV68 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3369]) ).
thf(3548,plain,
! [SV712: $i,SV349: $i,SV69: $i,SV856: $i] :
( ( ( in @ SV856 @ ( setminus @ SV69 @ ( binintersect @ SV349 @ SV712 ) ) )
= $false )
| ( ( in @ SV856 @ ( binunion @ ( setminus @ SV69 @ SV349 ) @ ( setminus @ SV69 @ SV712 ) ) )
= $true )
| ( ( in @ SV856 @ SV69 )
= $false )
| ( ( in @ SV712 @ ( powerset @ SV69 ) )
= $false )
| ( ( in @ SV349 @ ( powerset @ SV69 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3549,plain,
! [SV573: $i > $i > $o,SV74: $i,SV893: $i,SV354: $i] :
( ( ( ~ ( reflwellordering @ SV354 @ SV893 ) )
= $true )
| ( ( ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3765: $i] :
~ ( ~ ( SV573 @ SY3764 @ SY3765 )
| ~ ! [SY3766: $i] :
( ~ ( in @ SY3766 @ SV354 )
| ~ ( SV573 @ SY3764 @ SY3766 )
| ( in @ ( kpair @ SY3765 @ SY3766 ) @ SV893 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3373]) ).
thf(3550,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i,SV894: $i] :
( ( ( ~ ( in @ SV894 @ SV354 ) )
= $true )
| ( ( ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3374]) ).
thf(3551,plain,
! [SV76: $i,SV356: $i > $o,SV789: $i] :
( ( ( ~ ( in @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) @ SV76 )
| ~ ~ ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3375]) ).
thf(3552,plain,
( ( in @ ( kpair @ sK31_SY3607 @ sK49_SY3731 ) @ sK8_SY3448 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3377]) ).
thf(3553,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i] :
( ( ( ~ ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 ) )
= $false )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3379]) ).
thf(3554,plain,
! [SV791: $i,SV577: $i,SV361: $i,SV81: $i] :
( ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3379]) ).
thf(3555,plain,
! [SV363: $i,SV792: $i,SV83: $i,SV715: $i] :
( ( ( ~ ( in @ SV715 @ SV83 ) )
= $true )
| ( ( in @ SV792 @ SV363 )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3380]) ).
thf(3556,plain,
! [SV83: $i,SV715: $i,SV363: $i,SV792: $i] :
( ( ( ~ ( in @ SV792 @ SV363 ) )
= $true )
| ( ( in @ SV715 @ SV83 )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3381]) ).
thf(3557,plain,
! [SV85: $i,SV859: $o,SV716: $i,SV365: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3558,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV896 @ SV365 )
| $true )
| ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3559,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV897 @ SV365 )
| $false )
| ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3560,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| SV688 )
= $false )
| ( SV688 = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3385]) ).
thf(3561,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( SV688 = $true )
| ( SV688 = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3386]) ).
thf(3562,plain,
! [SV366: $i,SV86: $i,SV578: $i,SV688: $o] :
( ( SV688 = $false )
| ( SV688 = $true )
| ( SV688 = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3386]) ).
thf(3563,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3564,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3388]) ).
thf(3565,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3388]) ).
thf(3566,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3389]) ).
thf(3567,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3568,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3390]) ).
thf(3569,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3570,plain,
! [SV795: $o,SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
| SV795 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3392]) ).
thf(3571,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3572,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3573,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
| $true )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3395]) ).
thf(3574,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3575,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3397]) ).
thf(3576,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
| $false )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3577,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3578,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3400]) ).
thf(3579,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3401]) ).
thf(3580,plain,
! [SV95: $i > $o,SV717: $i] :
( ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3401]) ).
thf(3581,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( ~ ~ ( ~ ( SV97 @ SV921 )
| ~ ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3402]) ).
thf(3582,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3583,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3584,plain,
! [SV377: $i > $o,SV98: $i,SV908: $i] :
( ( ( ~ ( ~ ( in @ SV908 @ SV98 )
| ~ ( SV377 @ SV908 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3405]) ).
thf(3585,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3406]) ).
thf(3586,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3407]) ).
thf(3587,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3408]) ).
thf(3588,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3409]) ).
thf(3589,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) ) )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3590,plain,
! [SV105: $i > $o,SV722: $i] :
( ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3591,plain,
! [SV386: $i > $o,SV106: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV106 )
| ~ ( SV386 @ SV922 ) )
= $true )
| ( ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3411]) ).
thf(3592,plain,
! [SV386: $i > $o,SV106: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ SV106 )
| ~ ( SV386 @ SV923 ) )
= $true )
| ( ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3412]) ).
thf(3593,plain,
! [SV107: $i,SV723: $i,SV387: $i,SV861: $i] :
( ( ( ~ ( in @ SV861 @ SV387 ) )
= $false )
| ( ( ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV861 @ SV107 )
= $false )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3594,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3414]) ).
thf(3595,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( ~ ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 ) )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3415]) ).
thf(3596,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3415]) ).
thf(3597,plain,
! [SV112: $i,SV725: $i,SV392: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV392 ) )
= $false )
| ( ( ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3416]) ).
thf(3598,plain,
! [SV400: $i > $o,SV121: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV121 )
| ~ ( SV400 @ SV902 ) )
= $true )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3420]) ).
thf(3599,plain,
! [SV400: $i > $o,SV121: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV121 )
| ~ ( SV400 @ SV903 ) )
= $true )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3421]) ).
thf(3600,plain,
! [SV727: $i,SV401: $i,SV122: $i,SV864: $i] :
( ( ( in @ SV864 @ ( setminus @ SV122 @ ( binunion @ SV401 @ SV727 ) ) )
= $false )
| ( ( in @ SV864 @ ( setminus @ SV122 @ SV401 ) )
= $true )
| ( ( in @ SV864 @ SV122 )
= $false )
| ( ( in @ SV727 @ ( powerset @ SV122 ) )
= $false )
| ( ( in @ SV401 @ ( powerset @ SV122 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3422]) ).
thf(3601,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ SV601 )
| ( SV805 @ SV924 ) )
= $true )
| ( ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3423]) ).
thf(3602,plain,
! [SV405: $i,SV805: $i > $o,SV601: $i,SV126: $i] :
( ( ( ~ ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3424]) ).
thf(3603,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
| ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3424]) ).
thf(3604,plain,
! [SV729: $i,SV406: $i,SV127: $i,SV865: $i] :
( ( ( in @ SV865 @ ( setminus @ SV127 @ SV406 ) )
= $false )
| ( ( in @ SV865 @ ( setminus @ SV127 @ ( binintersect @ SV406 @ SV729 ) ) )
= $true )
| ( ( in @ SV865 @ SV127 )
= $false )
| ( ( in @ SV729 @ ( powerset @ SV127 ) )
= $false )
| ( ( in @ SV406 @ ( powerset @ SV127 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3605,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3606,plain,
! [SV129: $i > $o,SV730: $i] :
( ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3607,plain,
! [SV731: $i,SV409: $i,SV132: $i,SV866: $i] :
( ( ( in @ SV866 @ ( binintersect @ ( setminus @ SV132 @ SV409 ) @ ( setminus @ SV132 @ SV731 ) ) )
= $false )
| ( ( in @ SV866 @ ( setminus @ SV132 @ ( binunion @ SV409 @ SV731 ) ) )
= $true )
| ( ( in @ SV866 @ SV132 )
= $false )
| ( ( in @ SV731 @ ( powerset @ SV132 ) )
= $false )
| ( ( in @ SV409 @ ( powerset @ SV132 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3608,plain,
! [SV134: $i,SV867: $i,SV732: $i,SV411: $i] :
( ( ( in @ SV411 @ ( powerset @ SV732 ) )
= $false )
| ( ( ~ ( in @ SV867 @ SV411 )
| ( in @ SV867 @ SV732 ) )
= $true )
| ( ( in @ SV867 @ SV134 )
= $false )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3428]) ).
thf(3609,plain,
! [SV137: $i,SV413: $i,SV605: $i,SV806: $i] :
( ( ( ~ ( in @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) @ SV137 ) )
= $false )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3610,plain,
! [SV806: $i,SV605: $i,SV413: $i,SV137: $i] :
( ( ( ( ap @ SV137 @ SV413 @ SV605 @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) )
= ( ap @ SV137 @ SV413 @ SV806 @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) ) )
= $false )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3611,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) ) )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3430]) ).
thf(3612,plain,
! [SV139: $i > $o,SV733: $i] :
( ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3430]) ).
thf(3613,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3431]) ).
thf(3614,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3615,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3433]) ).
thf(3616,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3617,plain,
! [SV142: $i,SV610: $i,SV417: $i] :
( ( ( ! [SY3732: $i] :
~ ~ ( ~ ( in @ SY3732 @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ SY3732 ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3436]) ).
thf(3618,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV909: $i] :
( ( ( ~ ( in @ SV909 @ SV419 ) )
= $true )
| ( ( SV735 @ SV909 )
= $true )
| ( ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3437]) ).
thf(3619,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i] :
( ( ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 )
= $true )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3438]) ).
thf(3620,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3621,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) )
= $false )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3622,plain,
! [SV145: $i,SV736: $i,SV868: $i,SV420: $i] :
( ( ( subset @ SV420 @ SV868 )
= $false )
| ( ( subset @ ( binintersect @ SV420 @ SV736 ) @ SV868 )
= $true )
| ( ( in @ SV868 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV736 @ ( powerset @ SV145 ) )
= $false )
| ( ( in @ SV420 @ ( powerset @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3623,plain,
! [SV425: $i,SV737: $i,SV151: $i,SV904: $i] :
( ( ( in @ SV904 @ SV151 )
= $false )
| ( ( ~ ( in @ SV904 @ SV737 )
| ( in @ SV904 @ ( setminus @ SV151 @ SV425 ) ) )
= $true )
| ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3624,plain,
! [SV152: $i,SV869: $i,SV738: $i,SV426: $i] :
( ( ( subset @ SV426 @ SV738 )
= $false )
| ( ( ~ ( subset @ SV426 @ SV869 )
| ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) ) )
= $true )
| ( ( in @ SV869 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3448]) ).
thf(3625,plain,
! [SV870: $i,SV739: $i,SV427: $i,SV154: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ SV154 ) )
= $true )
| ( ( ~ ( in @ SV910 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SV910 @ ( binunion @ SV427 @ SV870 ) ) )
= $true )
| ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3449]) ).
thf(3626,plain,
! [SV816: $i,SV428: $i > $o,SV155: $i] :
( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV816 @ SV155 )
= $false )
| ( ( SV428 @ SV816 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3450]) ).
thf(3627,plain,
! [SV740: $i,SV429: $i,SV156: $i,SV871: $i] :
( ( ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) )
= $false )
| ( ( ~ ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) ) )
= $true )
| ( ( in @ SV871 @ SV156 )
= $false )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3451]) ).
thf(3628,plain,
! [SV432: $i > $o,SV159: $i,SV911: $i] :
( ( ( ~ ( ~ ( in @ SV911 @ SV159 )
| ~ ( SV432 @ SV911 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3452]) ).
thf(3629,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3453]) ).
thf(3630,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3631,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3455]) ).
thf(3632,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3456]) ).
thf(3633,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( ~ ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
| ~ ( ~ ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) )
| ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3457]) ).
thf(3634,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) )
= $true )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3635,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ SV627 )
| ( SV819 @ SV925 ) )
= $true )
| ( ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3636,plain,
! [SV445: $i,SV819: $i > $o,SV627: $i,SV173: $i] :
( ( ( ~ ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3637,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
| ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3638,plain,
! [SV449: $i,SV177: $i] :
( ( ( in @ ( sK60_SY3217 @ SV177 @ SV449 ) @ SV449 )
= $true )
| ( ( SV177 = SV449 )
= $true )
| ( ( in @ ( sK16_SY3216 @ SV449 @ SV177 ) @ SV177 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3639,plain,
! [SV452: $i,SV180: $i,SV631: $i,SV898: $i,SV820: $i] :
( ( ( ~ ( in @ ( kpair @ SV820 @ SV898 ) @ SV631 ) )
= $true )
| ( ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SV898 )
= $true )
| ( ( in @ SV898 @ SV452 )
= $false )
| ( ( in @ SV820 @ SV180 )
= $false )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3464]) ).
thf(3640,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( in @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ SV185 )
= $true )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3465]) ).
thf(3641,plain,
! [SV185: $i,SV743: $i,SV455: $i] :
( ( ( ~ ( in @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) @ SV185 )
| ~ ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV455 )
| ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV743 ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3466]) ).
thf(3642,plain,
! [SV873: $i,SV744: $i,SV457: $i,SV187: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ SV187 ) )
= $true )
| ( ( ~ ( in @ SV913 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SV913 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) )
= $true )
| ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3467]) ).
thf(3643,plain,
! [SV458: $i,SV188: $i,SV745: $i,SV874: $i] :
( ( ( in @ ( kpair @ SV874 @ SV745 ) @ ( breln1invset @ SV188 @ SV458 ) )
= $false )
| ( ( in @ ( kpair @ SV745 @ SV874 ) @ SV458 )
= $true )
| ( ( in @ SV874 @ SV188 )
= $false )
| ( ( in @ SV745 @ SV188 )
= $false )
| ( ( breln1 @ SV188 @ SV458 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3468]) ).
thf(3644,plain,
! [SV192: $i,SV747: $i,SV462: $i,SV875: $i] :
( ( ( ~ ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) ) )
= $false )
| ( ( ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV875 @ SV192 )
= $false )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3472]) ).
thf(3645,plain,
! [SV748: $i,SV463: $i,SV193: $i,SV876: $i] :
( ( ( in @ SV876 @ ( binunion @ ( setminus @ SV193 @ SV463 ) @ ( setminus @ SV193 @ SV748 ) ) )
= $false )
| ( ( in @ SV876 @ ( setminus @ SV193 @ ( binintersect @ SV463 @ SV748 ) ) )
= $true )
| ( ( in @ SV876 @ SV193 )
= $false )
| ( ( in @ SV748 @ ( powerset @ SV193 ) )
= $false )
| ( ( in @ SV463 @ ( powerset @ SV193 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3473]) ).
thf(3646,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| SV821 )
= $false )
| ( SV821 = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3474]) ).
thf(3647,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( SV821 = $true )
| ( SV821 = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3475]) ).
thf(3648,plain,
! [SV465: $i,SV195: $i,SV635: $i,SV821: $o] :
( ( SV821 = $false )
| ( SV821 = $true )
| ( SV821 = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3475]) ).
thf(3649,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3476]) ).
thf(3650,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3651,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3477]) ).
thf(3652,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3653,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3479]) ).
thf(3654,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3479]) ).
thf(3655,plain,
! [SV878: $i,SV752: $i,SV474: $i,SV204: $i,SV914: $i] :
( ( ( ~ ( in @ SV914 @ ( powerset @ SV204 ) ) )
= $true )
| ( ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SV914 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SV914 ) ) ) )
= $true )
| ( ( in @ SV878 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3482]) ).
thf(3656,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3483]) ).
thf(3657,plain,
! [SV207: $i > $o,SV753: $i] :
( ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3483]) ).
thf(3658,plain,
! [SV755: $i,SV483: $i,SV879: $i,SV215: $i,SV915: $i] :
( ( ( ~ ( in @ SV915 @ SV215 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV879 @ SV915 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SV915 ) @ ( binunion @ SV483 @ SV755 ) ) )
= $true )
| ( ( in @ SV879 @ SV215 )
= $false )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3484]) ).
thf(3659,plain,
! [SV221: $i,SV489: $i > $o,SV826: $i] :
( ( ( ~ ( in @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) @ SV221 )
| ~ ~ ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3660,plain,
! [SV760: $i,SV491: $i,SV223: $i,SV880: $i] :
( ( ( in @ SV880 @ ( setminus @ SV223 @ ( binunion @ SV491 @ SV760 ) ) )
= $false )
| ( ( in @ SV880 @ ( binintersect @ ( setminus @ SV223 @ SV491 ) @ ( setminus @ SV223 @ SV760 ) ) )
= $true )
| ( ( in @ SV880 @ SV223 )
= $false )
| ( ( in @ SV760 @ ( powerset @ SV223 ) )
= $false )
| ( ( in @ SV491 @ ( powerset @ SV223 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3486]) ).
thf(3661,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( ~ ( in @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SV226 ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3662,plain,
! [SV226: $i,SV648: $i,SV827: $i,SV494: $i] :
( ( ( ! [SY3782: $i] :
( ~ ( in @ SY3782 @ SV494 )
| ~ ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SY3782 ) @ SV648 )
| ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SY3782 ) @ SV827 ) ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3663,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV232 )
= $true )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3664,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( ~ ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV500 ) )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3665,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV762 )
= $false )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3489]) ).
thf(3666,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV233 )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3490]) ).
thf(3667,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( ~ ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV501 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3491]) ).
thf(3668,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV763 )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3491]) ).
thf(3669,plain,
! [SV881: $i,SV765: $i,SV506: $i,SV238: $i,SV916: $i] :
( ( ( ~ ( in @ SV916 @ SV238 ) )
= $true )
| ( ( ~ ( in @ SV916 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SV916 @ ( binunion @ SV765 @ SV881 ) ) )
= $true )
| ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3492]) ).
thf(3670,plain,
! [SV766: $i,SV508: $i,SV882: $i,SV240: $i,SV917: $i] :
( ( ( ~ ( in @ SV917 @ SV240 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3783: $o] :
( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3784 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3784 @ SV917 ) @ SV766 )
| SY3783 )
| SY3783 ) )
= $true )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3493]) ).
thf(3671,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV918: $i] :
( ( ( ~ ( in @ SV918 @ SV509 ) )
= $true )
| ( ( SV767 @ SV918 )
= $true )
| ( ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3494]) ).
thf(3672,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i] :
( ( ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3495]) ).
thf(3673,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3496]) ).
thf(3674,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) )
= $false )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3496]) ).
thf(3675,plain,
! [SV768: $i,SV510: $i,SV242: $i,SV883: $i] :
( ( ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
= $false )
| ( ( ~ ( in @ SV883 @ SV510 ) )
= $true )
| ( ( in @ SV883 @ SV242 )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3676,plain,
! [SV769: $i,SV511: $i,SV243: $i,SV884: $i] :
( ( ( in @ SV884 @ ( setminus @ SV243 @ ( binunion @ SV511 @ SV769 ) ) )
= $false )
| ( ( in @ SV884 @ ( setminus @ SV243 @ SV769 ) )
= $true )
| ( ( in @ SV884 @ SV243 )
= $false )
| ( ( in @ SV769 @ ( powerset @ SV243 ) )
= $false )
| ( ( in @ SV511 @ ( powerset @ SV243 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3677,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ~ ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3500]) ).
thf(3678,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3501]) ).
thf(3679,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( ~ ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3680,plain,
! [SV251: $i,SV658: $i,SV832: $i,SV518: $i] :
( ( ( ! [SY3785: $i] :
( ~ ( in @ SY3785 @ SV518 )
| ~ ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SY3785 ) @ SV658 )
| ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SY3785 ) @ SV832 ) ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3681,plain,
! [SV885: $i,SV771: $i,SV252: $i,SV519: $i] :
( ( ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
= $false )
| ( ( ~ ( in @ SV885 @ SV771 )
| ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( in @ SV885 @ SV252 )
= $false )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3503]) ).
thf(3682,plain,
! [SV522: $i > $o,SV256: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV256 )
| ~ ( SV522 @ SV926 ) )
= $true )
| ( ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3504]) ).
thf(3683,plain,
! [SV522: $i > $o,SV256: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV256 )
| ~ ( SV522 @ SV927 ) )
= $true )
| ( ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3505]) ).
thf(3684,plain,
! [SV773: $i,SV524: $i,SV886: $i,SV258: $i,SV919: $i] :
( ( ( ~ ( in @ SV919 @ SV258 ) )
= $true )
| ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3786 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3786 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3506]) ).
thf(3685,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3507]) ).
thf(3686,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
| ~ ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
| ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3508]) ).
thf(3687,plain,
! [SV261: $i,SV527: $i] :
( ( ( ~ ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 ) )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3688,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $false )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3509]) ).
thf(3689,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $true )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $false )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3510]) ).
thf(3690,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3512]) ).
thf(3691,plain,
! [SV263: $i > $o,SV775: $i] :
( ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3512]) ).
thf(3692,plain,
! [SV264: $i,SV887: $i,SV776: $i,SV529: $i] :
( ( ( subset @ SV529 @ SV776 )
= $false )
| ( ( ~ ~ ( in @ SV887 @ SV776 )
| ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3693,plain,
! [SV265: $i,SV777: $i] :
( ( ( in @ ( sK46_SY2861 @ SV777 @ SV265 ) @ SV265 )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3514]) ).
thf(3694,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3515]) ).
thf(3695,plain,
! [SV779: $i,SV537: $i,SV275: $i,SV888: $i] :
( ( ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
= $false )
| ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
| ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) ) )
= $true )
| ( ( in @ SV888 @ SV275 )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3696,plain,
! [SV278: $i,SV838: $i,SV540: $i > $o] :
( ( ( SV540 @ SV838 )
= $true )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( ~ ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3517]) ).
thf(3697,plain,
! [SV279: $i,SV541: $i,SV889: $i,SV780: $i] :
( ( ( in @ ( kpair @ SV780 @ SV889 ) @ SV541 )
= $false )
| ( ( in @ ( kpair @ SV889 @ SV780 ) @ ( breln1invset @ SV279 @ SV541 ) )
= $true )
| ( ( in @ SV889 @ SV279 )
= $false )
| ( ( in @ SV780 @ SV279 )
= $false )
| ( ( breln1 @ SV279 @ SV541 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3518]) ).
thf(3698,plain,
! [SV548: $i,SV287: $i,SV673: $i,SV900: $i,SV839: $i] :
( ( ( ~ ( in @ ( kpair @ SV839 @ SV900 ) @ SV673 ) )
= $true )
| ( ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SV900 )
= $true )
| ( ( in @ SV900 @ SV548 )
= $false )
| ( ( in @ SV839 @ SV287 )
= $false )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3520]) ).
thf(3699,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3521]) ).
thf(3700,plain,
! [SV291: $i > $o,SV782: $i] :
( ( ( SV782
= ( sK81_SY3687 @ SV782 @ SV291 ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3521]) ).
thf(3701,plain,
! [SV699: $i,SV848: $i,SV322: $i,SV37: $i,SV905: $i] :
( ( ( in @ SV905 @ ( powerset @ SV37 ) )
= $false )
| ( ( ~ ( subset @ SV322 @ SV848 )
| ~ ( subset @ SV699 @ SV905 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) ) )
= $true )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3522]) ).
thf(3702,plain,
! [SV700: $i,SV38: $i > $o] :
( ( ( SV38 @ ( sK67_SY3590 @ SV700 @ SV38 ) )
= $true )
| ( ( SV38 @ SV700 )
= $false )
| ( ( SV38
@ ( descr
@ ^ [SY2206: $i] : ( SV38 @ SY2206 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3523]) ).
thf(3703,plain,
! [SV328: $i,SV784: $i > $o,SV702: $i > $o,SV44: $i] :
( ( ( in @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) @ SV328 )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3704,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
!= ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3526]) ).
thf(3705,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
| ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3526]) ).
thf(3706,plain,
! [SV45: $i] :
( ( ! [SY3401: $i] :
( ~ ( in @ SY3401 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY2226: $i] :
( ~ ( in @ SY2226 @ SY3401 )
| ( in @ SY2226 @ SV45 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3527]) ).
thf(3707,plain,
! [SV45: $i] :
( ( ! [SY3403: $i,SY3404: $i] :
( ~ ~ ( ~ ( in @ SY3403 @ SV45 )
| ~ ( in @ SY3404 @ SV45 ) )
| ~ ! [SY3405: $i] :
( ~ ( in @ SY3405 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SY3403 @ SY3405 )
| ( in @ SY3404 @ SY3405 ) )
| ~ ( ~ ( in @ SY3404 @ SY3405 )
| ( in @ SY3403 @ SY3405 ) ) ) )
| ( SY3403 = SY3404 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3708,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ( ~ ~ ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) ) )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3529]) ).
thf(3709,plain,
! [SV45: $i,SV849: $i] :
( ( ( ! [SY3736: $i] :
( ~ ( in @ SY3736 @ SV849 )
| ( in @ SY3736 @ SV45 ) ) )
= $false )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3710,plain,
! [SV46: $i,SV703: $i,SV850: $i,SV329: $i > $o] :
( ( ( ~ ( SV329 @ SV850 ) )
= $true )
| ( ( SV703 = SV850 )
= $true )
| ( ( SV329 @ SV703 )
= $false )
| ( ( in @ SV850 @ SV46 )
= $false )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3531]) ).
thf(3711,plain,
! [SV52: $i] :
( ( ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3532]) ).
thf(3712,plain,
! [SV52: $i] :
( ( ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( ! [SY2255: $i] :
( ~ ( in @ SY2255 @ omega )
| ( in @ SY2255 @ SV52 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3533]) ).
thf(3713,plain,
! [SV53: $i,SV333: $i] :
( ( ( in @ SV333 @ ( sK48_SY2973 @ SV53 @ SV333 ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3714,plain,
! [SV333: $i,SV53: $i] :
( ( ( in @ ( sK48_SY2973 @ SV53 @ SV333 ) @ SV53 )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3536]) ).
thf(3715,plain,
! [SV53: $i,SV891: $i,SV333: $i] :
( ( ( in @ SV333 @ SV891 )
= $false )
| ( ( ~ ( in @ SV891 @ SV53 ) )
= $true )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3537]) ).
thf(3716,plain,
! [SV54: $i,SV564: $i,SV334: $i > $o] :
( ( ( SV334 @ ( sK55_SY3420 @ SV564 @ SV334 @ SV54 ) )
= $true )
| ( ( ex1 @ SV54
@ ^ [SY2977: $i] : ( SV334 @ SY2977 ) )
= $true )
| ( ( SV334 @ SV564 )
= $false )
| ( ( in @ SV564 @ SV54 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3539]) ).
thf(3717,plain,
! [SV61: $i,SV341: $i,SV568: $i,SV786: $i] :
( ( ( in @ ( sK69_SY3692 @ SV786 @ SV568 @ SV341 @ SV61 ) @ SV61 )
= $true )
| ( ( SV568 = SV786 )
= $true )
| ( ( in @ SV786 @ ( funcSet @ SV61 @ SV341 ) )
= $false )
| ( ( in @ SV568 @ ( funcSet @ SV61 @ SV341 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3542]) ).
thf(3718,plain,
! [SV63: $i,SV707: $i,SV343: $i,SV852: $i] :
( ( ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) )
= $true )
| ( ( ~ ( in @ SV852 @ SV707 ) )
= $true )
| ( ( in @ SV852 @ SV63 )
= $false )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3544]) ).
thf(3719,plain,
! [SV65: $i,SV345: $i,SV709: $i,SV854: $i] :
( ( ( in @ SV854 @ SV709 )
= $true )
| ( ( ~ ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) ) )
= $true )
| ( ( in @ SV854 @ SV65 )
= $false )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3546]) ).
thf(3720,plain,
! [SV711: $i,SV348: $i,SV855: $i,SV68: $i,SV907: $i] :
( ( ( in @ SV907 @ SV68 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
| ~ ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3721,plain,
! [SV573: $i > $i > $o,SV74: $i,SV893: $i,SV354: $i] :
( ( ( reflwellordering @ SV354 @ SV893 )
= $false )
| ( ( ! [SY3764: $i] :
( ~ ( in @ SY3764 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3765: $i] :
~ ( ~ ( SV573 @ SY3764 @ SY3765 )
| ~ ! [SY3766: $i] :
( ~ ( in @ SY3766 @ SV354 )
| ~ ( SV573 @ SY3764 @ SY3766 )
| ( in @ ( kpair @ SY3765 @ SY3766 ) @ SV893 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3722,plain,
! [SV74: $i,SV573: $i > $i > $o,SV354: $i,SV894: $i] :
( ( ( in @ SV894 @ SV354 )
= $false )
| ( ( ~ ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 ) )
= $true )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3550]) ).
thf(3723,plain,
! [SV76: $i,SV356: $i > $o,SV789: $i] :
( ( ( ~ ( in @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) @ SV76 ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3724,plain,
! [SV76: $i,SV789: $i,SV356: $i > $o] :
( ( ( ~ ~ ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3551]) ).
thf(3725,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i] :
( ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( ! [SY3695: $i] :
( ~ ( in @ SY3695 @ SV81 )
| ! [SY3696: $i] :
( ~ ( in @ SY3696 @ SV361 )
| ~ ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV791 )
| ( in @ ( kpair @ SY3695 @ SY3696 ) @ SV577 ) ) ) )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(3726,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV81 )
| ! [SY3790: $i] :
( ~ ( in @ SY3790 @ SV361 )
| ~ ( in @ ( kpair @ SV928 @ SY3790 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SY3790 ) @ SV577 ) ) )
= $true )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3554]) ).
thf(3727,plain,
! [SV363: $i,SV792: $i,SV83: $i,SV715: $i] :
( ( ( in @ SV715 @ SV83 )
= $false )
| ( ( in @ SV792 @ SV363 )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3555]) ).
thf(3728,plain,
! [SV83: $i,SV715: $i,SV363: $i,SV792: $i] :
( ( ( in @ SV792 @ SV363 )
= $false )
| ( ( in @ SV715 @ SV83 )
= $true )
| ( ( SV715 = SV792 )
= $false )
| ( ( SV83 = SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3729,plain,
! [SV85: $i,SV859: $o,SV716: $i,SV365: $i,SV895: $i] :
( ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 )
| ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3730,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV896 @ SV365 )
| $true )
| ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3558]) ).
thf(3731,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV897 @ SV365 )
| $false )
| ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3732,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( SV688 = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3733,plain,
! [SV366: $i,SV86: $i,SV578: $i,SV688: $o] :
( ( SV688 = $false )
| ( SV688 = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3560]) ).
thf(3734,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( SV688 = $true )
| ( SV688 = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3561]) ).
thf(3735,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3563]) ).
thf(3736,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3563]) ).
thf(3737,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3564]) ).
thf(3738,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV366 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3566]) ).
thf(3739,plain,
! [SV366: $i,SV86: $i,SV578: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3566]) ).
thf(3740,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3567]) ).
thf(3741,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3569]) ).
thf(3742,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3569]) ).
thf(3743,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 ) )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3570]) ).
thf(3744,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3571]) ).
thf(3745,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3571]) ).
thf(3746,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3572]) ).
thf(3747,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3572]) ).
thf(3748,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3573]) ).
thf(3749,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3750,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3574]) ).
thf(3751,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3575]) ).
thf(3752,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3575]) ).
thf(3753,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3576]) ).
thf(3754,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3755,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3577]) ).
thf(3756,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $false )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3578]) ).
thf(3757,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( ~ ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3579]) ).
thf(3758,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $false )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3580]) ).
thf(3759,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ SV921 )
| ~ ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3581]) ).
thf(3760,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
| ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3582]) ).
thf(3761,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3762,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3583]) ).
thf(3763,plain,
! [SV377: $i > $o,SV98: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV98 )
| ~ ( SV377 @ SV908 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3584]) ).
thf(3764,plain,
! [SV377: $i > $o,SV98: $i,SV929: $i] :
( ( ( ~ ~ ( ~ ( in @ SV929 @ SV98 )
| ~ ( SV377 @ SV929 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3585]) ).
thf(3765,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3586]) ).
thf(3766,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ~ ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3587]) ).
thf(3767,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3588]) ).
thf(3768,plain,
! [SV722: $i,SV105: $i > $o] :
( ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( ! [SY2425: $i,SY2426: $i] :
( ~ ( SV105 @ SY2425 )
| ~ ( SV105 @ SY2426 )
| ( SY2425 = SY2426 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3589]) ).
thf(3769,plain,
! [SV722: $i,SV930: $i,SV105: $i > $o] :
( ( ( ! [SY3791: $i] :
( ~ ( SV105 @ SV930 )
| ~ ( SV105 @ SY3791 )
| ( SV930 = SY3791 ) ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3590]) ).
thf(3770,plain,
! [SV386: $i > $o,SV106: $i,SV922: $i] :
( ( ( ~ ( in @ SV922 @ SV106 ) )
= $true )
| ( ( ~ ( SV386 @ SV922 ) )
= $true )
| ( ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3591]) ).
thf(3771,plain,
! [SV386: $i > $o,SV106: $i,SV923: $i] :
( ( ( ~ ( in @ SV923 @ SV106 ) )
= $true )
| ( ( ~ ( SV386 @ SV923 ) )
= $true )
| ( ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3592]) ).
thf(3772,plain,
! [SV107: $i,SV723: $i,SV387: $i,SV861: $i] :
( ( ( in @ SV861 @ SV387 )
= $true )
| ( ( ~ ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) ) )
= $true )
| ( ( in @ SV861 @ SV107 )
= $false )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3593]) ).
thf(3773,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3594]) ).
thf(3774,plain,
! [SV111: $i,SV391: $i,SV724: $i] :
( ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) )
| ( SV391 = SV724 ) )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3595]) ).
thf(3775,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3596]) ).
thf(3776,plain,
! [SV112: $i,SV725: $i,SV392: $i,SV862: $i] :
( ( ( in @ SV862 @ SV392 )
= $true )
| ( ( ~ ~ ( in @ SV862 @ SV725 )
| ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3597]) ).
thf(3777,plain,
! [SV400: $i > $o,SV121: $i,SV902: $i] :
( ( ( ~ ( in @ SV902 @ SV121 ) )
= $true )
| ( ( ~ ( SV400 @ SV902 ) )
= $true )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3598]) ).
thf(3778,plain,
! [SV400: $i > $o,SV121: $i,SV903: $i] :
( ( ( ~ ( in @ SV903 @ SV121 ) )
= $true )
| ( ( ~ ( SV400 @ SV903 ) )
= $true )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3599]) ).
thf(3779,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV924: $i] :
( ( ( ~ ( in @ SV924 @ SV601 ) )
= $true )
| ( ( SV805 @ SV924 )
= $true )
| ( ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3601]) ).
thf(3780,plain,
! [SV405: $i,SV805: $i > $o,SV601: $i,SV126: $i] :
( ( ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 )
= $true )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3781,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3782,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) )
= $false )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3603]) ).
thf(3783,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( ~ ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3784,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3785,plain,
! [SV134: $i,SV732: $i,SV411: $i,SV867: $i] :
( ( ( ~ ( in @ SV867 @ SV411 ) )
= $true )
| ( ( in @ SV867 @ SV732 )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV732 ) )
= $false )
| ( ( in @ SV867 @ SV134 )
= $false )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3608]) ).
thf(3786,plain,
! [SV137: $i,SV413: $i,SV605: $i,SV806: $i] :
( ( ( in @ ( sK74_SY3703 @ SV806 @ SV605 @ SV413 @ SV137 ) @ SV137 )
= $true )
| ( ( SV605 = SV806 )
= $true )
| ( ( func @ SV137 @ SV413 @ SV806 )
= $false )
| ( ( func @ SV137 @ SV413 @ SV605 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(3787,plain,
! [SV733: $i,SV139: $i > $o] :
( ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( ! [SY2517: $i,SY2518: $i] :
( ~ ( SV139 @ SY2517 )
| ~ ( SV139 @ SY2518 )
| ( SY2517 = SY2518 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(3788,plain,
! [SV733: $i,SV931: $i,SV139: $i > $o] :
( ( ( ! [SY3792: $i] :
( ~ ( SV139 @ SV931 )
| ~ ( SV139 @ SY3792 )
| ( SV931 = SY3792 ) ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3612]) ).
thf(3789,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3790,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3614]) ).
thf(3791,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
| ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3792,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3616]) ).
thf(3793,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3616]) ).
thf(3794,plain,
! [SV417: $i,SV610: $i,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3617]) ).
thf(3795,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV909: $i] :
( ( ( in @ SV909 @ SV419 )
= $false )
| ( ( SV735 @ SV909 )
= $true )
| ( ( in @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3618]) ).
thf(3796,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV419 )
| ( SV735 @ SV932 ) )
= $true )
| ( ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3619]) ).
thf(3797,plain,
! [SV144: $i,SV419: $i,SV735: $i > $o] :
( ( ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
= $true )
| ( ( ! [SY3634: $i] :
( ~ ( in @ SY3634 @ SV419 )
| ( SV735 @ SY3634 ) ) )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3620]) ).
thf(3798,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV419 )
| ( SV735 @ SV933 ) )
= $true )
| ( ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) )
= $false )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3621]) ).
thf(3799,plain,
! [SV425: $i,SV151: $i,SV737: $i,SV904: $i] :
( ( ( ~ ( in @ SV904 @ SV737 ) )
= $true )
| ( ( in @ SV904 @ ( setminus @ SV151 @ SV425 ) )
= $true )
| ( ( in @ SV904 @ SV151 )
= $false )
| ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3623]) ).
thf(3800,plain,
! [SV152: $i,SV738: $i,SV869: $i,SV426: $i] :
( ( ( ~ ( subset @ SV426 @ SV869 ) )
= $true )
| ( ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) )
= $true )
| ( ( subset @ SV426 @ SV738 )
= $false )
| ( ( in @ SV869 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3624]) ).
thf(3801,plain,
! [SV870: $i,SV739: $i,SV427: $i,SV154: $i,SV910: $i] :
( ( ( in @ SV910 @ SV154 )
= $false )
| ( ( ~ ( in @ SV910 @ ( binintersect @ SV427 @ SV739 ) )
| ( in @ SV910 @ ( binunion @ SV427 @ SV870 ) ) )
= $true )
| ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3802,plain,
! [SV816: $i,SV428: $i > $o,SV155: $i] :
( ( ( ( dsetconstr @ SV155
@ ^ [SY3177: $i] : ( SV428 @ SY3177 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV816 @ SV155 )
= $false )
| ( ( SV428 @ SV816 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3626]) ).
thf(3803,plain,
! [SV156: $i,SV740: $i,SV429: $i,SV871: $i] :
( ( ( in @ SV871 @ ( binintersect @ SV429 @ SV740 ) )
= $false )
| ( ( in @ SV871 @ ( setminus @ SV156 @ SV429 ) )
= $false )
| ( ( in @ SV871 @ SV156 )
= $false )
| ( ( in @ SV740 @ ( powerset @ SV156 ) )
= $false )
| ( ( in @ SV429 @ ( powerset @ SV156 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3627]) ).
thf(3804,plain,
! [SV432: $i > $o,SV159: $i,SV911: $i] :
( ( ( ~ ( in @ SV911 @ SV159 )
| ~ ( SV432 @ SV911 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3628]) ).
thf(3805,plain,
! [SV432: $i > $o,SV159: $i,SV934: $i] :
( ( ( ~ ~ ( ~ ( in @ SV934 @ SV159 )
| ~ ( SV432 @ SV934 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3629]) ).
thf(3806,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3630]) ).
thf(3807,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ~ ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3631]) ).
thf(3808,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3632]) ).
thf(3809,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( ~ ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3633]) ).
thf(3810,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ( ~ ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) )
| ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3633]) ).
thf(3811,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ! [SY3749: $i] :
( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SY3749 )
| ( SV872 = SY3749 ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3634]) ).
thf(3812,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV925: $i] :
( ( ( ~ ( in @ SV925 @ SV627 ) )
= $true )
| ( ( SV819 @ SV925 )
= $true )
| ( ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3635]) ).
thf(3813,plain,
! [SV445: $i,SV819: $i > $o,SV627: $i,SV173: $i] :
( ( ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 )
= $true )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3636]) ).
thf(3814,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3815,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) )
= $false )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3637]) ).
thf(3816,plain,
! [SV452: $i,SV180: $i,SV631: $i,SV898: $i,SV820: $i] :
( ( ( in @ ( kpair @ SV820 @ SV898 ) @ SV631 )
= $false )
| ( ( ( ap @ SV180 @ SV452 @ SV631 @ SV820 )
= SV898 )
= $true )
| ( ( in @ SV898 @ SV452 )
= $false )
| ( ( in @ SV820 @ SV180 )
= $false )
| ( ( in @ SV631 @ ( funcSet @ SV180 @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3817,plain,
! [SV185: $i,SV743: $i,SV455: $i] :
( ( ( ~ ( in @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) @ SV185 ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3818,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV455 )
| ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV743 ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3641]) ).
thf(3819,plain,
! [SV873: $i,SV744: $i,SV457: $i,SV187: $i,SV913: $i] :
( ( ( in @ SV913 @ SV187 )
= $false )
| ( ( ~ ( in @ SV913 @ ( binintersect @ SV457 @ SV744 ) )
| ( in @ SV913 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) ) )
= $true )
| ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3820,plain,
! [SV192: $i,SV747: $i,SV462: $i,SV875: $i] :
( ( ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) )
= $true )
| ( ( ~ ( in @ SV875 @ SV462 ) )
= $true )
| ( ( in @ SV875 @ SV192 )
= $false )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3644]) ).
thf(3821,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( SV821 = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3646]) ).
thf(3822,plain,
! [SV465: $i,SV195: $i,SV635: $i,SV821: $o] :
( ( SV821 = $false )
| ( SV821 = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3646]) ).
thf(3823,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( SV821 = $true )
| ( SV821 = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3647]) ).
thf(3824,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( $true = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3825,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3826,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3650]) ).
thf(3827,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( ~ ( in @ SV635 @ SV465 ) )
= $false )
| ( $false = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3652]) ).
thf(3828,plain,
! [SV465: $i,SV195: $i,SV635: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3652]) ).
thf(3829,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3653]) ).
thf(3830,plain,
! [SV878: $i,SV752: $i,SV474: $i,SV204: $i,SV914: $i] :
( ( ( in @ SV914 @ ( powerset @ SV204 ) )
= $false )
| ( ( ( setminus @ SV204 @ ( binintersect @ ( binunion @ SV474 @ SV752 ) @ ( binunion @ SV878 @ SV914 ) ) )
= ( binunion @ ( binintersect @ ( setminus @ SV204 @ SV474 ) @ ( setminus @ SV204 @ SV752 ) ) @ ( binintersect @ ( setminus @ SV204 @ SV878 ) @ ( setminus @ SV204 @ SV914 ) ) ) )
= $true )
| ( ( in @ SV878 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV752 @ ( powerset @ SV204 ) )
= $false )
| ( ( in @ SV474 @ ( powerset @ SV204 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3655]) ).
thf(3831,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( ~ ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3656]) ).
thf(3832,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3833,plain,
! [SV755: $i,SV483: $i,SV879: $i,SV215: $i,SV915: $i] :
( ( ( in @ SV915 @ SV215 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV879 @ SV915 ) @ SV483 )
| ( in @ ( kpair @ SV879 @ SV915 ) @ ( binunion @ SV483 @ SV755 ) ) )
= $true )
| ( ( in @ SV879 @ SV215 )
= $false )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3834,plain,
! [SV221: $i,SV489: $i > $o,SV826: $i] :
( ( ( ~ ( in @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) @ SV221 ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3659]) ).
thf(3835,plain,
! [SV221: $i,SV826: $i,SV489: $i > $o] :
( ( ( ~ ~ ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3659]) ).
thf(3836,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( in @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ SV226 )
= $true )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3661]) ).
thf(3837,plain,
! [SV494: $i,SV827: $i,SV648: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) @ SV494 )
| ~ ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV648 )
| ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV827 ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3662]) ).
thf(3838,plain,
! [SV232: $i,SV500: $i,SV762: $i] :
( ( ( in @ ( sK63_SY3661 @ SV762 @ SV500 @ SV232 ) @ SV500 )
= $true )
| ( ( subset @ SV500 @ SV762 )
= $true )
| ( ( in @ SV762 @ ( powerset @ SV232 ) )
= $false )
| ( ( in @ SV500 @ ( powerset @ SV232 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3664]) ).
thf(3839,plain,
! [SV233: $i,SV501: $i,SV763: $i] :
( ( ( in @ ( sK64_SY3662 @ SV763 @ SV501 @ SV233 ) @ SV501 )
= $true )
| ( ( in @ SV501 @ ( powerset @ SV763 ) )
= $true )
| ( ( in @ SV763 @ ( powerset @ SV233 ) )
= $false )
| ( ( in @ SV501 @ ( powerset @ SV233 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3667]) ).
thf(3840,plain,
! [SV881: $i,SV765: $i,SV506: $i,SV238: $i,SV916: $i] :
( ( ( in @ SV916 @ SV238 )
= $false )
| ( ( ~ ( in @ SV916 @ ( binintersect @ SV506 @ SV765 ) )
| ( in @ SV916 @ ( binunion @ SV765 @ SV881 ) ) )
= $true )
| ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3669]) ).
thf(3841,plain,
! [SV766: $i,SV508: $i,SV882: $i,SV240: $i,SV917: $i] :
( ( ( in @ SV917 @ SV240 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
| ! [SY3783: $o] :
( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3784 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3784 @ SV917 ) @ SV766 )
| SY3783 )
| SY3783 ) )
= $true )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3670]) ).
thf(3842,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV918: $i] :
( ( ( in @ SV918 @ SV509 )
= $false )
| ( ( SV767 @ SV918 )
= $true )
| ( ( in @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3671]) ).
thf(3843,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV509 )
| ( SV767 @ SV935 ) )
= $true )
| ( ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3672]) ).
thf(3844,plain,
! [SV241: $i,SV509: $i,SV767: $i > $o] :
( ( ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
= $true )
| ( ( ! [SY3671: $i] :
( ~ ( in @ SY3671 @ SV509 )
| ( SV767 @ SY3671 ) ) )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3673]) ).
thf(3845,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV509 )
| ( SV767 @ SV936 ) )
= $true )
| ( ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) )
= $false )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3674]) ).
thf(3846,plain,
! [SV768: $i,SV242: $i,SV510: $i,SV883: $i] :
( ( ( in @ SV883 @ SV510 )
= $false )
| ( ( in @ SV883 @ ( setminus @ SV242 @ ( binunion @ SV510 @ SV768 ) ) )
= $false )
| ( ( in @ SV883 @ SV242 )
= $false )
| ( ( in @ SV768 @ ( powerset @ SV242 ) )
= $false )
| ( ( in @ SV510 @ ( powerset @ SV242 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3675]) ).
thf(3847,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
| ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3677]) ).
thf(3848,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3678]) ).
thf(3849,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3678]) ).
thf(3850,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3679]) ).
thf(3851,plain,
! [SV518: $i,SV832: $i,SV658: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
| ~ ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
| ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3680]) ).
thf(3852,plain,
! [SV252: $i,SV519: $i,SV771: $i,SV885: $i] :
( ( ( ~ ( in @ SV885 @ SV771 ) )
= $true )
| ( ( ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
= $false )
| ( ( in @ SV885 @ SV252 )
= $false )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3681]) ).
thf(3853,plain,
! [SV522: $i > $o,SV256: $i,SV926: $i] :
( ( ( ~ ( in @ SV926 @ SV256 ) )
= $true )
| ( ( ~ ( SV522 @ SV926 ) )
= $true )
| ( ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3682]) ).
thf(3854,plain,
! [SV522: $i > $o,SV256: $i,SV927: $i] :
( ( ( ~ ( in @ SV927 @ SV256 ) )
= $true )
| ( ( ~ ( SV522 @ SV927 ) )
= $true )
| ( ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3683]) ).
thf(3855,plain,
! [SV773: $i,SV524: $i,SV886: $i,SV258: $i,SV919: $i] :
( ( ( in @ SV919 @ SV258 )
= $false )
| ( ( ! [SY3786: $i] :
( ~ ( in @ SY3786 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SY3786 ) @ SV524 )
| ~ ( in @ ( kpair @ SY3786 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) ) )
= $true )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3684]) ).
thf(3856,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3685]) ).
thf(3857,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3858,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
| ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3686]) ).
thf(3859,plain,
! [SV261: $i,SV527: $i] :
( ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV527 )
= $true )
| ( ( in @ ( sK17_SY3346 @ SV527 @ SV261 ) @ SV261 )
= $true )
| ( ( SV261 = SV527 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3860,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( ~ ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3690]) ).
thf(3861,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3691]) ).
thf(3862,plain,
! [SV264: $i,SV529: $i,SV776: $i,SV887: $i] :
( ( ( ~ ~ ( in @ SV887 @ SV776 ) )
= $true )
| ( ( ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( subset @ SV529 @ SV776 )
= $false )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3692]) ).
thf(3863,plain,
! [SV265: $i,SV777: $i] :
( ( ( ~ ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3694]) ).
thf(3864,plain,
! [SV537: $i,SV779: $i,SV275: $i,SV888: $i] :
( ( ( ~ ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) ) )
= $true )
| ( ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) )
= $true )
| ( ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
= $false )
| ( ( in @ SV888 @ SV275 )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3695]) ).
thf(3865,plain,
! [SV838: $i,SV540: $i > $o,SV278: $i] :
( ( ( ! [SY3368: $i] :
( ~ ( in @ SY3368 @ SV278 )
| ( SV540 @ SY3368 ) ) )
= $false )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( SV540 @ SV838 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3866,plain,
! [SV548: $i,SV287: $i,SV673: $i,SV900: $i,SV839: $i] :
( ( ( in @ ( kpair @ SV839 @ SV900 ) @ SV673 )
= $false )
| ( ( ( ap @ SV287 @ SV548 @ SV673 @ SV839 )
= SV900 )
= $true )
| ( ( in @ SV900 @ SV548 )
= $false )
| ( ( in @ SV839 @ SV287 )
= $false )
| ( ( func @ SV287 @ SV548 @ SV673 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3867,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) )
= $true )
| ( ( SV291 @ SV782 )
= $false )
| ( ( ~ ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3699]) ).
thf(3868,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV782
= ( sK81_SY3687 @ SV782 @ SV291 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3869,plain,
! [SV37: $i,SV905: $i,SV699: $i,SV848: $i,SV322: $i] :
( ( ( ~ ( subset @ SV322 @ SV848 ) )
= $true )
| ( ( ~ ( subset @ SV699 @ SV905 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) ) )
= $true )
| ( ( in @ SV905 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3701]) ).
thf(3870,plain,
! [SV44: $i,SV328: $i,SV702: $i > $o,SV784: $i > $o] :
( ( ( ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 )
= ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(3871,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
| ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3872,plain,
! [SV45: $i,SV937: $i] :
( ( ~ ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV937 )
| ( in @ SY3793 @ SV45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3873,plain,
! [SV45: $i,SV938: $i] :
( ( ! [SY3794: $i] :
( ~ ~ ( ~ ( in @ SV938 @ SV45 )
| ~ ( in @ SY3794 @ SV45 ) )
| ~ ! [SY3795: $i] :
( ~ ( in @ SY3795 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3795 )
| ( in @ SY3794 @ SY3795 ) )
| ~ ( ~ ( in @ SY3794 @ SY3795 )
| ( in @ SV938 @ SY3795 ) ) ) )
| ( SV938 = SY3794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3707]) ).
thf(3874,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ( ~ ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) ) )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3708]) ).
thf(3875,plain,
! [SV849: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
| ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 ) )
= $false )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3709]) ).
thf(3876,plain,
! [SV46: $i,SV703: $i,SV850: $i,SV329: $i > $o] :
( ( ( SV329 @ SV850 )
= $false )
| ( ( SV703 = SV850 )
= $true )
| ( ( SV329 @ SV703 )
= $false )
| ( ( in @ SV850 @ SV46 )
= $false )
| ( ( in @ SV703 @ SV46 )
= $false )
| ( ( ex1 @ SV46
@ ^ [SY2966: $i] : ( SV329 @ SY2966 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3877,plain,
! [SV52: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ omega )
| ( in @ SV939 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3711]) ).
thf(3878,plain,
! [SV52: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ omega )
| ( in @ SV940 @ SV52 ) )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3712]) ).
thf(3879,plain,
! [SV333: $i,SV53: $i,SV891: $i] :
( ( ( in @ SV891 @ SV53 )
= $false )
| ( ( in @ SV333 @ SV891 )
= $false )
| ( ( in @ SV333 @ ( setunion @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3715]) ).
thf(3880,plain,
! [SV63: $i,SV343: $i,SV707: $i,SV852: $i] :
( ( ( in @ SV852 @ SV707 )
= $false )
| ( ( in @ SV852 @ ( binunion @ SV343 @ SV707 ) )
= $true )
| ( ( in @ SV852 @ SV63 )
= $false )
| ( ( in @ SV707 @ ( powerset @ SV63 ) )
= $false )
| ( ( in @ SV343 @ ( powerset @ SV63 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3718]) ).
thf(3881,plain,
! [SV65: $i,SV709: $i,SV345: $i,SV854: $i] :
( ( ( in @ SV854 @ ( binintersect @ SV345 @ SV709 ) )
= $false )
| ( ( in @ SV854 @ SV709 )
= $true )
| ( ( in @ SV854 @ SV65 )
= $false )
| ( ( in @ SV709 @ ( powerset @ SV65 ) )
= $false )
| ( ( in @ SV345 @ ( powerset @ SV65 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3719]) ).
thf(3882,plain,
! [SV711: $i,SV348: $i,SV68: $i,SV907: $i,SV855: $i] :
( ( ( ~ ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) ) )
= $true )
| ( ( ~ ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3720]) ).
thf(3883,plain,
! [SV893: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3796: $i] :
~ ( ~ ( SV573 @ SV941 @ SY3796 )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV354 )
| ~ ( SV573 @ SV941 @ SY3797 )
| ( in @ ( kpair @ SY3796 @ SY3797 ) @ SV893 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV893 )
= $false )
| ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(3884,plain,
! [SV894: $i,SV74: $i,SV354: $i,SV573: $i > $i > $o] :
( ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( ! [SY3443: $i] :
( ~ ( in @ SY3443 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SY3443 )
| ! [SY3444: $i] :
( ~ ( in @ SY3444 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3445: $i] :
~ ( ~ ( SV573 @ SY3444 @ SY3445 )
| ~ ! [SY3446: $i] :
( ~ ( in @ SY3446 @ SV354 )
| ~ ( SV573 @ SY3444 @ SY3446 )
| ( in @ ( kpair @ SY3445 @ SY3446 ) @ SY3443 ) ) ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3722]) ).
thf(3885,plain,
! [SV76: $i,SV356: $i > $o,SV789: $i] :
( ( ( in @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) @ SV76 )
= $true )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(3886,plain,
! [SV76: $i,SV789: $i,SV356: $i > $o] :
( ( ( ~ ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) ) )
= $true )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3724]) ).
thf(3887,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV81 )
| ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV361 )
| ~ ( in @ ( kpair @ SV942 @ SY3798 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SY3798 ) @ SV577 ) ) )
= $true )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(3888,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV928: $i] :
( ( ( ~ ( in @ SV928 @ SV81 ) )
= $true )
| ( ( ! [SY3790: $i] :
( ~ ( in @ SY3790 @ SV361 )
| ~ ( in @ ( kpair @ SV928 @ SY3790 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SY3790 ) @ SV577 ) ) )
= $true )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3726]) ).
thf(3889,plain,
! [SV85: $i,SV716: $i,SV859: $o,SV365: $i,SV895: $i] :
( ( ( ~ ( ~ ( in @ SV895 @ SV365 )
| SV859 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3729]) ).
thf(3890,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( ~ ( ~ ( in @ SV896 @ SV365 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3730]) ).
thf(3891,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ SV897 @ SV365 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3731]) ).
thf(3892,plain,
! [SV86: $i,SV688: $o,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( SV688 = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3732]) ).
thf(3893,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( $true = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3735]) ).
thf(3894,plain,
! [SV86: $i,SV366: $i,SV578: $i] :
( ( ( in @ SV578 @ SV366 )
= $true )
| ( $false = $true )
| ( ( in @ SV578 @ SV86 )
= $true )
| ( ( in @ SV578 @ ( binunion @ SV86 @ SV366 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3738]) ).
thf(3895,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3741]) ).
thf(3896,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3742]) ).
thf(3897,plain,
! [SV373: $i,SV93: $i,SV584: $i,SV795: $o] :
( ( SV795 = $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3742]) ).
thf(3898,plain,
! [SV795: $o,SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3743]) ).
thf(3899,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3744]) ).
thf(3900,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3745]) ).
thf(3901,plain,
! [SV373: $i,SV93: $i,SV584: $i,SV795: $o] :
( ( SV795 = $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3745]) ).
thf(3902,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3746]) ).
thf(3903,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3747]) ).
thf(3904,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3747]) ).
thf(3905,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3748]) ).
thf(3906,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3749]) ).
thf(3907,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3908,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3750]) ).
thf(3909,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3751]) ).
thf(3910,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3752]) ).
thf(3911,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3752]) ).
thf(3912,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 )
| ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3753]) ).
thf(3913,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3754]) ).
thf(3914,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3915,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3755]) ).
thf(3916,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ~ ( ~ ( SV95 @ ( sK88_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3799: $i] :
( ~ ( SV95 @ SY3799 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SY3799 ) ) ) )
= $false )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3756]) ).
thf(3917,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY2391: $i] :
~ ~ ( ~ ( SV95 @ SY2391 )
| ~ ! [SY2392: $i] :
( ~ ( SV95 @ SY2392 )
| ( SY2391 = SY2392 ) ) ) )
= $false )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3757]) ).
thf(3918,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ~ ( ~ ( SV95 @ ( sK89_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3800: $i] :
( ~ ( SV95 @ SY3800 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SY3800 ) ) ) )
= $false )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3758]) ).
thf(3919,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV921 )
| ~ ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(3920,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3921,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3760]) ).
thf(3922,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3761]) ).
thf(3923,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3762]) ).
thf(3924,plain,
! [SV377: $i > $o,SV98: $i,SV908: $i] :
( ( ( ~ ( in @ SV908 @ SV98 ) )
= $true )
| ( ( ~ ( SV377 @ SV908 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3763]) ).
thf(3925,plain,
! [SV377: $i > $o,SV98: $i,SV929: $i] :
( ( ( ~ ( ~ ( in @ SV929 @ SV98 )
| ~ ( SV377 @ SV929 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3764]) ).
thf(3926,plain,
! [SV377: $i > $o,SV98: $i,SV943: $i] :
( ( ( ~ ~ ( ~ ( in @ SV943 @ SV98 )
| ~ ( SV377 @ SV943 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3765]) ).
thf(3927,plain,
! [SV377: $i > $o,SV98: $i] :
( ( ( ! [SY3079: $i] :
~ ~ ( ~ ( in @ SY3079 @ SV98 )
| ~ ( SV377 @ SY3079 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3766]) ).
thf(3928,plain,
! [SV377: $i > $o,SV98: $i,SV944: $i] :
( ( ( ~ ~ ( ~ ( in @ SV944 @ SV98 )
| ~ ( SV377 @ SV944 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(3929,plain,
! [SV722: $i,SV945: $i,SV105: $i > $o] :
( ( ( ! [SY3801: $i] :
( ~ ( SV105 @ SV945 )
| ~ ( SV105 @ SY3801 )
| ( SV945 = SY3801 ) ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3768]) ).
thf(3930,plain,
! [SV722: $i,SV946: $i,SV930: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV930 )
| ~ ( SV105 @ SV946 )
| ( SV930 = SV946 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3769]) ).
thf(3931,plain,
! [SV386: $i > $o,SV106: $i,SV922: $i] :
( ( ( in @ SV922 @ SV106 )
= $false )
| ( ( ~ ( SV386 @ SV922 ) )
= $true )
| ( ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3770]) ).
thf(3932,plain,
! [SV386: $i > $o,SV106: $i,SV923: $i] :
( ( ( in @ SV923 @ SV106 )
= $false )
| ( ( ~ ( SV386 @ SV923 ) )
= $true )
| ( ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3771]) ).
thf(3933,plain,
! [SV107: $i,SV723: $i,SV387: $i,SV861: $i] :
( ( ( in @ SV861 @ ( binintersect @ SV387 @ SV723 ) )
= $false )
| ( ( in @ SV861 @ SV387 )
= $true )
| ( ( in @ SV861 @ SV107 )
= $false )
| ( ( in @ SV723 @ ( powerset @ SV107 ) )
= $false )
| ( ( in @ SV387 @ ( powerset @ SV107 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3772]) ).
thf(3934,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3773]) ).
thf(3935,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ~ ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3936,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3775]) ).
thf(3937,plain,
! [SV112: $i,SV392: $i,SV725: $i,SV862: $i] :
( ( ( ~ ~ ( in @ SV862 @ SV725 ) )
= $true )
| ( ( ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV392 )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3776]) ).
thf(3938,plain,
! [SV400: $i > $o,SV121: $i,SV902: $i] :
( ( ( in @ SV902 @ SV121 )
= $false )
| ( ( ~ ( SV400 @ SV902 ) )
= $true )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3777]) ).
thf(3939,plain,
! [SV400: $i > $o,SV121: $i,SV903: $i] :
( ( ( in @ SV903 @ SV121 )
= $false )
| ( ( ~ ( SV400 @ SV903 ) )
= $true )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3940,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV924: $i] :
( ( ( in @ SV924 @ SV601 )
= $false )
| ( ( SV805 @ SV924 )
= $true )
| ( ( in @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ SV126 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3779]) ).
thf(3941,plain,
! [SV405: $i,SV126: $i,SV805: $i > $o,SV601: $i,SV947: $i] :
( ( ( ~ ( in @ SV947 @ SV601 )
| ( SV805 @ SV947 ) )
= $true )
| ( ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3780]) ).
thf(3942,plain,
! [SV126: $i,SV405: $i,SV601: $i,SV805: $i > $o] :
( ( ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
= $true )
| ( ( ! [SY3702: $i] :
( ~ ( in @ SY3702 @ SV601 )
| ( SV805 @ SY3702 ) ) )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3781]) ).
thf(3943,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ SV601 )
| ( SV805 @ SV948 ) )
= $true )
| ( ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) )
= $false )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3782]) ).
thf(3944,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ! [SY2492: $i] :
~ ~ ( ~ ( SV129 @ SY2492 )
| ~ ! [SY2493: $i] :
( ~ ( SV129 @ SY2493 )
| ( SY2492 = SY2493 ) ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3783]) ).
thf(3945,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ~ ( ~ ( SV129 @ ( sK90_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3802: $i] :
( ~ ( SV129 @ SY3802 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SY3802 ) ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3784]) ).
thf(3946,plain,
! [SV134: $i,SV732: $i,SV411: $i,SV867: $i] :
( ( ( in @ SV867 @ SV411 )
= $false )
| ( ( in @ SV867 @ SV732 )
= $true )
| ( ( in @ SV411 @ ( powerset @ SV732 ) )
= $false )
| ( ( in @ SV867 @ SV134 )
= $false )
| ( ( in @ SV732 @ ( powerset @ SV134 ) )
= $false )
| ( ( in @ SV411 @ ( powerset @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3785]) ).
thf(3947,plain,
! [SV733: $i,SV949: $i,SV139: $i > $o] :
( ( ( ! [SY3803: $i] :
( ~ ( SV139 @ SV949 )
| ~ ( SV139 @ SY3803 )
| ( SV949 = SY3803 ) ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3787]) ).
thf(3948,plain,
! [SV733: $i,SV950: $i,SV931: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV931 )
| ~ ( SV139 @ SV950 )
| ( SV931 = SV950 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3788]) ).
thf(3949,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3789]) ).
thf(3950,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3790]) ).
thf(3951,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3791]) ).
thf(3952,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3791]) ).
thf(3953,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3792]) ).
thf(3954,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3793]) ).
thf(3955,plain,
! [SV417: $i,SV610: $i,SV142: $i] :
( ( ( ~ ( ~ ( in @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) ) ) ) )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3794]) ).
thf(3956,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV932: $i] :
( ( ( ~ ( in @ SV932 @ SV419 ) )
= $true )
| ( ( SV735 @ SV932 )
= $true )
| ( ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3796]) ).
thf(3957,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV951: $i] :
( ( ( ~ ( in @ SV951 @ SV419 )
| ( SV735 @ SV951 ) )
= $true )
| ( ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(3958,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV933: $i] :
( ( ( ~ ( in @ SV933 @ SV419 ) )
= $true )
| ( ( SV735 @ SV933 )
= $true )
| ( ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) )
= $false )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(3959,plain,
! [SV425: $i,SV151: $i,SV737: $i,SV904: $i] :
( ( ( in @ SV904 @ SV737 )
= $false )
| ( ( in @ SV904 @ ( setminus @ SV151 @ SV425 ) )
= $true )
| ( ( in @ SV904 @ SV151 )
= $false )
| ( ( subset @ SV425 @ ( setminus @ SV151 @ SV737 ) )
= $false )
| ( ( in @ SV737 @ ( powerset @ SV151 ) )
= $false )
| ( ( in @ SV425 @ ( powerset @ SV151 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3799]) ).
thf(3960,plain,
! [SV152: $i,SV738: $i,SV869: $i,SV426: $i] :
( ( ( subset @ SV426 @ SV869 )
= $false )
| ( ( subset @ SV426 @ ( binintersect @ SV738 @ SV869 ) )
= $true )
| ( ( subset @ SV426 @ SV738 )
= $false )
| ( ( in @ SV869 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV738 @ ( powerset @ SV152 ) )
= $false )
| ( ( in @ SV426 @ ( powerset @ SV152 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(3961,plain,
! [SV154: $i,SV870: $i,SV739: $i,SV427: $i,SV910: $i] :
( ( ( ~ ( in @ SV910 @ ( binintersect @ SV427 @ SV739 ) ) )
= $true )
| ( ( in @ SV910 @ ( binunion @ SV427 @ SV870 ) )
= $true )
| ( ( in @ SV910 @ SV154 )
= $false )
| ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(3962,plain,
! [SV432: $i > $o,SV159: $i,SV911: $i] :
( ( ( ~ ( in @ SV911 @ SV159 ) )
= $true )
| ( ( ~ ( SV432 @ SV911 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3804]) ).
thf(3963,plain,
! [SV432: $i > $o,SV159: $i,SV934: $i] :
( ( ( ~ ( ~ ( in @ SV934 @ SV159 )
| ~ ( SV432 @ SV934 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3805]) ).
thf(3964,plain,
! [SV432: $i > $o,SV159: $i,SV952: $i] :
( ( ( ~ ~ ( ~ ( in @ SV952 @ SV159 )
| ~ ( SV432 @ SV952 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3806]) ).
thf(3965,plain,
! [SV432: $i > $o,SV159: $i] :
( ( ( ! [SY3183: $i] :
~ ~ ( ~ ( in @ SY3183 @ SV159 )
| ~ ( SV432 @ SY3183 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3807]) ).
thf(3966,plain,
! [SV432: $i > $o,SV159: $i,SV953: $i] :
( ( ( ~ ~ ( ~ ( in @ SV953 @ SV159 )
| ~ ( SV432 @ SV953 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3808]) ).
thf(3967,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
| ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3809]) ).
thf(3968,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) )
| ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3810]) ).
thf(3969,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
| ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3811]) ).
thf(3970,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV925: $i] :
( ( ( in @ SV925 @ SV627 )
= $false )
| ( ( SV819 @ SV925 )
= $true )
| ( ( in @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ SV173 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3812]) ).
thf(3971,plain,
! [SV445: $i,SV173: $i,SV819: $i > $o,SV627: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ SV627 )
| ( SV819 @ SV954 ) )
= $true )
| ( ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3813]) ).
thf(3972,plain,
! [SV173: $i,SV445: $i,SV627: $i,SV819: $i > $o] :
( ( ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
= $true )
| ( ( ! [SY3712: $i] :
( ~ ( in @ SY3712 @ SV627 )
| ( SV819 @ SY3712 ) ) )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(3973,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV955: $i] :
( ( ( ~ ( in @ SV955 @ SV627 )
| ( SV819 @ SV955 ) )
= $true )
| ( ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) )
= $false )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3815]) ).
thf(3974,plain,
! [SV185: $i,SV743: $i,SV455: $i] :
( ( ( in @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) @ SV185 )
= $true )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3817]) ).
thf(3975,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV455 ) )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3818]) ).
thf(3976,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV743 )
= $false )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3818]) ).
thf(3977,plain,
! [SV187: $i,SV873: $i,SV744: $i,SV457: $i,SV913: $i] :
( ( ( ~ ( in @ SV913 @ ( binintersect @ SV457 @ SV744 ) ) )
= $true )
| ( ( in @ SV913 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) )
= $true )
| ( ( in @ SV913 @ SV187 )
= $false )
| ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3819]) ).
thf(3978,plain,
! [SV192: $i,SV747: $i,SV462: $i,SV875: $i] :
( ( ( in @ SV875 @ SV462 )
= $false )
| ( ( in @ SV875 @ ( binunion @ SV462 @ SV747 ) )
= $true )
| ( ( in @ SV875 @ SV192 )
= $false )
| ( ( in @ SV747 @ ( powerset @ SV192 ) )
= $false )
| ( ( in @ SV462 @ ( powerset @ SV192 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3820]) ).
thf(3979,plain,
! [SV195: $i,SV821: $o,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( SV821 = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3821]) ).
thf(3980,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( $true = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3824]) ).
thf(3981,plain,
! [SV195: $i,SV465: $i,SV635: $i] :
( ( ( in @ SV635 @ SV465 )
= $true )
| ( $false = $true )
| ( ( SV635 = SV195 )
= $true )
| ( ( in @ SV635 @ ( setadjoin @ SV195 @ SV465 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3827]) ).
thf(3982,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ! [SY2702: $i] :
~ ~ ( ~ ( SV207 @ SY2702 )
| ~ ! [SY2703: $i] :
( ~ ( SV207 @ SY2703 )
| ( SY2702 = SY2703 ) ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3983,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ~ ( ~ ( SV207 @ ( sK92_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3804: $i] :
( ~ ( SV207 @ SY3804 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SY3804 ) ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3832]) ).
thf(3984,plain,
! [SV215: $i,SV755: $i,SV483: $i,SV915: $i,SV879: $i] :
( ( ( ~ ( in @ ( kpair @ SV879 @ SV915 ) @ SV483 ) )
= $true )
| ( ( in @ ( kpair @ SV879 @ SV915 ) @ ( binunion @ SV483 @ SV755 ) )
= $true )
| ( ( in @ SV915 @ SV215 )
= $false )
| ( ( in @ SV879 @ SV215 )
= $false )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3833]) ).
thf(3985,plain,
! [SV221: $i,SV489: $i > $o,SV826: $i] :
( ( ( in @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) @ SV221 )
= $true )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3834]) ).
thf(3986,plain,
! [SV221: $i,SV826: $i,SV489: $i > $o] :
( ( ( ~ ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) ) )
= $true )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3835]) ).
thf(3987,plain,
! [SV494: $i,SV827: $i,SV648: $i,SV226: $i] :
( ( ( ~ ( in @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) @ SV494 ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3837]) ).
thf(3988,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV648 )
| ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV827 ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3837]) ).
thf(3989,plain,
! [SV238: $i,SV881: $i,SV765: $i,SV506: $i,SV916: $i] :
( ( ( ~ ( in @ SV916 @ ( binintersect @ SV506 @ SV765 ) ) )
= $true )
| ( ( in @ SV916 @ ( binunion @ SV765 @ SV881 ) )
= $true )
| ( ( in @ SV916 @ SV238 )
= $false )
| ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3840]) ).
thf(3990,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV917: $i,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) ) )
= $true )
| ( ( ! [SY3783: $o] :
( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3784 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3784 @ SV917 ) @ SV766 )
| SY3783 )
| SY3783 ) )
= $true )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3841]) ).
thf(3991,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV935: $i] :
( ( ( ~ ( in @ SV935 @ SV509 ) )
= $true )
| ( ( SV767 @ SV935 )
= $true )
| ( ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3843]) ).
thf(3992,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV509 )
| ( SV767 @ SV956 ) )
= $true )
| ( ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3844]) ).
thf(3993,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV936: $i] :
( ( ( ~ ( in @ SV936 @ SV509 ) )
= $true )
| ( ( SV767 @ SV936 )
= $true )
| ( ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) )
= $false )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3845]) ).
thf(3994,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
!= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3847]) ).
thf(3995,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3847]) ).
thf(3996,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3848]) ).
thf(3997,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3849]) ).
thf(3998,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3850]) ).
thf(3999,plain,
! [SV518: $i,SV832: $i,SV658: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3851]) ).
thf(4000,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
| ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3851]) ).
thf(4001,plain,
! [SV252: $i,SV519: $i,SV771: $i,SV885: $i] :
( ( ( in @ SV885 @ SV771 )
= $false )
| ( ( ~ ( in @ SV885 @ SV519 ) )
= $true )
| ( ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
= $false )
| ( ( in @ SV885 @ SV252 )
= $false )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3852]) ).
thf(4002,plain,
! [SV522: $i > $o,SV256: $i,SV926: $i] :
( ( ( in @ SV926 @ SV256 )
= $false )
| ( ( ~ ( SV522 @ SV926 ) )
= $true )
| ( ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(4003,plain,
! [SV522: $i > $o,SV256: $i,SV927: $i] :
( ( ( in @ SV927 @ SV256 )
= $false )
| ( ( ~ ( SV522 @ SV927 ) )
= $true )
| ( ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3854]) ).
thf(4004,plain,
! [SV773: $i,SV919: $i,SV524: $i,SV886: $i,SV258: $i,SV957: $i] :
( ( ( ~ ( in @ SV957 @ SV258 )
| ~ ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
| ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) )
= $true )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3855]) ).
thf(4005,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3856]) ).
thf(4006,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3857]) ).
thf(4007,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(4008,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3858]) ).
thf(4009,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ! [SY2855: $i] :
~ ! [SY2856: $i] :
~ ( ~ ( ~ ( SV263 @ SY2856 )
| ( SY2856 = SY2855 ) )
| ~ ( ( SY2856 != SY2855 )
| ( SV263 @ SY2856 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3860]) ).
thf(4010,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ! [SY3805: $i] :
~ ( ~ ( ~ ( SV263 @ SY3805 )
| ( SY3805
= ( sK93_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SY3805
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SY3805 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3861]) ).
thf(4011,plain,
! [SV264: $i,SV529: $i,SV776: $i,SV887: $i] :
( ( ( ~ ( in @ SV887 @ SV776 ) )
= $false )
| ( ( ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( subset @ SV529 @ SV776 )
= $false )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3862]) ).
thf(4012,plain,
! [SV265: $i,SV777: $i] :
( ( ( ! [SY3760: $i] :
~ ~ ( ~ ( in @ SY3760 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SY3760 @ SV265 ) ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3863]) ).
thf(4013,plain,
! [SV537: $i,SV779: $i,SV275: $i,SV888: $i] :
( ( ( in @ SV888 @ ( setminus @ SV275 @ SV779 ) )
= $false )
| ( ( in @ SV888 @ ( setminus @ SV275 @ ( binunion @ SV537 @ SV779 ) ) )
= $true )
| ( ( in @ SV888 @ ( setminus @ SV275 @ SV537 ) )
= $false )
| ( ( in @ SV888 @ SV275 )
= $false )
| ( ( in @ SV779 @ ( powerset @ SV275 ) )
= $false )
| ( ( in @ SV537 @ ( powerset @ SV275 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3864]) ).
thf(4014,plain,
! [SV278: $i,SV540: $i > $o,SV838: $i] :
( ( ( ~ ( in @ ( sK94_SY3368 @ SV838 @ SV540 @ SV278 ) @ SV278 )
| ( SV540 @ ( sK94_SY3368 @ SV838 @ SV540 @ SV278 ) ) )
= $false )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( SV540 @ SV838 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3865]) ).
thf(4015,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ! [SY2929: $i] :
~ ( SV291 @ SY2929 ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3867]) ).
thf(4016,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ ( sK95_SY2929 @ SV782 @ SV291 ) ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV782
= ( sK81_SY3687 @ SV782 @ SV291 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3868]) ).
thf(4017,plain,
! [SV37: $i,SV905: $i,SV699: $i,SV848: $i,SV322: $i] :
( ( ( subset @ SV322 @ SV848 )
= $false )
| ( ( ~ ( subset @ SV699 @ SV905 )
| ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) ) )
= $true )
| ( ( in @ SV905 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3869]) ).
thf(4018,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( ~ ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3871]) ).
thf(4019,plain,
! [SV45: $i,SV937: $i] :
( ( ( ~ ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV937 )
| ( in @ SY3793 @ SV45 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3872]) ).
thf(4020,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ~ ~ ( ~ ( in @ SV938 @ SV45 )
| ~ ( in @ SV958 @ SV45 ) )
| ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[3873]) ).
thf(4021,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3874]) ).
thf(4022,plain,
! [SV849: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 ) )
= $false )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3875]) ).
thf(4023,plain,
! [SV849: $i,SV45: $i] :
( ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3875]) ).
thf(4024,plain,
! [SV52: $i,SV939: $i] :
( ( ( ~ ( in @ SV939 @ omega ) )
= $true )
| ( ( in @ SV939 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3877]) ).
thf(4025,plain,
! [SV52: $i,SV940: $i] :
( ( ( ~ ( in @ SV940 @ omega ) )
= $true )
| ( ( in @ SV940 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3878]) ).
thf(4026,plain,
! [SV711: $i,SV348: $i,SV68: $i,SV907: $i,SV855: $i] :
( ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( ~ ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3882]) ).
thf(4027,plain,
! [SV893: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV941: $i] :
( ( ( ~ ( in @ SV941 @ SV74 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3796: $i] :
~ ( ~ ( SV573 @ SV941 @ SY3796 )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV354 )
| ~ ( SV573 @ SV941 @ SY3797 )
| ( in @ ( kpair @ SY3796 @ SY3797 ) @ SV893 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV893 )
= $false )
| ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3883]) ).
thf(4028,plain,
! [SV894: $i,SV573: $i > $i > $o,SV74: $i,SV354: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ ( breln1Set @ SV354 ) )
| ~ ( reflwellordering @ SV354 @ SV959 )
| ! [SY3807: $i] :
( ~ ( in @ SY3807 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3808: $i] :
~ ( ~ ( SV573 @ SY3807 @ SY3808 )
| ~ ! [SY3809: $i] :
( ~ ( in @ SY3809 @ SV354 )
| ~ ( SV573 @ SY3807 @ SY3809 )
| ( in @ ( kpair @ SY3808 @ SY3809 ) @ SV959 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3884]) ).
thf(4029,plain,
! [SV76: $i,SV789: $i,SV356: $i > $o] :
( ( ( SV356 @ ( sK56_SY3033 @ SV789 @ SV356 @ SV76 ) )
= $false )
| ( ( SV356 @ SV789 )
= $true )
| ( ( in @ SV789 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3886]) ).
thf(4030,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV942: $i] :
( ( ( ~ ( in @ SV942 @ SV81 ) )
= $true )
| ( ( ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV361 )
| ~ ( in @ ( kpair @ SV942 @ SY3798 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SY3798 ) @ SV577 ) ) )
= $true )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3887]) ).
thf(4031,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV928: $i] :
( ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ! [SY3790: $i] :
( ~ ( in @ SY3790 @ SV361 )
| ~ ( in @ ( kpair @ SV928 @ SY3790 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SY3790 ) @ SV577 ) ) )
= $true )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3888]) ).
thf(4032,plain,
! [SV85: $i,SV716: $i,SV859: $o,SV365: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV365 )
| SV859 )
= $false )
| ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3889]) ).
thf(4033,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV365 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3890]) ).
thf(4034,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV365 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3891]) ).
thf(4035,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3895]) ).
thf(4036,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3896]) ).
thf(4037,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3898]) ).
thf(4038,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| SV795 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3898]) ).
thf(4039,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3899]) ).
thf(4040,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( SV795 = $true )
| ( SV795 = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3900]) ).
thf(4041,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3902]) ).
thf(4042,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3903]) ).
thf(4043,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3905]) ).
thf(4044,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3905]) ).
thf(4045,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3906]) ).
thf(4046,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3907]) ).
thf(4047,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3909]) ).
thf(4048,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV93 )
= $true )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3910]) ).
thf(4049,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ~ ( in @ SV584 @ SV93 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4050,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3912]) ).
thf(4051,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3913]) ).
thf(4052,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3914]) ).
thf(4053,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( ~ ( SV95 @ ( sK88_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3799: $i] :
( ~ ( SV95 @ SY3799 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SY3799 ) ) ) )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3916]) ).
thf(4054,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ~ ( ~ ( SV95 @ ( sK96_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3810: $i] :
( ~ ( SV95 @ SY3810 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SY3810 ) ) ) )
= $false )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3917]) ).
thf(4055,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( ~ ( SV95 @ ( sK89_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3800: $i] :
( ~ ( SV95 @ SY3800 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SY3800 ) ) ) )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3918]) ).
thf(4056,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV921 ) )
= $true )
| ( ( ~ ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3919]) ).
thf(4057,plain,
! [SV97: $i > $o,SV376: $i > $o] :
( ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) )
| ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3920]) ).
thf(4058,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3921]) ).
thf(4059,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3922]) ).
thf(4060,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3923]) ).
thf(4061,plain,
! [SV377: $i > $o,SV98: $i,SV908: $i] :
( ( ( in @ SV908 @ SV98 )
= $false )
| ( ( ~ ( SV377 @ SV908 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3924]) ).
thf(4062,plain,
! [SV377: $i > $o,SV98: $i,SV929: $i] :
( ( ( ~ ( in @ SV929 @ SV98 )
| ~ ( SV377 @ SV929 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3925]) ).
thf(4063,plain,
! [SV377: $i > $o,SV98: $i,SV943: $i] :
( ( ( ~ ( ~ ( in @ SV943 @ SV98 )
| ~ ( SV377 @ SV943 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3926]) ).
thf(4064,plain,
! [SV377: $i > $o,SV98: $i,SV960: $i] :
( ( ( ~ ~ ( ~ ( in @ SV960 @ SV98 )
| ~ ( SV377 @ SV960 ) ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3927]) ).
thf(4065,plain,
! [SV377: $i > $o,SV98: $i,SV944: $i] :
( ( ( ~ ( ~ ( in @ SV944 @ SV98 )
| ~ ( SV377 @ SV944 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3928]) ).
thf(4066,plain,
! [SV722: $i,SV961: $i,SV945: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV945 )
| ~ ( SV105 @ SV961 )
| ( SV945 = SV961 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3929]) ).
thf(4067,plain,
! [SV722: $i,SV946: $i,SV930: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV930 ) )
= $true )
| ( ( ~ ( SV105 @ SV946 )
| ( SV930 = SV946 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3930]) ).
thf(4068,plain,
! [SV106: $i,SV922: $i,SV386: $i > $o] :
( ( ( SV386 @ SV922 )
= $false )
| ( ( in @ SV922 @ SV106 )
= $false )
| ( ( in @ ( sK33_SY3088 @ SV386 @ SV106 ) @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3931]) ).
thf(4069,plain,
! [SV106: $i,SV923: $i,SV386: $i > $o] :
( ( ( SV386 @ SV923 )
= $false )
| ( ( in @ SV923 @ SV106 )
= $false )
| ( ( SV386 @ ( sK33_SY3088 @ SV386 @ SV106 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3932]) ).
thf(4070,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3934]) ).
thf(4071,plain,
! [SV391: $i,SV724: $i,SV111: $i] :
( ( ( ! [SY3620: $i] :
( ~ ( in @ SY3620 @ SV111 )
| ~ ( in @ SY3620 @ SV724 )
| ( in @ SY3620 @ SV391 ) ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3935]) ).
thf(4072,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3936]) ).
thf(4073,plain,
! [SV112: $i,SV392: $i,SV725: $i,SV862: $i] :
( ( ( ~ ( in @ SV862 @ SV725 ) )
= $false )
| ( ( ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV392 )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3937]) ).
thf(4074,plain,
! [SV121: $i,SV902: $i,SV400: $i > $o] :
( ( ( SV400 @ SV902 )
= $false )
| ( ( in @ SV902 @ SV121 )
= $false )
| ( ( in @ ( sK12_SY3109 @ SV400 @ SV121 ) @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3938]) ).
thf(4075,plain,
! [SV121: $i,SV903: $i,SV400: $i > $o] :
( ( ( SV400 @ SV903 )
= $false )
| ( ( in @ SV903 @ SV121 )
= $false )
| ( ( SV400 @ ( sK12_SY3109 @ SV400 @ SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3939]) ).
thf(4076,plain,
! [SV405: $i,SV126: $i,SV805: $i > $o,SV601: $i,SV947: $i] :
( ( ( ~ ( in @ SV947 @ SV601 ) )
= $true )
| ( ( SV805 @ SV947 )
= $true )
| ( ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3941]) ).
thf(4077,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ SV601 )
| ( SV805 @ SV962 ) )
= $true )
| ( ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3942]) ).
thf(4078,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV948: $i] :
( ( ( ~ ( in @ SV948 @ SV601 ) )
= $true )
| ( ( SV805 @ SV948 )
= $true )
| ( ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) )
= $false )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3943]) ).
thf(4079,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ~ ( ~ ( SV129 @ ( sK99_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3811: $i] :
( ~ ( SV129 @ SY3811 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SY3811 ) ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3944]) ).
thf(4080,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK90_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3802: $i] :
( ~ ( SV129 @ SY3802 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SY3802 ) ) ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3945]) ).
thf(4081,plain,
! [SV733: $i,SV963: $i,SV949: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV949 )
| ~ ( SV139 @ SV963 )
| ( SV949 = SV963 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3947]) ).
thf(4082,plain,
! [SV733: $i,SV950: $i,SV931: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV931 ) )
= $true )
| ( ( ~ ( SV139 @ SV950 )
| ( SV931 = SV950 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3948]) ).
thf(4083,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ SV964 )
| ~ ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3949]) ).
thf(4084,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ SV965 )
| ~ ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3950]) ).
thf(4085,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3951]) ).
thf(4086,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3952]) ).
thf(4087,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3953]) ).
thf(4088,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3954]) ).
thf(4089,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3954]) ).
thf(4090,plain,
! [SV417: $i,SV610: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) @ SV417 )
| ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3955]) ).
thf(4091,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV932: $i] :
( ( ( in @ SV932 @ SV419 )
= $false )
| ( ( SV735 @ SV932 )
= $true )
| ( ( in @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) @ SV144 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3956]) ).
thf(4092,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV951: $i] :
( ( ( ~ ( in @ SV951 @ SV419 ) )
= $true )
| ( ( SV735 @ SV951 )
= $true )
| ( ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3957]) ).
thf(4093,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV933: $i] :
( ( ( in @ SV933 @ SV419 )
= $false )
| ( ( SV735 @ SV933 )
= $true )
| ( ( SV735 @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) )
= $false )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3958]) ).
thf(4094,plain,
! [SV154: $i,SV870: $i,SV739: $i,SV427: $i,SV910: $i] :
( ( ( in @ SV910 @ ( binintersect @ SV427 @ SV739 ) )
= $false )
| ( ( in @ SV910 @ ( binunion @ SV427 @ SV870 ) )
= $true )
| ( ( in @ SV910 @ SV154 )
= $false )
| ( ( in @ SV870 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV739 @ ( powerset @ SV154 ) )
= $false )
| ( ( in @ SV427 @ ( powerset @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3961]) ).
thf(4095,plain,
! [SV432: $i > $o,SV159: $i,SV911: $i] :
( ( ( in @ SV911 @ SV159 )
= $false )
| ( ( ~ ( SV432 @ SV911 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3962]) ).
thf(4096,plain,
! [SV432: $i > $o,SV159: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV159 )
| ~ ( SV432 @ SV934 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3963]) ).
thf(4097,plain,
! [SV432: $i > $o,SV159: $i,SV952: $i] :
( ( ( ~ ( ~ ( in @ SV952 @ SV159 )
| ~ ( SV432 @ SV952 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3964]) ).
thf(4098,plain,
! [SV432: $i > $o,SV159: $i,SV966: $i] :
( ( ( ~ ~ ( ~ ( in @ SV966 @ SV159 )
| ~ ( SV432 @ SV966 ) ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3965]) ).
thf(4099,plain,
! [SV432: $i > $o,SV159: $i,SV953: $i] :
( ( ( ~ ( ~ ( in @ SV953 @ SV159 )
| ~ ( SV432 @ SV953 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3966]) ).
thf(4100,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) ) )
= $true )
| ( ( ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3967]) ).
thf(4101,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3968]) ).
thf(4102,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4103,plain,
! [SV170: $i > $i > $o,SV442: $i,SV872: $i] :
( ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3969]) ).
thf(4104,plain,
! [SV445: $i,SV173: $i,SV819: $i > $o,SV627: $i,SV954: $i] :
( ( ( ~ ( in @ SV954 @ SV627 ) )
= $true )
| ( ( SV819 @ SV954 )
= $true )
| ( ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3971]) ).
thf(4105,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV627 )
| ( SV819 @ SV967 ) )
= $true )
| ( ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3972]) ).
thf(4106,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV955: $i] :
( ( ( ~ ( in @ SV955 @ SV627 ) )
= $true )
| ( ( SV819 @ SV955 )
= $true )
| ( ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) )
= $false )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3973]) ).
thf(4107,plain,
! [SV185: $i,SV455: $i,SV743: $i] :
( ( ( in @ ( kpair @ ( sK61_SY3644 @ SV743 @ SV455 @ SV185 ) @ ( sK82_SY3774 @ SV455 @ SV743 @ SV185 ) ) @ SV455 )
= $true )
| ( ( subset @ SV455 @ SV743 )
= $true )
| ( ( breln1 @ SV185 @ SV743 )
= $false )
| ( ( breln1 @ SV185 @ SV455 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3975]) ).
thf(4108,plain,
! [SV187: $i,SV873: $i,SV744: $i,SV457: $i,SV913: $i] :
( ( ( in @ SV913 @ ( binintersect @ SV457 @ SV744 ) )
= $false )
| ( ( in @ SV913 @ ( binintersect @ ( binunion @ SV457 @ SV873 ) @ ( binunion @ SV744 @ SV873 ) ) )
= $true )
| ( ( in @ SV913 @ SV187 )
= $false )
| ( ( in @ SV873 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV744 @ ( powerset @ SV187 ) )
= $false )
| ( ( in @ SV457 @ ( powerset @ SV187 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3977]) ).
thf(4109,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ~ ( ~ ( SV207 @ ( sK100_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3814: $i] :
( ~ ( SV207 @ SY3814 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SY3814 ) ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3982]) ).
thf(4110,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( SV207 @ ( sK92_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3804: $i] :
( ~ ( SV207 @ SY3804 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SY3804 ) ) ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3983]) ).
thf(4111,plain,
! [SV215: $i,SV755: $i,SV483: $i,SV915: $i,SV879: $i] :
( ( ( in @ ( kpair @ SV879 @ SV915 ) @ SV483 )
= $false )
| ( ( in @ ( kpair @ SV879 @ SV915 ) @ ( binunion @ SV483 @ SV755 ) )
= $true )
| ( ( in @ SV915 @ SV215 )
= $false )
| ( ( in @ SV879 @ SV215 )
= $false )
| ( ( breln1 @ SV215 @ SV755 )
= $false )
| ( ( breln1 @ SV215 @ SV483 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3984]) ).
thf(4112,plain,
! [SV221: $i,SV826: $i,SV489: $i > $o] :
( ( ( SV489 @ ( sK62_SY3278 @ SV826 @ SV489 @ SV221 ) )
= $false )
| ( ( SV489 @ SV826 )
= $true )
| ( ( in @ SV826 @ SV221 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3986]) ).
thf(4113,plain,
! [SV494: $i,SV827: $i,SV648: $i,SV226: $i] :
( ( ( in @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) @ SV494 )
= $true )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3987]) ).
thf(4114,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV648 ) )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3988]) ).
thf(4115,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV827 )
= $false )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3988]) ).
thf(4116,plain,
! [SV238: $i,SV881: $i,SV765: $i,SV506: $i,SV916: $i] :
( ( ( in @ SV916 @ ( binintersect @ SV506 @ SV765 ) )
= $false )
| ( ( in @ SV916 @ ( binunion @ SV765 @ SV881 ) )
= $true )
| ( ( in @ SV916 @ SV238 )
= $false )
| ( ( in @ SV881 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV765 @ ( powerset @ SV238 ) )
= $false )
| ( ( in @ SV506 @ ( powerset @ SV238 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3989]) ).
thf(4117,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV917: $i,SV882: $i] :
( ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( ! [SY3783: $o] :
( ~ ! [SY3784: $i] :
( ~ ( in @ SY3784 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3784 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3784 @ SV917 ) @ SV766 )
| SY3783 )
| SY3783 ) )
= $true )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3990]) ).
thf(4118,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV935: $i] :
( ( ( in @ SV935 @ SV509 )
= $false )
| ( ( SV767 @ SV935 )
= $true )
| ( ( in @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) @ SV241 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3991]) ).
thf(4119,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV956: $i] :
( ( ( ~ ( in @ SV956 @ SV509 ) )
= $true )
| ( ( SV767 @ SV956 )
= $true )
| ( ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3992]) ).
thf(4120,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV936: $i] :
( ( ( in @ SV936 @ SV509 )
= $false )
| ( ( SV767 @ SV936 )
= $true )
| ( ( SV767 @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) )
= $false )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3993]) ).
thf(4121,plain,
! [SV250: $i > $o,SV770: $i] :
( ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ~ ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3994]) ).
thf(4122,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3995]) ).
thf(4123,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3996]) ).
thf(4124,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK101_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3815: $i] :
( ~ ( SV250 @ SY3815 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SY3815 ) ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3997]) ).
thf(4125,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3998]) ).
thf(4126,plain,
! [SV518: $i,SV832: $i,SV658: $i,SV251: $i] :
( ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3999]) ).
thf(4127,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4000]) ).
thf(4128,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4000]) ).
thf(4129,plain,
! [SV252: $i,SV771: $i,SV519: $i,SV885: $i] :
( ( ( in @ SV885 @ SV519 )
= $false )
| ( ( in @ SV885 @ SV771 )
= $false )
| ( ( subset @ SV519 @ ( setminus @ SV252 @ SV771 ) )
= $false )
| ( ( in @ SV885 @ SV252 )
= $false )
| ( ( in @ SV771 @ ( powerset @ SV252 ) )
= $false )
| ( ( in @ SV519 @ ( powerset @ SV252 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4001]) ).
thf(4130,plain,
! [SV256: $i,SV926: $i,SV522: $i > $o] :
( ( ( SV522 @ SV926 )
= $false )
| ( ( in @ SV926 @ SV256 )
= $false )
| ( ( in @ ( sK38_SY3333 @ SV522 @ SV256 ) @ SV256 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4002]) ).
thf(4131,plain,
! [SV256: $i,SV927: $i,SV522: $i > $o] :
( ( ( SV522 @ SV927 )
= $false )
| ( ( in @ SV927 @ SV256 )
= $false )
| ( ( SV522 @ ( sK38_SY3333 @ SV522 @ SV256 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4003]) ).
thf(4132,plain,
! [SV773: $i,SV919: $i,SV524: $i,SV886: $i,SV258: $i,SV957: $i] :
( ( ( ~ ( in @ SV957 @ SV258 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
| ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) )
= $true )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4004]) ).
thf(4133,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
| ! [SY3816: $i] :
( ~ ( in @ SY3816 @ SV259 )
| ~ ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3816 ) @ SV774 )
| ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3816 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4005]) ).
thf(4134,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4006]) ).
thf(4135,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) )
| ( SV525 = SV774 ) )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4007]) ).
thf(4136,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4008]) ).
thf(4137,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ~ ! [SY3817: $i] :
~ ( ~ ( ~ ( SV263 @ SY3817 )
| ( SY3817
= ( sK103_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SY3817
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SY3817 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4009]) ).
thf(4138,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ! [SY3805: $i] :
~ ( ~ ( ~ ( SV263 @ SY3805 )
| ( SY3805
= ( sK93_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SY3805
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SY3805 ) ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4010]) ).
thf(4139,plain,
! [SV264: $i,SV529: $i,SV776: $i,SV887: $i] :
( ( ( in @ SV887 @ SV776 )
= $true )
| ( ( ~ ( in @ SV887 @ SV529 ) )
= $true )
| ( ( subset @ SV529 @ SV776 )
= $false )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4011]) ).
thf(4140,plain,
! [SV265: $i,SV777: $i,SV968: $i] :
( ( ( ~ ~ ( ~ ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SV968 @ SV265 ) ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4012]) ).
thf(4141,plain,
! [SV278: $i,SV540: $i > $o,SV838: $i] :
( ( ( ~ ( in @ ( sK94_SY3368 @ SV838 @ SV540 @ SV278 ) @ SV278 ) )
= $false )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( SV540 @ SV838 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4014]) ).
thf(4142,plain,
! [SV278: $i,SV838: $i,SV540: $i > $o] :
( ( ( SV540 @ ( sK94_SY3368 @ SV838 @ SV540 @ SV278 ) )
= $false )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( SV540 @ SV838 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4014]) ).
thf(4143,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( ~ ( SV291 @ ( sK104_SY2929 @ SV782 @ SV291 ) ) )
= $false )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4015]) ).
thf(4144,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( SV291 @ ( sK95_SY2929 @ SV782 @ SV291 ) )
= $true )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV782
= ( sK81_SY3687 @ SV782 @ SV291 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4016]) ).
thf(4145,plain,
! [SV37: $i,SV848: $i,SV322: $i,SV905: $i,SV699: $i] :
( ( ( ~ ( subset @ SV699 @ SV905 ) )
= $true )
| ( ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) )
= $true )
| ( ( subset @ SV322 @ SV848 )
= $false )
| ( ( in @ SV905 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4017]) ).
thf(4146,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
| ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
= $false )
| ( ( ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4018]) ).
thf(4147,plain,
! [SV45: $i,SV937: $i] :
( ( ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( ! [SY3793: $i] :
( ~ ( in @ SY3793 @ SV937 )
| ( in @ SY3793 @ SV45 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4019]) ).
thf(4148,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ( ~ ~ ( ~ ( in @ SV938 @ SV45 )
| ~ ( in @ SV958 @ SV45 ) ) )
= $true )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4020]) ).
thf(4149,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ( ~ ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4021]) ).
thf(4150,plain,
! [SV849: $i,SV45: $i] :
( ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( ~ ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4022]) ).
thf(4151,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4023]) ).
thf(4152,plain,
! [SV52: $i,SV939: $i] :
( ( ( in @ SV939 @ omega )
= $false )
| ( ( in @ SV939 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4024]) ).
thf(4153,plain,
! [SV52: $i,SV940: $i] :
( ( ( in @ SV940 @ omega )
= $false )
| ( ( in @ SV940 @ SV52 )
= $true )
| ( ( in @ emptyset @ SV52 )
= $false )
| ( ( in @ ( sK39_SY2254 @ SV52 ) @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4025]) ).
thf(4154,plain,
! [SV711: $i,SV907: $i,SV348: $i,SV855: $i,SV68: $i] :
( ( ( ! [SY3779: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY3779 @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ SY3779 ) @ SV348 ) )
| ~ ( in @ ( kpair @ SY3779 @ SV907 ) @ SV711 ) ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4026]) ).
thf(4155,plain,
! [SV893: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV941: $i] :
( ( ( in @ SV941 @ SV74 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3796: $i] :
~ ( ~ ( SV573 @ SV941 @ SY3796 )
| ~ ! [SY3797: $i] :
( ~ ( in @ SY3797 @ SV354 )
| ~ ( SV573 @ SV941 @ SY3797 )
| ( in @ ( kpair @ SY3796 @ SY3797 ) @ SV893 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV893 )
= $false )
| ( ( in @ SV893 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4027]) ).
thf(4156,plain,
! [SV894: $i,SV573: $i > $i > $o,SV74: $i,SV354: $i,SV959: $i] :
( ( ( ~ ( in @ SV959 @ ( breln1Set @ SV354 ) ) )
= $true )
| ( ( ~ ( reflwellordering @ SV354 @ SV959 )
| ! [SY3807: $i] :
( ~ ( in @ SY3807 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3808: $i] :
~ ( ~ ( SV573 @ SY3807 @ SY3808 )
| ~ ! [SY3809: $i] :
( ~ ( in @ SY3809 @ SV354 )
| ~ ( SV573 @ SY3807 @ SY3809 )
| ( in @ ( kpair @ SY3808 @ SY3809 ) @ SV959 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4028]) ).
thf(4157,plain,
! [SV577: $i,SV791: $i,SV361: $i,SV81: $i,SV942: $i] :
( ( ( in @ SV942 @ SV81 )
= $false )
| ( ( ! [SY3798: $i] :
( ~ ( in @ SY3798 @ SV361 )
| ~ ( in @ ( kpair @ SV942 @ SY3798 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SY3798 ) @ SV577 ) ) )
= $true )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4030]) ).
thf(4158,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV928: $i,SV361: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV361 )
| ~ ( in @ ( kpair @ SV928 @ SV969 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SV969 ) @ SV577 ) )
= $true )
| ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4031]) ).
thf(4159,plain,
! [SV85: $i,SV859: $o,SV716: $i,SV365: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4032]) ).
thf(4160,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV895: $i,SV859: $o] :
( ( SV859 = $false )
| ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4032]) ).
thf(4161,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4162,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4033]) ).
thf(4163,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV365 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4034]) ).
thf(4164,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4034]) ).
thf(4165,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4037]) ).
thf(4166,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4038]) ).
thf(4167,plain,
! [SV93: $i,SV373: $i,SV584: $i,SV795: $o] :
( ( SV795 = $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4038]) ).
thf(4168,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4043]) ).
thf(4169,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4044]) ).
thf(4170,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4044]) ).
thf(4171,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV93 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4049]) ).
thf(4172,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( ~ ( in @ SV584 @ SV373 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4173,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4050]) ).
thf(4174,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK88_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3799: $i] :
( ~ ( SV95 @ SY3799 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SY3799 ) ) )
= $false )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4053]) ).
thf(4175,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( ~ ( SV95 @ ( sK96_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3810: $i] :
( ~ ( SV95 @ SY3810 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SY3810 ) ) ) )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4054]) ).
thf(4176,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK89_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3800: $i] :
( ~ ( SV95 @ SY3800 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SY3800 ) ) )
= $false )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4055]) ).
thf(4177,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4056]) ).
thf(4178,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4057]) ).
thf(4179,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4058]) ).
thf(4180,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4059]) ).
thf(4181,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4060]) ).
thf(4182,plain,
! [SV98: $i,SV908: $i,SV377: $i > $o] :
( ( ( SV377 @ SV908 )
= $false )
| ( ( in @ SV908 @ SV98 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK10_SY3077 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4061]) ).
thf(4183,plain,
! [SV377: $i > $o,SV98: $i,SV929: $i] :
( ( ( ~ ( in @ SV929 @ SV98 ) )
= $true )
| ( ( ~ ( SV377 @ SV929 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4062]) ).
thf(4184,plain,
! [SV377: $i > $o,SV98: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ SV98 )
| ~ ( SV377 @ SV943 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4063]) ).
thf(4185,plain,
! [SV377: $i > $o,SV98: $i,SV960: $i] :
( ( ( ~ ( ~ ( in @ SV960 @ SV98 )
| ~ ( SV377 @ SV960 ) ) )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4064]) ).
thf(4186,plain,
! [SV377: $i > $o,SV98: $i,SV944: $i] :
( ( ( ~ ( in @ SV944 @ SV98 )
| ~ ( SV377 @ SV944 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4065]) ).
thf(4187,plain,
! [SV722: $i,SV961: $i,SV945: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV945 ) )
= $true )
| ( ( ~ ( SV105 @ SV961 )
| ( SV945 = SV961 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4066]) ).
thf(4188,plain,
! [SV722: $i,SV946: $i,SV930: $i,SV105: $i > $o] :
( ( ( SV105 @ SV930 )
= $false )
| ( ( ~ ( SV105 @ SV946 )
| ( SV930 = SV946 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4067]) ).
thf(4189,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4190,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4070]) ).
thf(4191,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
| ~ ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4071]) ).
thf(4192,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4072]) ).
thf(4193,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4072]) ).
thf(4194,plain,
! [SV112: $i,SV392: $i,SV725: $i,SV862: $i] :
( ( ( in @ SV862 @ SV725 )
= $true )
| ( ( ~ ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) ) )
= $true )
| ( ( in @ SV862 @ SV392 )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4073]) ).
thf(4195,plain,
! [SV405: $i,SV126: $i,SV805: $i > $o,SV601: $i,SV947: $i] :
( ( ( in @ SV947 @ SV601 )
= $false )
| ( ( SV805 @ SV947 )
= $true )
| ( ( in @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) @ SV405 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4076]) ).
thf(4196,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV962: $i] :
( ( ( ~ ( in @ SV962 @ SV601 ) )
= $true )
| ( ( SV805 @ SV962 )
= $true )
| ( ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4077]) ).
thf(4197,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV948: $i] :
( ( ( in @ SV948 @ SV601 )
= $false )
| ( ( SV805 @ SV948 )
= $true )
| ( ( SV805 @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) )
= $false )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4078]) ).
thf(4198,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK99_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3811: $i] :
( ~ ( SV129 @ SY3811 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SY3811 ) ) ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4079]) ).
thf(4199,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK90_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3802: $i] :
( ~ ( SV129 @ SY3802 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SY3802 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4080]) ).
thf(4200,plain,
! [SV733: $i,SV963: $i,SV949: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV949 ) )
= $true )
| ( ( ~ ( SV139 @ SV963 )
| ( SV949 = SV963 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4081]) ).
thf(4201,plain,
! [SV733: $i,SV950: $i,SV931: $i,SV139: $i > $o] :
( ( ( SV139 @ SV931 )
= $false )
| ( ( ~ ( SV139 @ SV950 )
| ( SV931 = SV950 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4082]) ).
thf(4202,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ SV964 )
| ~ ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4083]) ).
thf(4203,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ SV965 )
| ~ ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4084]) ).
thf(4204,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
| ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4085]) ).
thf(4205,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4086]) ).
thf(4206,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4086]) ).
thf(4207,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4208,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4087]) ).
thf(4209,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4088]) ).
thf(4210,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4089]) ).
thf(4211,plain,
! [SV417: $i,SV610: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) @ SV417 ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4090]) ).
thf(4212,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( SV610
!= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) ) )
= $false )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4090]) ).
thf(4213,plain,
! [SV144: $i,SV735: $i > $o,SV419: $i,SV951: $i] :
( ( ( in @ SV951 @ SV419 )
= $false )
| ( ( SV735 @ SV951 )
= $true )
| ( ( in @ ( kpair @ ( sK41_SY3632 @ SV735 @ SV419 @ SV144 ) @ ( sK59_SY3747 @ SV419 @ SV735 @ SV144 ) ) @ SV419 )
= $true )
| ( ( breln1 @ SV144 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4092]) ).
thf(4214,plain,
! [SV159: $i,SV911: $i,SV432: $i > $o] :
( ( ( SV432 @ SV911 )
= $false )
| ( ( in @ SV911 @ SV159 )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK14_SY3181 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4095]) ).
thf(4215,plain,
! [SV432: $i > $o,SV159: $i,SV934: $i] :
( ( ( ~ ( in @ SV934 @ SV159 ) )
= $true )
| ( ( ~ ( SV432 @ SV934 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4096]) ).
thf(4216,plain,
! [SV432: $i > $o,SV159: $i,SV952: $i] :
( ( ( ~ ( in @ SV952 @ SV159 )
| ~ ( SV432 @ SV952 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4097]) ).
thf(4217,plain,
! [SV432: $i > $o,SV159: $i,SV966: $i] :
( ( ( ~ ( ~ ( in @ SV966 @ SV159 )
| ~ ( SV432 @ SV966 ) ) )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4098]) ).
thf(4218,plain,
! [SV432: $i > $o,SV159: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ SV159 )
| ~ ( SV432 @ SV953 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4099]) ).
thf(4219,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( ~ ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4100]) ).
thf(4220,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4101]) ).
thf(4221,plain,
! [SV872: $i,SV442: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( ~ ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4102]) ).
thf(4222,plain,
! [SV872: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4103]) ).
thf(4223,plain,
! [SV445: $i,SV173: $i,SV819: $i > $o,SV627: $i,SV954: $i] :
( ( ( in @ SV954 @ SV627 )
= $false )
| ( ( SV819 @ SV954 )
= $true )
| ( ( in @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) @ SV445 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4104]) ).
thf(4224,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV967: $i] :
( ( ( ~ ( in @ SV967 @ SV627 ) )
= $true )
| ( ( SV819 @ SV967 )
= $true )
| ( ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4105]) ).
thf(4225,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV955: $i] :
( ( ( in @ SV955 @ SV627 )
= $false )
| ( ( SV819 @ SV955 )
= $true )
| ( ( SV819 @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) )
= $false )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4106]) ).
thf(4226,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( ~ ( SV207 @ ( sK100_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3814: $i] :
( ~ ( SV207 @ SY3814 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SY3814 ) ) ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4109]) ).
thf(4227,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK92_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3804: $i] :
( ~ ( SV207 @ SY3804 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SY3804 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4110]) ).
thf(4228,plain,
! [SV226: $i,SV494: $i,SV648: $i,SV827: $i] :
( ( ( in @ ( kpair @ ( sK78_SY3714 @ SV827 @ SV648 @ SV494 @ SV226 ) @ ( sK85_SY3782 @ SV226 @ SV648 @ SV827 @ SV494 ) ) @ SV648 )
= $true )
| ( ( subset @ SV648 @ SV827 )
= $true )
| ( ( breln @ SV226 @ SV494 @ SV827 )
= $false )
| ( ( breln @ SV226 @ SV494 @ SV648 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4114]) ).
thf(4229,plain,
! [SV970: $o,SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3818 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3818 @ SV917 ) @ SV766 )
| SV970 )
| SV970 )
= $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4117]) ).
thf(4230,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $true )
| $true )
= $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4117]) ).
thf(4231,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $false )
| $false )
= $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[4117]) ).
thf(4232,plain,
! [SV241: $i,SV767: $i > $o,SV509: $i,SV956: $i] :
( ( ( in @ SV956 @ SV509 )
= $false )
| ( ( SV767 @ SV956 )
= $true )
| ( ( in @ ( kpair @ ( sK45_SY3669 @ SV767 @ SV509 @ SV241 ) @ ( sK65_SY3757 @ SV509 @ SV767 @ SV241 ) ) @ SV509 )
= $true )
| ( ( breln1 @ SV241 @ SV509 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4119]) ).
thf(4233,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY2813: $i] :
~ ~ ( ~ ( SV250 @ SY2813 )
| ~ ! [SY2814: $i] :
( ~ ( SV250 @ SY2814 )
| ( SY2813 = SY2814 ) ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4121]) ).
thf(4234,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK106_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3819: $i] :
( ~ ( SV250 @ SY3819 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SY3819 ) ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4122]) ).
thf(4235,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK107_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3820: $i] :
( ~ ( SV250 @ SY3820 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SY3820 ) ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4123]) ).
thf(4236,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK101_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3815: $i] :
( ~ ( SV250 @ SY3815 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SY3815 ) ) ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4124]) ).
thf(4237,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
| ! [SY3821: $i] :
( ~ ( in @ SY3821 @ SV518 )
| ~ ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3821 ) @ SV832 )
| ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3821 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4125]) ).
thf(4238,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4126]) ).
thf(4239,plain,
! [SV251: $i,SV518: $i,SV658: $i,SV832: $i] :
( ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) )
| ( SV658 = SV832 ) )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4127]) ).
thf(4240,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4128]) ).
thf(4241,plain,
! [SV773: $i,SV919: $i,SV524: $i,SV886: $i,SV258: $i,SV957: $i] :
( ( ( in @ SV957 @ SV258 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
| ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) )
= $true )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4132]) ).
thf(4242,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4133]) ).
thf(4243,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ! [SY3816: $i] :
( ~ ( in @ SY3816 @ SV259 )
| ~ ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3816 ) @ SV774 )
| ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3816 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4133]) ).
thf(4244,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4134]) ).
thf(4245,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ~ ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4135]) ).
thf(4246,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4136]) ).
thf(4247,plain,
! [SV775: $i,SV263: $i > $o] :
( ( ( ! [SY3817: $i] :
~ ( ~ ( ~ ( SV263 @ SY3817 )
| ( SY3817
= ( sK103_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SY3817
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SY3817 ) ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4137]) ).
thf(4248,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV263 @ SV971 )
| ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SV971
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV971 ) ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4138]) ).
thf(4249,plain,
! [SV264: $i,SV776: $i,SV529: $i,SV887: $i] :
( ( ( in @ SV887 @ SV529 )
= $false )
| ( ( in @ SV887 @ SV776 )
= $true )
| ( ( subset @ SV529 @ SV776 )
= $false )
| ( ( in @ SV887 @ SV264 )
= $false )
| ( ( in @ SV776 @ ( powerset @ SV264 ) )
= $false )
| ( ( in @ SV529 @ ( powerset @ SV264 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4139]) ).
thf(4250,plain,
! [SV265: $i,SV777: $i,SV968: $i] :
( ( ( ~ ( ~ ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SV968 @ SV265 ) ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4140]) ).
thf(4251,plain,
! [SV278: $i,SV540: $i > $o,SV838: $i] :
( ( ( in @ ( sK94_SY3368 @ SV838 @ SV540 @ SV278 ) @ SV278 )
= $true )
| ( ( in @ SV838 @ SV278 )
= $false )
| ( ( SV540 @ SV838 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4141]) ).
thf(4252,plain,
! [SV782: $i,SV291: $i > $o] :
( ( ( SV291 @ ( sK104_SY2929 @ SV782 @ SV291 ) )
= $true )
| ( ( SV291 @ SV782 )
= $false )
| ( ( SV291 @ ( sK81_SY3687 @ SV782 @ SV291 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4143]) ).
thf(4253,plain,
! [SV37: $i,SV848: $i,SV322: $i,SV905: $i,SV699: $i] :
( ( ( subset @ SV699 @ SV905 )
= $false )
| ( ( subset @ ( binintersect @ SV322 @ SV699 ) @ ( binintersect @ SV848 @ SV905 ) )
= $true )
| ( ( subset @ SV322 @ SV848 )
= $false )
| ( ( in @ SV905 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV848 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV699 @ ( powerset @ SV37 ) )
= $false )
| ( ( in @ SV322 @ ( powerset @ SV37 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4145]) ).
thf(4254,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( ~ ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) )
= $false )
| ( ( ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4146]) ).
thf(4255,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4146]) ).
thf(4256,plain,
! [SV45: $i,SV937: $i,SV972: $i] :
( ( ( ~ ( in @ SV972 @ SV937 )
| ( in @ SV972 @ SV45 ) )
= $true )
| ( ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4147]) ).
thf(4257,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ( ~ ( ~ ( in @ SV938 @ SV45 )
| ~ ( in @ SV958 @ SV45 ) ) )
= $false )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4148]) ).
thf(4258,plain,
! [SV920: $i,SV45: $i,SV906: $i] :
( ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4149]) ).
thf(4259,plain,
! [SV45: $i,SV849: $i] :
( ( ( ~ ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4150]) ).
thf(4260,plain,
! [SV45: $i,SV849: $i] :
( ( ( ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4151]) ).
thf(4261,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) )
| ~ ( in @ ( kpair @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV907 ) @ SV711 ) ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4154]) ).
thf(4262,plain,
! [SV894: $i,SV573: $i > $i > $o,SV74: $i,SV354: $i,SV959: $i] :
( ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( ~ ( reflwellordering @ SV354 @ SV959 )
| ! [SY3807: $i] :
( ~ ( in @ SY3807 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3808: $i] :
~ ( ~ ( SV573 @ SY3807 @ SY3808 )
| ~ ! [SY3809: $i] :
( ~ ( in @ SY3809 @ SV354 )
| ~ ( SV573 @ SY3807 @ SY3809 )
| ( in @ ( kpair @ SY3808 @ SY3809 ) @ SV959 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4156]) ).
thf(4263,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV942: $i,SV361: $i,SV973: $i] :
( ( ( ~ ( in @ SV973 @ SV361 )
| ~ ( in @ ( kpair @ SV942 @ SV973 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SV973 ) @ SV577 ) )
= $true )
| ( ( in @ SV942 @ SV81 )
= $false )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4157]) ).
thf(4264,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV928: $i,SV361: $i,SV969: $i] :
( ( ( ~ ( in @ SV969 @ SV361 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV969 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SV969 ) @ SV577 ) )
= $true )
| ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4158]) ).
thf(4265,plain,
! [SV85: $i,SV859: $o,SV716: $i,SV365: $i,SV895: $i] :
( ( ( in @ SV895 @ SV365 )
= $true )
| ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 )
| SV859 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4159]) ).
thf(4266,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 ) )
= $true )
| ( SV859 = $true )
| ( SV859 = $false )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4160]) ).
thf(4267,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( ( in @ SV896 @ SV365 )
= $true )
| ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true )
| $true )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4161]) ).
thf(4268,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4162]) ).
thf(4269,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( ( in @ SV897 @ SV365 )
= $true )
| ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false )
| $false )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4163]) ).
thf(4270,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4164]) ).
thf(4271,plain,
! [SV373: $i,SV795: $o,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4165]) ).
thf(4272,plain,
! [SV93: $i,SV795: $o,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( SV795 = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4166]) ).
thf(4273,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4168]) ).
thf(4274,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $true = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4169]) ).
thf(4275,plain,
! [SV373: $i,SV93: $i,SV584: $i] :
( ( ( in @ SV584 @ SV93 )
= $false )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4171]) ).
thf(4276,plain,
! [SV93: $i,SV373: $i,SV584: $i] :
( ( ( in @ SV584 @ SV373 )
= $true )
| ( $false = $true )
| ( ( in @ SV584 @ SV373 )
= $false )
| ( ( in @ SV584 @ ( symdiff @ SV93 @ SV373 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4172]) ).
thf(4277,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK88_SY2391 @ SV717 @ SV95 ) ) )
= $false )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4278,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ! [SY3799: $i] :
( ~ ( SV95 @ SY3799 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SY3799 ) ) )
= $false )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4174]) ).
thf(4279,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK96_SY2391 @ SV717 @ SV95 ) )
| ~ ! [SY3810: $i] :
( ~ ( SV95 @ SY3810 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SY3810 ) ) )
= $false )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4175]) ).
thf(4280,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK89_SY2391 @ SV717 @ SV95 ) ) )
= $false )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4176]) ).
thf(4281,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ! [SY3800: $i] :
( ~ ( SV95 @ SY3800 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SY3800 ) ) )
= $false )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4176]) ).
thf(4282,plain,
! [SV376: $i > $o,SV921: $i,SV97: $i > $o] :
( ( ( ! [SY3789: $i] :
( ~ ( SV97 @ SY3789 )
| ( SV921 = SY3789 ) ) )
= $false )
| ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4177]) ).
thf(4283,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4178]) ).
thf(4284,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4179]) ).
thf(4285,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4180]) ).
thf(4286,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( ~ ~ ( ~ ( SV97 @ SV974 )
| ~ ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4181]) ).
thf(4287,plain,
! [SV377: $i > $o,SV98: $i,SV929: $i] :
( ( ( in @ SV929 @ SV98 )
= $false )
| ( ( ~ ( SV377 @ SV929 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4183]) ).
thf(4288,plain,
! [SV377: $i > $o,SV98: $i,SV943: $i] :
( ( ( ~ ( in @ SV943 @ SV98 ) )
= $true )
| ( ( ~ ( SV377 @ SV943 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4184]) ).
thf(4289,plain,
! [SV377: $i > $o,SV98: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV98 )
| ~ ( SV377 @ SV960 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4185]) ).
thf(4290,plain,
! [SV377: $i > $o,SV98: $i,SV944: $i] :
( ( ( ~ ( in @ SV944 @ SV98 ) )
= $true )
| ( ( ~ ( SV377 @ SV944 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4186]) ).
thf(4291,plain,
! [SV722: $i,SV961: $i,SV945: $i,SV105: $i > $o] :
( ( ( SV105 @ SV945 )
= $false )
| ( ( ~ ( SV105 @ SV961 )
| ( SV945 = SV961 ) )
= $true )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4187]) ).
thf(4292,plain,
! [SV722: $i,SV930: $i,SV946: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV946 ) )
= $true )
| ( ( SV930 = SV946 )
= $true )
| ( ( SV105 @ SV930 )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4188]) ).
thf(4293,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4189]) ).
thf(4294,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4295,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4190]) ).
thf(4296,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4191]) ).
thf(4297,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
| ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4191]) ).
thf(4298,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4192]) ).
thf(4299,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4193]) ).
thf(4300,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4193]) ).
thf(4301,plain,
! [SV112: $i,SV725: $i,SV392: $i,SV862: $i] :
( ( ( in @ SV862 @ ( binunion @ SV392 @ SV725 ) )
= $false )
| ( ( in @ SV862 @ SV725 )
= $true )
| ( ( in @ SV862 @ SV392 )
= $true )
| ( ( in @ SV862 @ SV112 )
= $false )
| ( ( in @ SV725 @ ( powerset @ SV112 ) )
= $false )
| ( ( in @ SV392 @ ( powerset @ SV112 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4194]) ).
thf(4302,plain,
! [SV126: $i,SV405: $i,SV805: $i > $o,SV601: $i,SV962: $i] :
( ( ( in @ SV962 @ SV601 )
= $false )
| ( ( SV805 @ SV962 )
= $true )
| ( ( in @ ( kpair @ ( sK51_SY3700 @ SV805 @ SV601 @ SV405 @ SV126 ) @ ( sK72_SY3768 @ SV126 @ SV601 @ SV805 @ SV405 ) ) @ SV601 )
= $true )
| ( ( breln @ SV126 @ SV405 @ SV601 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4196]) ).
thf(4303,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK99_SY2492 @ SV730 @ SV129 ) )
| ~ ! [SY3811: $i] :
( ~ ( SV129 @ SY3811 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SY3811 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4198]) ).
thf(4304,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK90_SY2492 @ SV730 @ SV129 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4199]) ).
thf(4305,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ! [SY3802: $i] :
( ~ ( SV129 @ SY3802 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SY3802 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4199]) ).
thf(4306,plain,
! [SV733: $i,SV963: $i,SV949: $i,SV139: $i > $o] :
( ( ( SV139 @ SV949 )
= $false )
| ( ( ~ ( SV139 @ SV963 )
| ( SV949 = SV963 ) )
= $true )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4200]) ).
thf(4307,plain,
! [SV733: $i,SV931: $i,SV950: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV950 ) )
= $true )
| ( ( SV931 = SV950 )
= $true )
| ( ( SV139 @ SV931 )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4201]) ).
thf(4308,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV964 )
| ~ ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4202]) ).
thf(4309,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV965 )
| ~ ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4203]) ).
thf(4310,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4204]) ).
thf(4311,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4204]) ).
thf(4312,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4205]) ).
thf(4313,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4206]) ).
thf(4314,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4207]) ).
thf(4315,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4208]) ).
thf(4316,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4209]) ).
thf(4317,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4210]) ).
thf(4318,plain,
! [SV417: $i,SV610: $i,SV142: $i] :
( ( ( in @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) @ SV417 )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4211]) ).
thf(4319,plain,
! [SV142: $i,SV417: $i,SV610: $i] :
( ( ( SV610
= ( kpair @ ( sK34_SY3488 @ SV610 @ SV417 @ SV142 ) @ ( sK84_SY3732 @ SV142 @ SV610 @ SV417 ) ) )
= $true )
| ( ( in @ SV610 @ ( cartprod @ SV142 @ SV417 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4212]) ).
thf(4320,plain,
! [SV432: $i > $o,SV159: $i,SV934: $i] :
( ( ( in @ SV934 @ SV159 )
= $false )
| ( ( ~ ( SV432 @ SV934 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4215]) ).
thf(4321,plain,
! [SV432: $i > $o,SV159: $i,SV952: $i] :
( ( ( ~ ( in @ SV952 @ SV159 ) )
= $true )
| ( ( ~ ( SV432 @ SV952 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4216]) ).
thf(4322,plain,
! [SV432: $i > $o,SV159: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ SV159 )
| ~ ( SV432 @ SV966 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4217]) ).
thf(4323,plain,
! [SV432: $i > $o,SV159: $i,SV953: $i] :
( ( ( ~ ( in @ SV953 @ SV159 ) )
= $true )
| ( ( ~ ( SV432 @ SV953 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4218]) ).
thf(4324,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3780: $i] :
~ ~ ( ~ ( in @ SY3780 @ SV442 )
| ~ ( SV170 @ SY3780 @ SV912 ) ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4219]) ).
thf(4325,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3781: $i] :
~ ~ ( ~ ( in @ SY3781 @ SV442 )
| ~ ( SV170 @ SY3781 @ SV912 ) ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4220]) ).
thf(4326,plain,
! [SV872: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3204: $i] :
~ ! [SY3205: $i] :
~ ( ~ ( ~ ( in @ SY3205 @ SY3204 )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3205 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3205 ) )
| ( in @ SY3205 @ SY3204 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4221]) ).
thf(4327,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i] :
( ( ( ~ ! [SY3823: $i] :
~ ( ~ ( ~ ( in @ SY3823 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3823 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3823 ) )
| ( in @ SY3823 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4222]) ).
thf(4328,plain,
! [SV173: $i,SV445: $i,SV819: $i > $o,SV627: $i,SV967: $i] :
( ( ( in @ SV967 @ SV627 )
= $false )
| ( ( SV819 @ SV967 )
= $true )
| ( ( in @ ( kpair @ ( sK53_SY3710 @ SV819 @ SV627 @ SV445 @ SV173 ) @ ( sK76_SY3772 @ SV173 @ SV627 @ SV819 @ SV445 ) ) @ SV627 )
= $true )
| ( ( breln @ SV173 @ SV445 @ SV627 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4224]) ).
thf(4329,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK100_SY2702 @ SV753 @ SV207 ) )
| ~ ! [SY3814: $i] :
( ~ ( SV207 @ SY3814 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SY3814 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4226]) ).
thf(4330,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK92_SY2702 @ SV753 @ SV207 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4227]) ).
thf(4331,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ! [SY3804: $i] :
( ~ ( SV207 @ SY3804 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SY3804 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4227]) ).
thf(4332,plain,
! [SV970: $o,SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3818 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3818 @ SV917 ) @ SV766 )
| SV970 ) )
= $true )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4229]) ).
thf(4333,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4230]) ).
thf(4334,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4231]) ).
thf(4335,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK111_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3826: $i] :
( ~ ( SV250 @ SY3826 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SY3826 ) ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4233]) ).
thf(4336,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK106_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3819: $i] :
( ~ ( SV250 @ SY3819 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SY3819 ) ) ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4234]) ).
thf(4337,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK107_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3820: $i] :
( ~ ( SV250 @ SY3820 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SY3820 ) ) ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4235]) ).
thf(4338,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK101_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3815: $i] :
( ~ ( SV250 @ SY3815 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SY3815 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4236]) ).
thf(4339,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4237]) ).
thf(4340,plain,
! [SV251: $i,SV832: $i,SV658: $i,SV518: $i] :
( ( ( ! [SY3821: $i] :
( ~ ( in @ SY3821 @ SV518 )
| ~ ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3821 ) @ SV832 )
| ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3821 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4237]) ).
thf(4341,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4238]) ).
thf(4342,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ~ ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4239]) ).
thf(4343,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4240]) ).
thf(4344,plain,
! [SV258: $i,SV773: $i,SV919: $i,SV524: $i,SV957: $i,SV886: $i] :
( ( ( ~ ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) )
= $true )
| ( ( in @ SV957 @ SV258 )
= $false )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4241]) ).
thf(4345,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4242]) ).
thf(4346,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) @ SV259 )
| ~ ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4243]) ).
thf(4347,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
| ! [SY3827: $i] :
( ~ ( in @ SY3827 @ SV259 )
| ~ ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3827 ) @ SV774 )
| ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3827 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4244]) ).
thf(4348,plain,
! [SV525: $i,SV774: $i,SV259: $i] :
( ( ( ! [SY3681: $i] :
( ~ ( in @ SY3681 @ SV259 )
| ! [SY3682: $i] :
( ~ ( in @ SY3682 @ SV259 )
| ~ ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV774 )
| ( in @ ( kpair @ SY3681 @ SY3682 ) @ SV525 ) ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4245]) ).
thf(4349,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
| ! [SY3828: $i] :
( ~ ( in @ SY3828 @ SV259 )
| ~ ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3828 ) @ SV774 )
| ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3828 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4246]) ).
thf(4350,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV263 @ SV975 )
| ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SV975
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV975 ) ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4247]) ).
thf(4351,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ SV971 )
| ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SV971
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV971 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4248]) ).
thf(4352,plain,
! [SV265: $i,SV777: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
| ~ ( in @ SV968 @ SV265 ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4250]) ).
thf(4353,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $true )
| ( ( ~ ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4254]) ).
thf(4354,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) )
= $false )
| ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4255]) ).
thf(4355,plain,
! [SV45: $i,SV937: $i,SV972: $i] :
( ( ( ~ ( in @ SV972 @ SV937 ) )
= $true )
| ( ( in @ SV972 @ SV45 )
= $true )
| ( ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4256]) ).
thf(4356,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV45 )
| ~ ( in @ SV958 @ SV45 ) )
= $true )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4257]) ).
thf(4357,plain,
! [SV906: $i,SV45: $i,SV920: $i] :
( ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) )
| ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4258]) ).
thf(4358,plain,
! [SV45: $i,SV849: $i] :
( ( ( ! [SY3737: $i] :
~ ( in @ SY3737 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4259]) ).
thf(4359,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( in @ SV976 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4260]) ).
thf(4360,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) )
| ~ ( in @ ( kpair @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV907 ) @ SV711 ) ) )
= $true )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4261]) ).
thf(4361,plain,
! [SV894: $i,SV573: $i > $i > $o,SV74: $i,SV959: $i,SV354: $i] :
( ( ( ~ ( reflwellordering @ SV354 @ SV959 ) )
= $true )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3808: $i] :
~ ( ~ ( SV573 @ SY3807 @ SY3808 )
| ~ ! [SY3809: $i] :
( ~ ( in @ SY3809 @ SV354 )
| ~ ( SV573 @ SY3807 @ SY3809 )
| ( in @ ( kpair @ SY3808 @ SY3809 ) @ SV959 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4262]) ).
thf(4362,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV942: $i,SV361: $i,SV973: $i] :
( ( ( ~ ( in @ SV973 @ SV361 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV942 @ SV973 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SV973 ) @ SV577 ) )
= $true )
| ( ( in @ SV942 @ SV81 )
= $false )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4263]) ).
thf(4363,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV928: $i,SV361: $i,SV969: $i] :
( ( ( in @ SV969 @ SV361 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV928 @ SV969 ) @ SV791 )
| ( in @ ( kpair @ SV928 @ SV969 ) @ SV577 ) )
= $true )
| ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4264]) ).
thf(4364,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( ~ ( in @ SV895 @ SV716 )
| SV859 ) )
= $true )
| ( SV859 = $true )
| ( ( in @ SV895 @ SV365 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4265]) ).
thf(4365,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV716 )
| SV859 )
= $false )
| ( SV859 = $true )
| ( SV859 = $false )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4266]) ).
thf(4366,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( ~ ( in @ SV896 @ SV716 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV896 @ SV365 )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4267]) ).
thf(4367,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV716 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4268]) ).
thf(4368,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( ~ ( in @ SV897 @ SV716 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV897 @ SV365 )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4269]) ).
thf(4369,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV716 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4270]) ).
thf(4370,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ ( sK88_SY2391 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4277]) ).
thf(4371,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY3799: $i] :
( ~ ( SV95 @ SY3799 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SY3799 ) ) )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4278]) ).
thf(4372,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ ( sK96_SY2391 @ SV717 @ SV95 ) ) )
= $false )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4373,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ~ ! [SY3810: $i] :
( ~ ( SV95 @ SY3810 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SY3810 ) ) )
= $false )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4279]) ).
thf(4374,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ ( sK89_SY2391 @ SV717 @ SV95 ) )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4280]) ).
thf(4375,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY3800: $i] :
( ~ ( SV95 @ SY3800 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SY3800 ) ) )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4281]) ).
thf(4376,plain,
! [SV921: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
| ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4282]) ).
thf(4377,plain,
! [SV376: $i > $o,SV97: $i > $o] :
( ( ( ! [SY2399: $i] :
~ ~ ( ~ ( SV97 @ SY2399 )
| ~ ! [SY2400: $i] :
( ~ ( SV97 @ SY2400 )
| ( SY2399 = SY2400 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4283]) ).
thf(4378,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( ~ ~ ( ~ ( SV97 @ SV977 )
| ~ ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4284]) ).
thf(4379,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( ~ ~ ( ~ ( SV97 @ SV978 )
| ~ ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4285]) ).
thf(4380,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ SV974 )
| ~ ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4286]) ).
thf(4381,plain,
! [SV98: $i,SV929: $i,SV377: $i > $o] :
( ( ( SV377 @ SV929 )
= $false )
| ( ( in @ SV929 @ SV98 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( in @ ( sK32_SY3615 @ SV377 @ SV98 ) @ SV98 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4287]) ).
thf(4382,plain,
! [SV377: $i > $o,SV98: $i,SV943: $i] :
( ( ( in @ SV943 @ SV98 )
= $false )
| ( ( ~ ( SV377 @ SV943 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4288]) ).
thf(4383,plain,
! [SV377: $i > $o,SV98: $i,SV960: $i] :
( ( ( ~ ( in @ SV960 @ SV98 ) )
= $true )
| ( ( ~ ( SV377 @ SV960 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4289]) ).
thf(4384,plain,
! [SV377: $i > $o,SV98: $i,SV944: $i] :
( ( ( in @ SV944 @ SV98 )
= $false )
| ( ( ~ ( SV377 @ SV944 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4290]) ).
thf(4385,plain,
! [SV722: $i,SV945: $i,SV961: $i,SV105: $i > $o] :
( ( ( ~ ( SV105 @ SV961 ) )
= $true )
| ( ( SV945 = SV961 )
= $true )
| ( ( SV105 @ SV945 )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4291]) ).
thf(4386,plain,
! [SV722: $i,SV930: $i,SV946: $i,SV105: $i > $o] :
( ( ( SV105 @ SV946 )
= $false )
| ( ( SV930 = SV946 )
= $true )
| ( ( SV105 @ SV930 )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV722
= ( sK71_SY3617 @ SV722 @ SV105 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4292]) ).
thf(4387,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK97_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV111 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4294]) ).
thf(4388,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV111 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4296]) ).
thf(4389,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( ~ ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 ) )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4297]) ).
thf(4390,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV391 )
= $false )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4297]) ).
thf(4391,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK98_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV724 )
= $false )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4299]) ).
thf(4392,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK99_SY2492 @ SV730 @ SV129 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4303]) ).
thf(4393,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ~ ! [SY3811: $i] :
( ~ ( SV129 @ SY3811 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SY3811 ) ) )
= $false )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4303]) ).
thf(4394,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK90_SY2492 @ SV730 @ SV129 ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4304]) ).
thf(4395,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ! [SY3802: $i] :
( ~ ( SV129 @ SY3802 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SY3802 ) ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4305]) ).
thf(4396,plain,
! [SV733: $i,SV949: $i,SV963: $i,SV139: $i > $o] :
( ( ( ~ ( SV139 @ SV963 ) )
= $true )
| ( ( SV949 = SV963 )
= $true )
| ( ( SV139 @ SV949 )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4306]) ).
thf(4397,plain,
! [SV733: $i,SV931: $i,SV950: $i,SV139: $i > $o] :
( ( ( SV139 @ SV950 )
= $false )
| ( ( SV931 = SV950 )
= $true )
| ( ( SV139 @ SV931 )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV733
= ( sK75_SY3630 @ SV733 @ SV139 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4307]) ).
thf(4398,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV964 ) )
= $true )
| ( ( ~ ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4308]) ).
thf(4399,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV965 ) )
= $true )
| ( ( ~ ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4309]) ).
thf(4400,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) )
| ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4310]) ).
thf(4401,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) )
| ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4311]) ).
thf(4402,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4312]) ).
thf(4403,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4313]) ).
thf(4404,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4314]) ).
thf(4405,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4315]) ).
thf(4406,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4316]) ).
thf(4407,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4317]) ).
thf(4408,plain,
! [SV159: $i,SV934: $i,SV432: $i > $o] :
( ( ( SV432 @ SV934 )
= $false )
| ( ( in @ SV934 @ SV159 )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( in @ ( sK35_SY3641 @ SV432 @ SV159 ) @ SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4320]) ).
thf(4409,plain,
! [SV432: $i > $o,SV159: $i,SV952: $i] :
( ( ( in @ SV952 @ SV159 )
= $false )
| ( ( ~ ( SV432 @ SV952 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4321]) ).
thf(4410,plain,
! [SV432: $i > $o,SV159: $i,SV966: $i] :
( ( ( ~ ( in @ SV966 @ SV159 ) )
= $true )
| ( ( ~ ( SV432 @ SV966 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4322]) ).
thf(4411,plain,
! [SV432: $i > $o,SV159: $i,SV953: $i] :
( ( ( in @ SV953 @ SV159 )
= $false )
| ( ( ~ ( SV432 @ SV953 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4323]) ).
thf(4412,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV912 ) ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4324]) ).
thf(4413,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i,SV979: $i] :
( ( ( ~ ~ ( ~ ( in @ SV979 @ SV442 )
| ~ ( SV170 @ SV979 @ SV912 ) ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4325]) ).
thf(4414,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i] :
( ( ( ~ ! [SY3831: $i] :
~ ( ~ ( ~ ( in @ SY3831 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3831 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3831 ) )
| ( in @ SY3831 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4326]) ).
thf(4415,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i] :
( ( ( ! [SY3823: $i] :
~ ( ~ ( ~ ( in @ SY3823 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3823 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3823 ) )
| ( in @ SY3823 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4327]) ).
thf(4416,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ ( sK100_SY2702 @ SV753 @ SV207 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4417,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ~ ! [SY3814: $i] :
( ~ ( SV207 @ SY3814 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SY3814 ) ) )
= $false )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4329]) ).
thf(4418,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( SV207 @ ( sK92_SY2702 @ SV753 @ SV207 ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4330]) ).
thf(4419,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ! [SY3804: $i] :
( ~ ( SV207 @ SY3804 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SY3804 ) ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4331]) ).
thf(4420,plain,
! [SV970: $o,SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ! [SY3818: $i] :
( ~ ( in @ SY3818 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SY3818 ) @ SV508 )
| ~ ( in @ ( kpair @ SY3818 @ SV917 ) @ SV766 )
| SV970 ) )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4332]) ).
thf(4421,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4333]) ).
thf(4422,plain,
! [SV766: $i,SV917: $i,SV508: $i,SV882: $i,SV240: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ SX0 ) @ SV508 )
| ~ ( in @ ( kpair @ SX0 @ SV917 ) @ SV766 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4334]) ).
thf(4423,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK111_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3826: $i] :
( ~ ( SV250 @ SY3826 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SY3826 ) ) ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4335]) ).
thf(4424,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK106_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3819: $i] :
( ~ ( SV250 @ SY3819 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SY3819 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4336]) ).
thf(4425,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK107_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3820: $i] :
( ~ ( SV250 @ SY3820 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SY3820 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4337]) ).
thf(4426,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK101_SY2813 @ SV770 @ SV250 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4427,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ! [SY3815: $i] :
( ~ ( SV250 @ SY3815 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SY3815 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4338]) ).
thf(4428,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4339]) ).
thf(4429,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
| ~ ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4340]) ).
thf(4430,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
| ! [SY3834: $i] :
( ~ ( in @ SY3834 @ SV518 )
| ~ ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3834 ) @ SV832 )
| ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3834 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4341]) ).
thf(4431,plain,
! [SV658: $i,SV832: $i,SV518: $i,SV251: $i] :
( ( ( ! [SY3718: $i] :
( ~ ( in @ SY3718 @ SV251 )
| ! [SY3719: $i] :
( ~ ( in @ SY3719 @ SV518 )
| ~ ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV832 )
| ( in @ ( kpair @ SY3718 @ SY3719 ) @ SV658 ) ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4342]) ).
thf(4432,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
| ! [SY3835: $i] :
( ~ ( in @ SY3835 @ SV518 )
| ~ ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3835 ) @ SV832 )
| ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3835 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4343]) ).
thf(4433,plain,
! [SV258: $i,SV773: $i,SV919: $i,SV524: $i,SV957: $i,SV886: $i] :
( ( ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
| ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) ) )
= $true )
| ( ( in @ SV957 @ SV258 )
= $false )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4344]) ).
thf(4434,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4346]) ).
thf(4435,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4346]) ).
thf(4436,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4347]) ).
thf(4437,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ! [SY3827: $i] :
( ~ ( in @ SY3827 @ SV259 )
| ~ ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3827 ) @ SV774 )
| ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3827 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4347]) ).
thf(4438,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
| ! [SY3836: $i] :
( ~ ( in @ SY3836 @ SV259 )
| ~ ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3836 ) @ SV774 )
| ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3836 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4348]) ).
thf(4439,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4349]) ).
thf(4440,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ! [SY3828: $i] :
( ~ ( in @ SY3828 @ SV259 )
| ~ ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3828 ) @ SV774 )
| ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3828 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4349]) ).
thf(4441,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ SV975 )
| ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) ) )
| ~ ( ( SV975
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV975 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4350]) ).
thf(4442,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ SV971 )
| ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4351]) ).
thf(4443,plain,
! [SV263: $i > $o,SV775: $i,SV971: $i] :
( ( ( ~ ( ( SV971
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV971 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4351]) ).
thf(4444,plain,
! [SV265: $i,SV777: $i,SV968: $i] :
( ( ( ~ ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) ) )
= $true )
| ( ( ~ ( in @ SV968 @ SV265 ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4352]) ).
thf(4445,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
| ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) ) )
= $false )
| ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4353]) ).
thf(4446,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
= $false )
| ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4447,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $false )
| ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4354]) ).
thf(4448,plain,
! [SV45: $i,SV937: $i,SV972: $i] :
( ( ( in @ SV972 @ SV937 )
= $false )
| ( ( in @ SV972 @ SV45 )
= $true )
| ( ( in @ SV937 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4355]) ).
thf(4449,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ SV45 ) )
= $true )
| ( ( ~ ( in @ SV958 @ SV45 ) )
= $true )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4356]) ).
thf(4450,plain,
! [SV45: $i,SV920: $i,SV906: $i] :
( ( ( ! [SY3787: $i] :
( ~ ( in @ SY3787 @ SV906 )
| ( in @ SY3787 @ SV920 ) ) )
= $true )
| ( ( ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4357]) ).
thf(4451,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( in @ SV980 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4358]) ).
thf(4452,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( in @ SV976 @ SV849 )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4359]) ).
thf(4453,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) )
| ~ ( in @ ( kpair @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV907 ) @ SV711 ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4360]) ).
thf(4454,plain,
! [SV894: $i,SV573: $i > $i > $o,SV74: $i,SV959: $i,SV354: $i] :
( ( ( reflwellordering @ SV354 @ SV959 )
= $false )
| ( ( ! [SY3807: $i] :
( ~ ( in @ SY3807 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3808: $i] :
~ ( ~ ( SV573 @ SY3807 @ SY3808 )
| ~ ! [SY3809: $i] :
( ~ ( in @ SY3809 @ SV354 )
| ~ ( SV573 @ SY3807 @ SY3809 )
| ( in @ ( kpair @ SY3808 @ SY3809 ) @ SV959 ) ) ) ) ) ) )
= $true )
| ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4361]) ).
thf(4455,plain,
! [SV81: $i,SV577: $i,SV791: $i,SV942: $i,SV361: $i,SV973: $i] :
( ( ( in @ SV973 @ SV361 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV942 @ SV973 ) @ SV791 )
| ( in @ ( kpair @ SV942 @ SV973 ) @ SV577 ) )
= $true )
| ( ( in @ SV942 @ SV81 )
= $false )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4362]) ).
thf(4456,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i,SV969: $i,SV928: $i] :
( ( ( ~ ( in @ ( kpair @ SV928 @ SV969 ) @ SV791 ) )
= $true )
| ( ( in @ ( kpair @ SV928 @ SV969 ) @ SV577 )
= $true )
| ( ( in @ SV969 @ SV361 )
= $false )
| ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4363]) ).
thf(4457,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV716 )
| SV859 )
= $false )
| ( SV859 = $true )
| ( ( in @ SV895 @ SV365 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4364]) ).
thf(4458,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV716 ) )
= $false )
| ( SV859 = $true )
| ( SV859 = $false )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4459,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV895: $i,SV859: $o] :
( ( SV859 = $false )
| ( SV859 = $true )
| ( SV859 = $false )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4365]) ).
thf(4460,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV716 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV896 @ SV365 )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4366]) ).
thf(4461,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV716 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4367]) ).
thf(4462,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4367]) ).
thf(4463,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV716 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV897 @ SV365 )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4368]) ).
thf(4464,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV716 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4369]) ).
thf(4465,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4369]) ).
thf(4466,plain,
! [SV717: $i,SV981: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV981 )
| ( ( sK88_SY2391 @ SV717 @ SV95 )
= SV981 ) )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4371]) ).
thf(4467,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( SV95 @ ( sK96_SY2391 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4372]) ).
thf(4468,plain,
! [SV717: $i,SV95: $i > $o] :
( ( ( ! [SY3810: $i] :
( ~ ( SV95 @ SY3810 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SY3810 ) ) )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4373]) ).
thf(4469,plain,
! [SV717: $i,SV982: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV982 )
| ( ( sK89_SY2391 @ SV717 @ SV95 )
= SV982 ) )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4375]) ).
thf(4470,plain,
! [SV921: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4376]) ).
thf(4471,plain,
! [SV97: $i > $o,SV376: $i > $o,SV921: $i] :
( ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4376]) ).
thf(4472,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( ~ ~ ( ~ ( SV97 @ SV983 )
| ~ ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4377]) ).
thf(4473,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ SV977 )
| ~ ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4378]) ).
thf(4474,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ SV978 )
| ~ ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4379]) ).
thf(4475,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV974 )
| ~ ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4380]) ).
thf(4476,plain,
! [SV98: $i,SV943: $i,SV377: $i > $o] :
( ( ( SV377 @ SV943 )
= $false )
| ( ( in @ SV943 @ SV98 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK10_SY3077 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4382]) ).
thf(4477,plain,
! [SV377: $i > $o,SV98: $i,SV960: $i] :
( ( ( in @ SV960 @ SV98 )
= $false )
| ( ( ~ ( SV377 @ SV960 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4383]) ).
thf(4478,plain,
! [SV98: $i,SV944: $i,SV377: $i > $o] :
( ( ( SV377 @ SV944 )
= $false )
| ( ( in @ SV944 @ SV98 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( ( sK10_SY3077 @ SV377 @ SV98 )
= ( sK32_SY3615 @ SV377 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4384]) ).
thf(4479,plain,
! [SV722: $i,SV945: $i,SV961: $i,SV105: $i > $o] :
( ( ( SV105 @ SV961 )
= $false )
| ( ( SV945 = SV961 )
= $true )
| ( ( SV105 @ SV945 )
= $false )
| ( ( SV105 @ SV722 )
= $false )
| ( ( SV105 @ ( sK71_SY3617 @ SV722 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4385]) ).
thf(4480,plain,
! [SV111: $i,SV724: $i,SV391: $i] :
( ( ( in @ ( sK105_SY3620 @ SV391 @ SV724 @ SV111 ) @ SV724 )
= $true )
| ( ( SV391 = SV724 )
= $true )
| ( ( in @ ( sK58_SY3619 @ SV724 @ SV391 @ SV111 ) @ SV391 )
= $true )
| ( ( in @ SV724 @ ( powerset @ SV111 ) )
= $false )
| ( ( in @ SV391 @ ( powerset @ SV111 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4389]) ).
thf(4481,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK99_SY2492 @ SV730 @ SV129 ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4392]) ).
thf(4482,plain,
! [SV730: $i,SV129: $i > $o] :
( ( ( ! [SY3811: $i] :
( ~ ( SV129 @ SY3811 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SY3811 ) ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4393]) ).
thf(4483,plain,
! [SV730: $i,SV984: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV984 )
| ( ( sK90_SY2492 @ SV730 @ SV129 )
= SV984 ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4395]) ).
thf(4484,plain,
! [SV733: $i,SV949: $i,SV963: $i,SV139: $i > $o] :
( ( ( SV139 @ SV963 )
= $false )
| ( ( SV949 = SV963 )
= $true )
| ( ( SV139 @ SV949 )
= $false )
| ( ( SV139 @ SV733 )
= $false )
| ( ( SV139 @ ( sK75_SY3630 @ SV733 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4396]) ).
thf(4485,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4398]) ).
thf(4486,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4399]) ).
thf(4487,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4400]) ).
thf(4488,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4401]) ).
thf(4489,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4402]) ).
thf(4490,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4403]) ).
thf(4491,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4404]) ).
thf(4492,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4405]) ).
thf(4493,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4406]) ).
thf(4494,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4407]) ).
thf(4495,plain,
! [SV159: $i,SV952: $i,SV432: $i > $o] :
( ( ( SV432 @ SV952 )
= $false )
| ( ( in @ SV952 @ SV159 )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK14_SY3181 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4409]) ).
thf(4496,plain,
! [SV432: $i > $o,SV159: $i,SV966: $i] :
( ( ( in @ SV966 @ SV159 )
= $false )
| ( ( ~ ( SV432 @ SV966 ) )
= $true )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4410]) ).
thf(4497,plain,
! [SV159: $i,SV953: $i,SV432: $i > $o] :
( ( ( SV432 @ SV953 )
= $false )
| ( ( in @ SV953 @ SV159 )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( ( sK14_SY3181 @ SV432 @ SV159 )
= ( sK35_SY3641 @ SV432 @ SV159 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4411]) ).
thf(4498,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( ~ ( in @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV912 ) ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4412]) ).
thf(4499,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i,SV979: $i] :
( ( ( ~ ( ~ ( in @ SV979 @ SV442 )
| ~ ( SV170 @ SV979 @ SV912 ) ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4413]) ).
thf(4500,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i] :
( ( ( ! [SY3831: $i] :
~ ( ~ ( ~ ( in @ SY3831 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3206: $i] :
~ ~ ( ~ ( in @ SY3206 @ SV442 )
| ~ ( SV170 @ SY3206 @ SY3831 ) ) )
| ~ ( ~ ~ ! [SY3207: $i] :
~ ~ ( ~ ( in @ SY3207 @ SV442 )
| ~ ( SV170 @ SY3207 @ SY3831 ) )
| ( in @ SY3831 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4414]) ).
thf(4501,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
| ~ ( ~ ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) )
| ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4415]) ).
thf(4502,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( SV207 @ ( sK100_SY2702 @ SV753 @ SV207 ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4416]) ).
thf(4503,plain,
! [SV753: $i,SV207: $i > $o] :
( ( ( ! [SY3814: $i] :
( ~ ( SV207 @ SY3814 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SY3814 ) ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4417]) ).
thf(4504,plain,
! [SV753: $i,SV986: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV986 )
| ( ( sK92_SY2702 @ SV753 @ SV207 )
= SV986 ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4419]) ).
thf(4505,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( ~ ( in @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| SV970 )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4420]) ).
thf(4506,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4421]) ).
thf(4507,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
| ~ ( in @ ( kpair @ SV882 @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4422]) ).
thf(4508,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK111_SY2813 @ SV770 @ SV250 ) )
| ~ ! [SY3826: $i] :
( ~ ( SV250 @ SY3826 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SY3826 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4423]) ).
thf(4509,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK106_SY2813 @ SV770 @ SV250 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4424]) ).
thf(4510,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ! [SY3819: $i] :
( ~ ( SV250 @ SY3819 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SY3819 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4424]) ).
thf(4511,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK107_SY2813 @ SV770 @ SV250 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4425]) ).
thf(4512,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ! [SY3820: $i] :
( ~ ( SV250 @ SY3820 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SY3820 ) ) )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4425]) ).
thf(4513,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK101_SY2813 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4426]) ).
thf(4514,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY3815: $i] :
( ~ ( SV250 @ SY3815 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SY3815 ) ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4427]) ).
thf(4515,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4429]) ).
thf(4516,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4429]) ).
thf(4517,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4430]) ).
thf(4518,plain,
! [SV251: $i,SV832: $i,SV658: $i,SV518: $i] :
( ( ( ! [SY3834: $i] :
( ~ ( in @ SY3834 @ SV518 )
| ~ ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3834 ) @ SV832 )
| ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3834 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4430]) ).
thf(4519,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
| ! [SY3840: $i] :
( ~ ( in @ SY3840 @ SV518 )
| ~ ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3840 ) @ SV832 )
| ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3840 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4431]) ).
thf(4520,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4521,plain,
! [SV251: $i,SV832: $i,SV658: $i,SV518: $i] :
( ( ( ! [SY3835: $i] :
( ~ ( in @ SY3835 @ SV518 )
| ~ ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3835 ) @ SV832 )
| ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3835 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4432]) ).
thf(4522,plain,
! [SV524: $i,SV258: $i,SV886: $i,SV773: $i,SV919: $i,SV957: $i] :
( ( ( ~ ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 ) )
= $true )
| ( ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) )
= $true )
| ( ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
= $false )
| ( ( in @ SV957 @ SV258 )
= $false )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4433]) ).
thf(4523,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4434]) ).
thf(4524,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4435]) ).
thf(4525,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV525 )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4435]) ).
thf(4526,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4436]) ).
thf(4527,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) @ SV259 )
| ~ ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4437]) ).
thf(4528,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4438]) ).
thf(4529,plain,
! [SV774: $i,SV525: $i,SV259: $i] :
( ( ( ! [SY3836: $i] :
( ~ ( in @ SY3836 @ SV259 )
| ~ ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3836 ) @ SV774 )
| ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SY3836 ) @ SV525 ) ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4438]) ).
thf(4530,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4439]) ).
thf(4531,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) @ SV259 )
| ~ ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4440]) ).
thf(4532,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ SV975 )
| ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4441]) ).
thf(4533,plain,
! [SV263: $i > $o,SV775: $i,SV975: $i] :
( ( ( ~ ( ( SV975
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV975 ) ) )
= $false )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4441]) ).
thf(4534,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV971 )
| ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4442]) ).
thf(4535,plain,
! [SV263: $i > $o,SV775: $i,SV971: $i] :
( ( ( ( SV971
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV971 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4443]) ).
thf(4536,plain,
! [SV265: $i,SV777: $i,SV968: $i] :
( ( ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
= $false )
| ( ( ~ ( in @ SV968 @ SV265 ) )
= $true )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4444]) ).
thf(4537,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( ~ ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) ) )
= $false )
| ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4445]) ).
thf(4538,plain,
! [SV44: $i,SV328: $i,SV784: $i > $o,SV702: $i > $o] :
( ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $false )
| ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4445]) ).
thf(4539,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $true )
| ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $false )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4446]) ).
thf(4540,plain,
! [SV958: $i,SV45: $i,SV938: $i] :
( ( ( in @ SV938 @ SV45 )
= $false )
| ( ( ~ ( in @ SV958 @ SV45 ) )
= $true )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4449]) ).
thf(4541,plain,
! [SV45: $i,SV920: $i,SV906: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV906 )
| ( in @ SV987 @ SV920 ) )
= $true )
| ( ( ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4450]) ).
thf(4542,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( in @ SV980 @ SV849 )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( ~ ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4451]) ).
thf(4543,plain,
! [SV976: $i,SV849: $i,SV45: $i] :
( ( ( ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4452]) ).
thf(4544,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4453]) ).
thf(4545,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV907 ) @ SV711 ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4453]) ).
thf(4546,plain,
! [SV894: $i,SV959: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV74 )
| ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3841: $i] :
~ ( ~ ( SV573 @ SV988 @ SY3841 )
| ~ ! [SY3842: $i] :
( ~ ( in @ SY3842 @ SV354 )
| ~ ( SV573 @ SV988 @ SY3842 )
| ( in @ ( kpair @ SY3841 @ SY3842 ) @ SV959 ) ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV959 )
= $false )
| ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4454]) ).
thf(4547,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i,SV973: $i,SV942: $i] :
( ( ( ~ ( in @ ( kpair @ SV942 @ SV973 ) @ SV791 ) )
= $true )
| ( ( in @ ( kpair @ SV942 @ SV973 ) @ SV577 )
= $true )
| ( ( in @ SV973 @ SV361 )
= $false )
| ( ( in @ SV942 @ SV81 )
= $false )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4455]) ).
thf(4548,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i,SV969: $i,SV928: $i] :
( ( ( in @ ( kpair @ SV928 @ SV969 ) @ SV791 )
= $false )
| ( ( in @ ( kpair @ SV928 @ SV969 ) @ SV577 )
= $true )
| ( ( in @ SV969 @ SV361 )
= $false )
| ( ( in @ SV928 @ SV81 )
= $false )
| ( ( ( ap @ SV81 @ SV361 @ SV577 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) )
= ( ap @ SV81 @ SV361 @ SV791 @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) ) )
= $false )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4456]) ).
thf(4549,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( ~ ( in @ SV895 @ SV716 ) )
= $false )
| ( SV859 = $true )
| ( ( in @ SV895 @ SV365 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4457]) ).
thf(4550,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV895: $i,SV859: $o] :
( ( SV859 = $false )
| ( SV859 = $true )
| ( ( in @ SV895 @ SV365 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4457]) ).
thf(4551,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( in @ SV895 @ SV716 )
= $true )
| ( SV859 = $true )
| ( SV859 = $false )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4458]) ).
thf(4552,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( ~ ( in @ SV896 @ SV716 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV896 @ SV365 )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4460]) ).
thf(4553,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV896: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV896 @ SV365 )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4460]) ).
thf(4554,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( in @ SV896 @ SV716 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4461]) ).
thf(4555,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( ~ ( in @ SV897 @ SV716 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV897 @ SV365 )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4463]) ).
thf(4556,plain,
! [SV85: $i,SV716: $i,SV365: $i,SV897: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV897 @ SV365 )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4463]) ).
thf(4557,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( in @ SV897 @ SV716 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4464]) ).
thf(4558,plain,
! [SV717: $i,SV981: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV981 ) )
= $true )
| ( ( ( sK88_SY2391 @ SV717 @ SV95 )
= SV981 )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4466]) ).
thf(4559,plain,
! [SV717: $i,SV989: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV989 )
| ( ( sK96_SY2391 @ SV717 @ SV95 )
= SV989 ) )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4468]) ).
thf(4560,plain,
! [SV717: $i,SV982: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV982 ) )
= $true )
| ( ( ( sK89_SY2391 @ SV717 @ SV95 )
= SV982 )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4469]) ).
thf(4561,plain,
! [SV921: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4470]) ).
thf(4562,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4471]) ).
thf(4563,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( ~ ( ~ ( SV97 @ SV983 )
| ~ ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4472]) ).
thf(4564,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV977 )
| ~ ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4473]) ).
thf(4565,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV978 )
| ~ ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4474]) ).
thf(4566,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV974 ) )
= $true )
| ( ( ~ ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4475]) ).
thf(4567,plain,
! [SV98: $i,SV960: $i,SV377: $i > $o] :
( ( ( SV377 @ SV960 )
= $false )
| ( ( in @ SV960 @ SV98 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV98
@ ^ [SY3080: $i] : ( SV377 @ SY3080 ) ) )
= $true )
| ( ( SV377 @ ( sK32_SY3615 @ SV377 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4477]) ).
thf(4568,plain,
! [SV730: $i,SV990: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV990 )
| ( ( sK99_SY2492 @ SV730 @ SV129 )
= SV990 ) )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4482]) ).
thf(4569,plain,
! [SV730: $i,SV984: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV984 ) )
= $true )
| ( ( ( sK90_SY2492 @ SV730 @ SV129 )
= SV984 )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4483]) ).
thf(4570,plain,
! [SV416: $i > $o,SV964: $i,SV141: $i > $o] :
( ( ( ! [SY3812: $i] :
( ~ ( SV141 @ SY3812 )
| ( SV964 = SY3812 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4485]) ).
thf(4571,plain,
! [SV141: $i > $o,SV965: $i,SV416: $i > $o] :
( ( ( ! [SY3813: $i] :
( ~ ( SV416 @ SY3813 )
| ( SV965 = SY3813 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4486]) ).
thf(4572,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4487]) ).
thf(4573,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4488]) ).
thf(4574,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4489]) ).
thf(4575,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4490]) ).
thf(4576,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4491]) ).
thf(4577,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4492]) ).
thf(4578,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ SV991 )
| ~ ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4493]) ).
thf(4579,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ SV992 )
| ~ ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4494]) ).
thf(4580,plain,
! [SV159: $i,SV966: $i,SV432: $i > $o] :
( ( ( SV432 @ SV966 )
= $false )
| ( ( in @ SV966 @ SV159 )
= $false )
| ( ( ex1 @ SV159
@ ^ [SY3184: $i] : ( SV432 @ SY3184 ) )
= $true )
| ( ( SV432 @ ( sK35_SY3641 @ SV432 @ SV159 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4496]) ).
thf(4581,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( in @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV912 ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4498]) ).
thf(4582,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV442 )
| ~ ( SV170 @ SV979 @ SV912 ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4499]) ).
thf(4583,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
| ~ ( ~ ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) )
| ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4500]) ).
thf(4584,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( ~ ( ~ ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
| ~ ( ~ ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) )
| ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4501]) ).
thf(4585,plain,
! [SV753: $i,SV994: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV994 )
| ( ( sK100_SY2702 @ SV753 @ SV207 )
= SV994 ) )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4503]) ).
thf(4586,plain,
! [SV753: $i,SV986: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV986 ) )
= $true )
| ( ( ( sK92_SY2702 @ SV753 @ SV207 )
= SV986 )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4504]) ).
thf(4587,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( ~ ( in @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 ) )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4588,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| SV970 )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4505]) ).
thf(4589,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4506]) ).
thf(4590,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4506]) ).
thf(4591,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4507]) ).
thf(4592,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
| ~ ( in @ ( kpair @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4507]) ).
thf(4593,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK111_SY2813 @ SV770 @ SV250 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4508]) ).
thf(4594,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ~ ! [SY3826: $i] :
( ~ ( SV250 @ SY3826 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SY3826 ) ) )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4508]) ).
thf(4595,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK106_SY2813 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4509]) ).
thf(4596,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY3819: $i] :
( ~ ( SV250 @ SY3819 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SY3819 ) ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4510]) ).
thf(4597,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK107_SY2813 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4511]) ).
thf(4598,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY3820: $i] :
( ~ ( SV250 @ SY3820 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SY3820 ) ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4512]) ).
thf(4599,plain,
! [SV770: $i,SV995: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV995 )
| ( ( sK101_SY2813 @ SV770 @ SV250 )
= SV995 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4514]) ).
thf(4600,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( in @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4515]) ).
thf(4601,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4516]) ).
thf(4602,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4516]) ).
thf(4603,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4517]) ).
thf(4604,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
| ~ ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4518]) ).
thf(4605,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4519]) ).
thf(4606,plain,
! [SV251: $i,SV832: $i,SV658: $i,SV518: $i] :
( ( ( ! [SY3840: $i] :
( ~ ( in @ SY3840 @ SV518 )
| ~ ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3840 ) @ SV832 )
| ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SY3840 ) @ SV658 ) ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4519]) ).
thf(4607,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4520]) ).
thf(4608,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
| ~ ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4521]) ).
thf(4609,plain,
! [SV524: $i,SV258: $i,SV886: $i,SV773: $i,SV919: $i,SV957: $i] :
( ( ( in @ ( kpair @ SV957 @ SV919 ) @ SV773 )
= $false )
| ( ( in @ ( kpair @ SV886 @ SV919 ) @ ( breln1compset @ SV258 @ SV524 @ SV773 ) )
= $true )
| ( ( in @ ( kpair @ SV886 @ SV957 ) @ SV524 )
= $false )
| ( ( in @ SV957 @ SV258 )
= $false )
| ( ( in @ SV919 @ SV258 )
= $false )
| ( ( in @ SV886 @ SV258 )
= $false )
| ( ( breln1 @ SV258 @ SV773 )
= $false )
| ( ( breln1 @ SV258 @ SV524 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4522]) ).
thf(4610,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK102_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK112_SY3816 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4524]) ).
thf(4611,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4527]) ).
thf(4612,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4527]) ).
thf(4613,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4528]) ).
thf(4614,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) @ SV259 )
| ~ ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4529]) ).
thf(4615,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4531]) ).
thf(4616,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4531]) ).
thf(4617,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV975 )
| ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4532]) ).
thf(4618,plain,
! [SV263: $i > $o,SV775: $i,SV975: $i] :
( ( ( ( SV975
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
| ( SV263 @ SV975 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4533]) ).
thf(4619,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV971 ) )
= $true )
| ( ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4534]) ).
thf(4620,plain,
! [SV263: $i > $o,SV775: $i,SV971: $i] :
( ( ( SV971
!= ( sK93_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV971 )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4535]) ).
thf(4621,plain,
! [SV777: $i,SV265: $i,SV968: $i] :
( ( ( in @ SV968 @ SV265 )
= $false )
| ( ( in @ SV968 @ ( sK46_SY2861 @ SV777 @ SV265 ) )
= $false )
| ( ( in @ SV777 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4536]) ).
thf(4622,plain,
! [SV328: $i,SV702: $i > $o,SV44: $i,SV784: $i > $o] :
( ( ( SV784 @ ( sK68_SY3762 @ SV44 @ SV702 @ SV784 @ SV328 ) )
= $true )
| ( ( SV702 @ ( sK47_SY3688 @ SV784 @ SV702 @ SV328 @ SV44 ) )
= $true )
| ( ( ( dsetconstr @ SV44
@ ^ [SY3594: $i] : ( SV702 @ SY3594 ) )
= ( dsetconstr @ SV328
@ ^ [SY3691: $i] : ( SV784 @ SY3691 ) ) )
= $true )
| ( ( SV44 = SV328 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4537]) ).
thf(4623,plain,
! [SV938: $i,SV45: $i,SV958: $i] :
( ( ( in @ SV958 @ SV45 )
= $false )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) )
| ( SV938 = SV958 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4540]) ).
thf(4624,plain,
! [SV45: $i,SV920: $i,SV906: $i,SV987: $i] :
( ( ( ~ ( in @ SV987 @ SV906 ) )
= $true )
| ( ( in @ SV987 @ SV920 )
= $true )
| ( ( ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4541]) ).
thf(4625,plain,
! [SV980: $i,SV849: $i,SV45: $i] :
( ( ( ! [SY3738: $i] :
~ ~ ! [SY3739: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY3738 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3739 @ SV849 ) )
| ~ ~ ~ ! [SY3740: $i] :
~ ~ ( ~ ( in @ SY3740 @ SY3738 )
| ~ ( in @ SY3740 @ SV849 ) ) )
| ~ ! [SY3416: $i] :
( ~ ( in @ SY3416 @ ( sK2_SY2224 @ SV45 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY3416 )
| ( in @ SX6 @ SY3738 ) )
| ( in @ SY3739 @ SY3416 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4542]) ).
thf(4626,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ! [SY3847: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3847 @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3849: $i] :
( ~ ( in @ SY3849 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3849 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ SY3847 @ SY3849 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4543]) ).
thf(4627,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) ) )
= $true )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4544]) ).
thf(4628,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( in @ ( kpair @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV907 ) @ SV711 )
= $true )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4545]) ).
thf(4629,plain,
! [SV894: $i,SV959: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV988: $i] :
( ( ( ~ ( in @ SV988 @ SV74 ) )
= $true )
| ( ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3841: $i] :
~ ( ~ ( SV573 @ SV988 @ SY3841 )
| ~ ! [SY3842: $i] :
( ~ ( in @ SY3842 @ SV354 )
| ~ ( SV573 @ SV988 @ SY3842 )
| ( in @ ( kpair @ SY3841 @ SY3842 ) @ SV959 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV959 )
= $false )
| ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4546]) ).
thf(4630,plain,
! [SV81: $i,SV361: $i,SV577: $i,SV791: $i,SV973: $i,SV942: $i] :
( ( ( in @ ( kpair @ SV942 @ SV973 ) @ SV791 )
= $false )
| ( ( in @ ( kpair @ SV942 @ SV973 ) @ SV577 )
= $true )
| ( ( in @ SV973 @ SV361 )
= $false )
| ( ( in @ SV942 @ SV81 )
= $false )
| ( ( in @ ( sK70_SY3694 @ SV791 @ SV577 @ SV361 @ SV81 ) @ SV81 )
= $true )
| ( ( func @ SV81 @ SV361 @ SV791 )
= $false )
| ( ( func @ SV81 @ SV361 @ SV577 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4547]) ).
thf(4631,plain,
! [SV85: $i,SV365: $i,SV859: $o,SV716: $i,SV895: $i] :
( ( ( in @ SV895 @ SV716 )
= $true )
| ( SV859 = $true )
| ( ( in @ SV895 @ SV365 )
= $true )
| ( ( in @ SV895 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV895 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4549]) ).
thf(4632,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV896: $i] :
( ( ( in @ SV896 @ SV716 )
= $true )
| ( $true = $true )
| ( ( in @ SV896 @ SV365 )
= $true )
| ( ( in @ SV896 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV896 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4552]) ).
thf(4633,plain,
! [SV85: $i,SV365: $i,SV716: $i,SV897: $i] :
( ( ( in @ SV897 @ SV716 )
= $true )
| ( $false = $true )
| ( ( in @ SV897 @ SV365 )
= $true )
| ( ( in @ SV897 @ ( binunion @ SV365 @ SV716 ) )
= $false )
| ( ( in @ SV897 @ SV85 )
= $false )
| ( ( in @ SV716 @ ( powerset @ SV85 ) )
= $false )
| ( ( in @ SV365 @ ( powerset @ SV85 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4555]) ).
thf(4634,plain,
! [SV717: $i,SV981: $i,SV95: $i > $o] :
( ( ( SV95 @ SV981 )
= $false )
| ( ( ( sK88_SY2391 @ SV717 @ SV95 )
= SV981 )
= $true )
| ( ( SV95 @ ( sK50_SY2389 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4558]) ).
thf(4635,plain,
! [SV717: $i,SV989: $i,SV95: $i > $o] :
( ( ( ~ ( SV95 @ SV989 ) )
= $true )
| ( ( ( sK96_SY2391 @ SV717 @ SV95 )
= SV989 )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4559]) ).
thf(4636,plain,
! [SV717: $i,SV982: $i,SV95: $i > $o] :
( ( ( SV95 @ SV982 )
= $false )
| ( ( ( sK89_SY2391 @ SV717 @ SV95 )
= SV982 )
= $true )
| ( ( ( sK50_SY2389 @ SV717 @ SV95 )
= ( sK57_SY3767 @ SV717 @ SV95 ) )
= $false )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4560]) ).
thf(4637,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4561]) ).
thf(4638,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4562]) ).
thf(4639,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV983 )
| ~ ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4563]) ).
thf(4640,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV977 ) )
= $true )
| ( ( ~ ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4564]) ).
thf(4641,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV978 ) )
= $true )
| ( ( ~ ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4565]) ).
thf(4642,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4566]) ).
thf(4643,plain,
! [SV730: $i,SV990: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV990 ) )
= $true )
| ( ( ( sK99_SY2492 @ SV730 @ SV129 )
= SV990 )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4568]) ).
thf(4644,plain,
! [SV730: $i,SV984: $i,SV129: $i > $o] :
( ( ( SV129 @ SV984 )
= $false )
| ( ( ( sK90_SY2492 @ SV730 @ SV129 )
= SV984 )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV730
= ( sK73_SY3627 @ SV730 @ SV129 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4569]) ).
thf(4645,plain,
! [SV964: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
| ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4570]) ).
thf(4646,plain,
! [SV965: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
| ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4571]) ).
thf(4647,plain,
! [SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2525: $i] :
~ ~ ( ~ ( SV141 @ SY2525 )
| ~ ! [SY2526: $i] :
( ~ ( SV141 @ SY2526 )
| ( SY2525 = SY2526 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4572]) ).
thf(4648,plain,
! [SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3149: $i] :
~ ~ ( ~ ( SV416 @ SY3149 )
| ~ ! [SY3150: $i] :
( ~ ( SV416 @ SY3150 )
| ( SY3149 = SY3150 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4573]) ).
thf(4649,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ SV996 )
| ~ ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4574]) ).
thf(4650,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ SV997 )
| ~ ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4575]) ).
thf(4651,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ SV998 )
| ~ ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4576]) ).
thf(4652,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ SV999 )
| ~ ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4577]) ).
thf(4653,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ SV991 )
| ~ ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4578]) ).
thf(4654,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ SV992 )
| ~ ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4579]) ).
thf(4655,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( ~ ( in @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV442 ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4581]) ).
thf(4656,plain,
! [SV442: $i,SV912: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV912 ) )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4581]) ).
thf(4657,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i,SV979: $i] :
( ( ( ~ ( in @ SV979 @ SV442 ) )
= $true )
| ( ( ~ ( SV170 @ SV979 @ SV912 ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4582]) ).
thf(4658,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( ~ ( ~ ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
| ~ ( ~ ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) )
| ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4583]) ).
thf(4659,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( ~ ( ~ ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4660,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ( ~ ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) )
| ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4584]) ).
thf(4661,plain,
! [SV753: $i,SV994: $i,SV207: $i > $o] :
( ( ( ~ ( SV207 @ SV994 ) )
= $true )
| ( ( ( sK100_SY2702 @ SV753 @ SV207 )
= SV994 )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4585]) ).
thf(4662,plain,
! [SV753: $i,SV986: $i,SV207: $i > $o] :
( ( ( SV207 @ SV986 )
= $false )
| ( ( ( sK92_SY2702 @ SV753 @ SV207 )
= SV986 )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV753
= ( sK77_SY3655 @ SV753 @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4586]) ).
thf(4663,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( in @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
= $true )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4587]) ).
thf(4664,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 ) )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4588]) ).
thf(4665,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| SV970 )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4588]) ).
thf(4666,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( in @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4589]) ).
thf(4667,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4590]) ).
thf(4668,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4590]) ).
thf(4669,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( in @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV240 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4591]) ).
thf(4670,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( ~ ( in @ ( kpair @ SV882 @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4592]) ).
thf(4671,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4592]) ).
thf(4672,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK111_SY2813 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4593]) ).
thf(4673,plain,
! [SV770: $i,SV250: $i > $o] :
( ( ( ! [SY3826: $i] :
( ~ ( SV250 @ SY3826 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SY3826 ) ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4594]) ).
thf(4674,plain,
! [SV770: $i,SV1000: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1000 )
| ( ( sK106_SY2813 @ SV770 @ SV250 )
= SV1000 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4596]) ).
thf(4675,plain,
! [SV770: $i,SV1001: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1001 )
| ( ( sK107_SY2813 @ SV770 @ SV250 )
= SV1001 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4598]) ).
thf(4676,plain,
! [SV770: $i,SV995: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV995 ) )
= $true )
| ( ( ( sK101_SY2813 @ SV770 @ SV250 )
= SV995 )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4599]) ).
thf(4677,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK108_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK118_SY3821 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4601]) ).
thf(4678,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4604]) ).
thf(4679,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4604]) ).
thf(4680,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ SV251 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4605]) ).
thf(4681,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
| ~ ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4606]) ).
thf(4682,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4608]) ).
thf(4683,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4608]) ).
thf(4684,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4611]) ).
thf(4685,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4612]) ).
thf(4686,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV525 )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4612]) ).
thf(4687,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( ~ ( in @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) @ SV259 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4614]) ).
thf(4688,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
| ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV525 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4614]) ).
thf(4689,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4615]) ).
thf(4690,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4616]) ).
thf(4691,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV525 )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4616]) ).
thf(4692,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ SV975 ) )
= $true )
| ( ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4617]) ).
thf(4693,plain,
! [SV263: $i > $o,SV775: $i,SV975: $i] :
( ( ( SV975
!= ( sK103_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV975 )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4618]) ).
thf(4694,plain,
! [SV775: $i,SV971: $i,SV263: $i > $o] :
( ( ( SV263 @ SV971 )
= $false )
| ( ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4619]) ).
thf(4695,plain,
! [SV263: $i > $o,SV775: $i,SV971: $i] :
( ( ( SV971
= ( sK93_SY2855 @ SV775 @ SV263 ) )
= $false )
| ( ( SV263 @ SV971 )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV775
= ( sK80_SY3683 @ SV775 @ SV263 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4620]) ).
thf(4696,plain,
! [SV958: $i,SV938: $i,SV45: $i] :
( ( ( ~ ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4623]) ).
thf(4697,plain,
! [SV45: $i,SV920: $i,SV906: $i,SV987: $i] :
( ( ( in @ SV987 @ SV906 )
= $false )
| ( ( in @ SV987 @ SV920 )
= $true )
| ( ( ! [SY3788: $i] :
( ~ ( in @ SY3788 @ SV920 )
| ( in @ SY3788 @ SV906 ) ) )
= $true )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4624]) ).
thf(4698,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ! [SY3855: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3855 @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3857: $i] :
( ~ ( in @ SY3857 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3857 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ SY3855 @ SY3857 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4625]) ).
thf(4699,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ! [SY3847: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3847 @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3849: $i] :
( ~ ( in @ SY3849 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3849 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ SY3847 @ SY3849 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4626]) ).
thf(4700,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
| ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4627]) ).
thf(4701,plain,
! [SV894: $i,SV959: $i,SV573: $i > $i > $o,SV354: $i,SV74: $i,SV988: $i] :
( ( ( in @ SV988 @ SV74 )
= $false )
| ( ( singleton
@ ( dsetconstr @ SV354
@ ^ [SY3841: $i] :
~ ( ~ ( SV573 @ SV988 @ SY3841 )
| ~ ! [SY3842: $i] :
( ~ ( in @ SY3842 @ SV354 )
| ~ ( SV573 @ SV988 @ SY3842 )
| ( in @ ( kpair @ SY3841 @ SY3842 ) @ SV959 ) ) ) ) )
= $true )
| ( ( reflwellordering @ SV354 @ SV959 )
= $false )
| ( ( in @ SV959 @ ( breln1Set @ SV354 ) )
= $false )
| ( ( in @ SV894 @ SV354 )
= $false )
| ( ( SV573 @ ( sK21_SY3441 @ SV573 @ SV354 @ SV74 ) @ SV894 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4629]) ).
thf(4702,plain,
! [SV717: $i,SV989: $i,SV95: $i > $o] :
( ( ( SV95 @ SV989 )
= $false )
| ( ( ( sK96_SY2391 @ SV717 @ SV95 )
= SV989 )
= $true )
| ( ( SV95 @ ( sK57_SY3767 @ SV717 @ SV95 ) )
= $true )
| ( ( SV95 @ SV717 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4635]) ).
thf(4703,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4637]) ).
thf(4704,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4638]) ).
thf(4705,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( ~ ( SV97 @ SV983 ) )
= $true )
| ( ( ~ ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4639]) ).
thf(4706,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4640]) ).
thf(4707,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4641]) ).
thf(4708,plain,
! [SV376: $i > $o,SV974: $i,SV97: $i > $o] :
( ( ( ! [SY3822: $i] :
( ~ ( SV97 @ SY3822 )
| ( SV974 = SY3822 ) ) )
= $false )
| ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4642]) ).
thf(4709,plain,
! [SV730: $i,SV990: $i,SV129: $i > $o] :
( ( ( SV129 @ SV990 )
= $false )
| ( ( ( sK99_SY2492 @ SV730 @ SV129 )
= SV990 )
= $true )
| ( ( SV129 @ SV730 )
= $false )
| ( ( SV129 @ ( sK73_SY3627 @ SV730 @ SV129 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4643]) ).
thf(4710,plain,
! [SV964: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4645]) ).
thf(4711,plain,
! [SV141: $i > $o,SV416: $i > $o,SV964: $i] :
( ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4645]) ).
thf(4712,plain,
! [SV965: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4646]) ).
thf(4713,plain,
! [SV416: $i > $o,SV141: $i > $o,SV965: $i] :
( ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4646]) ).
thf(4714,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ SV1002 )
| ~ ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4647]) ).
thf(4715,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ SV1003 )
| ~ ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4648]) ).
thf(4716,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ SV996 )
| ~ ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4649]) ).
thf(4717,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ SV997 )
| ~ ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4650]) ).
thf(4718,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ SV998 )
| ~ ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4651]) ).
thf(4719,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ SV999 )
| ~ ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4652]) ).
thf(4720,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV991 )
| ~ ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4653]) ).
thf(4721,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV992 )
| ~ ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4654]) ).
thf(4722,plain,
! [SV442: $i,SV170: $i > $i > $o,SV912: $i] :
( ( ( in @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV442 )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4655]) ).
thf(4723,plain,
! [SV442: $i,SV912: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ ( sK116_SY3780 @ SV912 @ SV170 @ SV442 ) @ SV912 )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $false )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4656]) ).
thf(4724,plain,
! [SV912: $i,SV170: $i > $i > $o,SV442: $i,SV979: $i] :
( ( ( in @ SV979 @ SV442 )
= $false )
| ( ( ~ ( SV170 @ SV979 @ SV912 ) )
= $true )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4657]) ).
thf(4725,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( ~ ( ~ ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4658]) ).
thf(4726,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ( ~ ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) )
| ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4658]) ).
thf(4727,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4659]) ).
thf(4728,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) )
| ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4660]) ).
thf(4729,plain,
! [SV753: $i,SV994: $i,SV207: $i > $o] :
( ( ( SV207 @ SV994 )
= $false )
| ( ( ( sK100_SY2702 @ SV753 @ SV207 )
= SV994 )
= $true )
| ( ( SV207 @ SV753 )
= $false )
| ( ( SV207 @ ( sK77_SY3655 @ SV753 @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4661]) ).
thf(4730,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o,SV882: $i] :
( ( ( in @ ( kpair @ SV882 @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
= $true )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4664]) ).
thf(4731,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( ~ ( in @ ( kpair @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 ) )
= $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4732,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV917: $i,SV882: $i,SV970: $o] :
( ( SV970 = $false )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4665]) ).
thf(4733,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( in @ ( kpair @ SV882 @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4667]) ).
thf(4734,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 ) )
= $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(4735,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV917: $i,SV882: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4668]) ).
thf(4736,plain,
! [SV240: $i,SV508: $i,SV917: $i,SV766: $i,SV882: $i] :
( ( ( in @ ( kpair @ SV882 @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) ) @ SV508 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4670]) ).
thf(4737,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 ) )
= $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4738,plain,
! [SV766: $i,SV508: $i,SV240: $i,SV917: $i,SV882: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4671]) ).
thf(4739,plain,
! [SV770: $i,SV1004: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1004 )
| ( ( sK111_SY2813 @ SV770 @ SV250 )
= SV1004 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4673]) ).
thf(4740,plain,
! [SV770: $i,SV1000: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1000 ) )
= $true )
| ( ( ( sK106_SY2813 @ SV770 @ SV250 )
= SV1000 )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4674]) ).
thf(4741,plain,
! [SV770: $i,SV1001: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1001 ) )
= $true )
| ( ( ( sK107_SY2813 @ SV770 @ SV250 )
= SV1001 )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4675]) ).
thf(4742,plain,
! [SV770: $i,SV995: $i,SV250: $i > $o] :
( ( ( SV250 @ SV995 )
= $false )
| ( ( ( sK101_SY2813 @ SV770 @ SV250 )
= SV995 )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4676]) ).
thf(4743,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( in @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4678]) ).
thf(4744,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4679]) ).
thf(4745,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4679]) ).
thf(4746,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4681]) ).
thf(4747,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
| ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4681]) ).
thf(4748,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( in @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4682]) ).
thf(4749,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4683]) ).
thf(4750,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4683]) ).
thf(4751,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK113_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK126_SY3827 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) @ SV259 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4685]) ).
thf(4752,plain,
! [SV259: $i,SV525: $i,SV774: $i] :
( ( ( in @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) @ SV259 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4687]) ).
thf(4753,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV774 ) )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4688]) ).
thf(4754,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV525 )
= $false )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4688]) ).
thf(4755,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK114_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK127_SY3828 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4690]) ).
thf(4756,plain,
! [SV775: $i,SV975: $i,SV263: $i > $o] :
( ( ( SV263 @ SV975 )
= $false )
| ( ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4692]) ).
thf(4757,plain,
! [SV263: $i > $o,SV775: $i,SV975: $i] :
( ( ( SV975
= ( sK103_SY2855 @ SV775 @ SV263 ) )
= $false )
| ( ( SV263 @ SV975 )
= $true )
| ( ( SV263 @ SV775 )
= $false )
| ( ( SV263 @ ( sK80_SY3683 @ SV775 @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4693]) ).
thf(4758,plain,
! [SV958: $i,SV938: $i,SV45: $i] :
( ( ( ! [SY3806: $i] :
( ~ ( in @ SY3806 @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ SY3806 )
| ( in @ SV958 @ SY3806 ) )
| ~ ( ~ ( in @ SV958 @ SY3806 )
| ( in @ SV938 @ SY3806 ) ) ) ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4696]) ).
thf(4759,plain,
! [SV45: $i,SV987: $i,SV906: $i,SV920: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ SV920 )
| ( in @ SV1005 @ SV906 ) )
= $true )
| ( ( in @ SV987 @ SV920 )
= $true )
| ( ( in @ SV987 @ SV906 )
= $false )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4697]) ).
thf(4760,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ! [SY3855: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3855 @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3857: $i] :
( ~ ( in @ SY3857 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3857 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ SY3855 @ SY3857 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4698]) ).
thf(4761,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ! [SY3847: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3847 @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3849: $i] :
( ~ ( in @ SY3849 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3849 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ SY3847 @ SY3849 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4699]) ).
thf(4762,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( ~ ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4763,plain,
! [SV68: $i,SV348: $i,SV907: $i,SV711: $i,SV855: $i] :
( ( ( ~ ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 ) )
= $false )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4700]) ).
thf(4764,plain,
! [SV921: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4703]) ).
thf(4765,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1006 )
| ~ ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4704]) ).
thf(4766,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) )
= $true )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4705]) ).
thf(4767,plain,
! [SV376: $i > $o,SV977: $i,SV97: $i > $o] :
( ( ( ! [SY3829: $i] :
( ~ ( SV97 @ SY3829 )
| ( SV977 = SY3829 ) ) )
= $false )
| ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4706]) ).
thf(4768,plain,
! [SV376: $i > $o,SV978: $i,SV97: $i > $o] :
( ( ( ! [SY3830: $i] :
( ~ ( SV97 @ SY3830 )
| ( SV978 = SY3830 ) ) )
= $false )
| ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4707]) ).
thf(4769,plain,
! [SV974: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
| ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4708]) ).
thf(4770,plain,
! [SV964: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4710]) ).
thf(4771,plain,
! [SV964: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4711]) ).
thf(4772,plain,
! [SV965: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4712]) ).
thf(4773,plain,
! [SV965: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4713]) ).
thf(4774,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ SV1002 )
| ~ ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) ) )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4714]) ).
thf(4775,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ SV1003 )
| ~ ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) ) )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4715]) ).
thf(4776,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV996 )
| ~ ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4716]) ).
thf(4777,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV997 )
| ~ ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4717]) ).
thf(4778,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV998 )
| ~ ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4718]) ).
thf(4779,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV999 )
| ~ ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4719]) ).
thf(4780,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV991 ) )
= $true )
| ( ( ~ ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4720]) ).
thf(4781,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV992 ) )
= $true )
| ( ( ~ ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4721]) ).
thf(4782,plain,
! [SV442: $i,SV912: $i,SV979: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ SV979 @ SV912 )
= $false )
| ( ( in @ SV979 @ SV442 )
= $false )
| ( ( in @ SV912 @ ( sK52_SY3204 @ SV170 @ SV442 ) )
= $true )
| ( ( in @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV442 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4724]) ).
thf(4783,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
| ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4725]) ).
thf(4784,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) )
| ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4726]) ).
thf(4785,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( ~ ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) ) )
= $true )
| ( ( ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4727]) ).
thf(4786,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4728]) ).
thf(4787,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i,SV970: $o] :
( ( ( in @ ( kpair @ ( sK122_SY3818 @ SV970 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
= $true )
| ( SV970 = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4731]) ).
thf(4788,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( in @ ( kpair @ ( sK123_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
= $true )
| ( $true = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4734]) ).
thf(4789,plain,
! [SV240: $i,SV882: $i,SV508: $i,SV917: $i,SV766: $i] :
( ( ( in @ ( kpair @ ( sK124_SX0 @ SV766 @ SV917 @ SV508 @ SV882 @ SV240 ) @ SV917 ) @ SV766 )
= $true )
| ( $false = $true )
| ( ( in @ ( kpair @ SV882 @ SV917 ) @ ( breln1compset @ SV240 @ SV508 @ SV766 ) )
= $false )
| ( ( in @ SV917 @ SV240 )
= $false )
| ( ( in @ SV882 @ SV240 )
= $false )
| ( ( breln1 @ SV240 @ SV766 )
= $false )
| ( ( breln1 @ SV240 @ SV508 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4737]) ).
thf(4790,plain,
! [SV770: $i,SV1004: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV1004 ) )
= $true )
| ( ( ( sK111_SY2813 @ SV770 @ SV250 )
= SV1004 )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4739]) ).
thf(4791,plain,
! [SV770: $i,SV1000: $i,SV250: $i > $o] :
( ( ( SV250 @ SV1000 )
= $false )
| ( ( ( sK106_SY2813 @ SV770 @ SV250 )
= SV1000 )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4740]) ).
thf(4792,plain,
! [SV770: $i,SV1001: $i,SV250: $i > $o] :
( ( ( SV250 @ SV1001 )
= $false )
| ( ( ( sK107_SY2813 @ SV770 @ SV250 )
= SV1001 )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $false )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4741]) ).
thf(4793,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK119_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK128_SY3834 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) @ SV518 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4744]) ).
thf(4794,plain,
! [SV518: $i,SV658: $i,SV832: $i,SV251: $i] :
( ( ( in @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) @ SV518 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4746]) ).
thf(4795,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 ) )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4747]) ).
thf(4796,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV658 )
= $false )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4747]) ).
thf(4797,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK120_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK129_SY3835 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4749]) ).
thf(4798,plain,
! [SV259: $i,SV774: $i,SV525: $i] :
( ( ( in @ ( kpair @ ( sK121_SY3681 @ SV525 @ SV774 @ SV259 ) @ ( sK130_SY3836 @ SV774 @ SV525 @ SV259 ) ) @ SV774 )
= $true )
| ( ( SV525 = SV774 )
= $true )
| ( ( in @ ( kpair @ ( sK66_SY3679 @ SV774 @ SV525 @ SV259 ) @ ( sK83_SY3775 @ SV525 @ SV774 @ SV259 ) ) @ SV525 )
= $true )
| ( ( breln1 @ SV259 @ SV774 )
= $false )
| ( ( breln1 @ SV259 @ SV525 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4753]) ).
thf(4799,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( ~ ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
| ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4758]) ).
thf(4800,plain,
! [SV45: $i,SV987: $i,SV906: $i,SV920: $i,SV1005: $i] :
( ( ( ~ ( in @ SV1005 @ SV920 ) )
= $true )
| ( ( in @ SV1005 @ SV906 )
= $true )
| ( ( in @ SV987 @ SV920 )
= $true )
| ( ( in @ SV987 @ SV906 )
= $false )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4759]) ).
thf(4801,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ! [SY3855: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ SY3855 @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3857: $i] :
( ~ ( in @ SY3857 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3857 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ SY3855 @ SY3857 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4760]) ).
thf(4802,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3863: $i] :
( ~ ( in @ SY3863 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3863 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SY3863 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4761]) ).
thf(4803,plain,
! [SV68: $i,SV855: $i,SV348: $i,SV907: $i,SV711: $i] :
( ( ( in @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) @ SV68 )
= $true )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4762]) ).
thf(4804,plain,
! [SV68: $i,SV348: $i,SV907: $i,SV711: $i,SV855: $i] :
( ( ( in @ ( kpair @ SV855 @ ( sK109_SY3779 @ SV711 @ SV907 @ SV348 @ SV855 @ SV68 ) ) @ SV348 )
= $true )
| ( ( in @ ( kpair @ SV855 @ SV907 ) @ ( breln1compset @ SV68 @ SV348 @ SV711 ) )
= $false )
| ( ( in @ SV907 @ SV68 )
= $false )
| ( ( in @ SV855 @ SV68 )
= $false )
| ( ( breln1 @ SV68 @ SV711 )
= $false )
| ( ( breln1 @ SV68 @ SV348 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4763]) ).
thf(4805,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1007 )
| ~ ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4764]) ).
thf(4806,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1006 )
| ~ ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4765]) ).
thf(4807,plain,
! [SV376: $i > $o,SV983: $i,SV97: $i > $o] :
( ( ( ! [SY3837: $i] :
( ~ ( SV97 @ SY3837 )
| ( SV983 = SY3837 ) ) )
= $false )
| ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4766]) ).
thf(4808,plain,
! [SV977: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
| ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4767]) ).
thf(4809,plain,
! [SV978: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
| ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4768]) ).
thf(4810,plain,
! [SV974: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4769]) ).
thf(4811,plain,
! [SV97: $i > $o,SV376: $i > $o,SV974: $i] :
( ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4769]) ).
thf(4812,plain,
! [SV964: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4770]) ).
thf(4813,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK141_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3866: $i] :
( ~ ( SV416 @ SY3866 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3866 ) ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4771]) ).
thf(4814,plain,
! [SV965: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4772]) ).
thf(4815,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK142_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3867: $i] :
( ~ ( SV141 @ SY3867 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3867 ) ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4773]) ).
thf(4816,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1002 )
| ~ ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4774]) ).
thf(4817,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1003 )
| ~ ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4775]) ).
thf(4818,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV996 ) )
= $true )
| ( ( ~ ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4776]) ).
thf(4819,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV997 ) )
= $true )
| ( ( ~ ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4777]) ).
thf(4820,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV998 ) )
= $true )
| ( ( ~ ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4778]) ).
thf(4821,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV999 ) )
= $true )
| ( ( ~ ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4779]) ).
thf(4822,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4780]) ).
thf(4823,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4781]) ).
thf(4824,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( ~ ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) ) )
= $true )
| ( ( ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4783]) ).
thf(4825,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4784]) ).
thf(4826,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV985: $i] :
( ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( ~ ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4785]) ).
thf(4827,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4786]) ).
thf(4828,plain,
! [SV770: $i,SV1004: $i,SV250: $i > $o] :
( ( ( SV250 @ SV1004 )
= $false )
| ( ( ( sK111_SY2813 @ SV770 @ SV250 )
= SV1004 )
= $true )
| ( ( SV250 @ ( sK37_SY3674 @ SV770 @ SV250 ) )
= $true )
| ( ( ( sK37_SY3674 @ SV770 @ SV250 )
= SV770 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4790]) ).
thf(4829,plain,
! [SV251: $i,SV518: $i,SV832: $i,SV658: $i] :
( ( ( in @ ( kpair @ ( sK125_SY3718 @ SV658 @ SV832 @ SV518 @ SV251 ) @ ( sK134_SY3840 @ SV251 @ SV832 @ SV658 @ SV518 ) ) @ SV832 )
= $true )
| ( ( SV658 = SV832 )
= $true )
| ( ( in @ ( kpair @ ( sK79_SY3716 @ SV832 @ SV658 @ SV518 @ SV251 ) @ ( sK86_SY3785 @ SV251 @ SV658 @ SV832 @ SV518 ) ) @ SV658 )
= $true )
| ( ( breln @ SV251 @ SV518 @ SV832 )
= $false )
| ( ( breln @ SV251 @ SV518 @ SV658 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4795]) ).
thf(4830,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4799]) ).
thf(4831,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
| ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4799]) ).
thf(4832,plain,
! [SV45: $i,SV987: $i,SV906: $i,SV920: $i,SV1005: $i] :
( ( ( in @ SV1005 @ SV920 )
= $false )
| ( ( in @ SV1005 @ SV906 )
= $true )
| ( ( in @ SV987 @ SV920 )
= $true )
| ( ( in @ SV987 @ SV906 )
= $false )
| ( ( in @ SV906 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ SV920 @ ( sK2_SY2224 @ SV45 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4800]) ).
thf(4833,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3869: $i] :
( ~ ( in @ SY3869 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3869 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SY3869 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4801]) ).
thf(4834,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3863: $i] :
( ~ ( in @ SY3863 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3863 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SY3863 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4802]) ).
thf(4835,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1007 )
| ~ ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4805]) ).
thf(4836,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1006 )
| ~ ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4806]) ).
thf(4837,plain,
! [SV983: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
| ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4807]) ).
thf(4838,plain,
! [SV977: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4808]) ).
thf(4839,plain,
! [SV97: $i > $o,SV376: $i > $o,SV977: $i] :
( ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4808]) ).
thf(4840,plain,
! [SV978: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4809]) ).
thf(4841,plain,
! [SV97: $i > $o,SV376: $i > $o,SV978: $i] :
( ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4809]) ).
thf(4842,plain,
! [SV974: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4810]) ).
thf(4843,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4811]) ).
thf(4844,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK145_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3871: $i] :
( ~ ( SV416 @ SY3871 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3871 ) ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4812]) ).
thf(4845,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK141_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3866: $i] :
( ~ ( SV416 @ SY3866 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3866 ) ) ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4813]) ).
thf(4846,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK146_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3872: $i] :
( ~ ( SV141 @ SY3872 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3872 ) ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4814]) ).
thf(4847,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK142_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3867: $i] :
( ~ ( SV141 @ SY3867 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3867 ) ) ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4815]) ).
thf(4848,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1002 ) )
= $true )
| ( ( ~ ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4816]) ).
thf(4849,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1003 ) )
= $true )
| ( ( ~ ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4817]) ).
thf(4850,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4818]) ).
thf(4851,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4819]) ).
thf(4852,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4820]) ).
thf(4853,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4821]) ).
thf(4854,plain,
! [SV416: $i > $o,SV991: $i,SV141: $i > $o] :
( ( ( ! [SY3843: $i] :
( ~ ( SV141 @ SY3843 )
| ( SV991 = SY3843 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4822]) ).
thf(4855,plain,
! [SV141: $i > $o,SV992: $i,SV416: $i > $o] :
( ( ( ! [SY3844: $i] :
( ~ ( SV416 @ SY3844 )
| ( SV992 = SY3844 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4823]) ).
thf(4856,plain,
! [SV442: $i,SV170: $i > $i > $o,SV872: $i,SV993: $i] :
( ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( ~ ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4824]) ).
thf(4857,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ~ ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4825]) ).
thf(4858,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3838: $i] :
~ ~ ( ~ ( in @ SY3838 @ SV442 )
| ~ ( SV170 @ SY3838 @ SV985 ) ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4826]) ).
thf(4859,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3839: $i] :
~ ~ ( ~ ( in @ SY3839 @ SV442 )
| ~ ( SV170 @ SY3839 @ SV985 ) ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4827]) ).
thf(4860,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( in @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4830]) ).
thf(4861,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( ~ ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
| ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4831]) ).
thf(4862,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3869: $i] :
( ~ ( in @ SY3869 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3869 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SY3869 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4833]) ).
thf(4863,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
| ~ ! [SY3863: $i] :
( ~ ( in @ SY3863 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3863 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SY3863 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4834]) ).
thf(4864,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1007 )
| ~ ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4835]) ).
thf(4865,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1006 ) )
= $true )
| ( ( ~ ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4836]) ).
thf(4866,plain,
! [SV983: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( ~ ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) ) )
= $false )
| ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4867,plain,
! [SV97: $i > $o,SV376: $i > $o,SV983: $i] :
( ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4837]) ).
thf(4868,plain,
! [SV977: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4838]) ).
thf(4869,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4839]) ).
thf(4870,plain,
! [SV978: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4840]) ).
thf(4871,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4841]) ).
thf(4872,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4842]) ).
thf(4873,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4843]) ).
thf(4874,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK145_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3871: $i] :
( ~ ( SV416 @ SY3871 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3871 ) ) ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4844]) ).
thf(4875,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK141_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3866: $i] :
( ~ ( SV416 @ SY3866 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3866 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4845]) ).
thf(4876,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK146_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3872: $i] :
( ~ ( SV141 @ SY3872 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3872 ) ) ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4846]) ).
thf(4877,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK142_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3867: $i] :
( ~ ( SV141 @ SY3867 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3867 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4847]) ).
thf(4878,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) )
= $true )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4848]) ).
thf(4879,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) )
= $true )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4849]) ).
thf(4880,plain,
! [SV416: $i > $o,SV996: $i,SV141: $i > $o] :
( ( ( ! [SY3851: $i] :
( ~ ( SV141 @ SY3851 )
| ( SV996 = SY3851 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4850]) ).
thf(4881,plain,
! [SV141: $i > $o,SV997: $i,SV416: $i > $o] :
( ( ( ! [SY3852: $i] :
( ~ ( SV416 @ SY3852 )
| ( SV997 = SY3852 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4851]) ).
thf(4882,plain,
! [SV416: $i > $o,SV998: $i,SV141: $i > $o] :
( ( ( ! [SY3853: $i] :
( ~ ( SV141 @ SY3853 )
| ( SV998 = SY3853 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4852]) ).
thf(4883,plain,
! [SV141: $i > $o,SV999: $i,SV416: $i > $o] :
( ( ( ! [SY3854: $i] :
( ~ ( SV416 @ SY3854 )
| ( SV999 = SY3854 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4853]) ).
thf(4884,plain,
! [SV991: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
| ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4854]) ).
thf(4885,plain,
! [SV992: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
| ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4855]) ).
thf(4886,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3845: $i] :
~ ~ ( ~ ( in @ SY3845 @ SV442 )
| ~ ( SV170 @ SY3845 @ SV993 ) ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4856]) ).
thf(4887,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i] :
( ( ( ! [SY3846: $i] :
~ ~ ( ~ ( in @ SY3846 @ SV442 )
| ~ ( SV170 @ SY3846 @ SV993 ) ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4857]) ).
thf(4888,plain,
! [SV442: $i,SV170: $i > $i > $o,SV985: $i,SV872: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV985 ) ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4858]) ).
thf(4889,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i,SV1008: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1008 @ SV442 )
| ~ ( SV170 @ SV1008 @ SV985 ) ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4859]) ).
thf(4890,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( ~ ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4861]) ).
thf(4891,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
| ~ ! [SY3869: $i] :
( ~ ( in @ SY3869 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3869 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SY3869 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4862]) ).
thf(4892,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4863]) ).
thf(4893,plain,
! [SV849: $i,SV976: $i,SV45: $i] :
( ( ( ~ ! [SY3863: $i] :
( ~ ( in @ SY3863 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3863 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SY3863 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4863]) ).
thf(4894,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1007 ) )
= $true )
| ( ( ~ ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4864]) ).
thf(4895,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1006 )
= $false )
| ( ( ~ ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4865]) ).
thf(4896,plain,
! [SV983: $i,SV376: $i > $o,SV97: $i > $o] :
( ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) )
| ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4866]) ).
thf(4897,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4867]) ).
thf(4898,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4868]) ).
thf(4899,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4869]) ).
thf(4900,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4870]) ).
thf(4901,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4871]) ).
thf(4902,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4872]) ).
thf(4903,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4873]) ).
thf(4904,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK145_SY3147 @ SV964 @ SV141 @ SV416 ) )
| ~ ! [SY3871: $i] :
( ~ ( SV416 @ SY3871 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3871 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4874]) ).
thf(4905,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK141_SY3147 @ SV964 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4906,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3866: $i] :
( ~ ( SV416 @ SY3866 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3866 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4875]) ).
thf(4907,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK146_SY2531 @ SV965 @ SV416 @ SV141 ) )
| ~ ! [SY3872: $i] :
( ~ ( SV141 @ SY3872 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3872 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4876]) ).
thf(4908,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK142_SY2531 @ SV965 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4877]) ).
thf(4909,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3867: $i] :
( ~ ( SV141 @ SY3867 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3867 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4877]) ).
thf(4910,plain,
! [SV416: $i > $o,SV1002: $i,SV141: $i > $o] :
( ( ( ! [SY3859: $i] :
( ~ ( SV141 @ SY3859 )
| ( SV1002 = SY3859 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4878]) ).
thf(4911,plain,
! [SV141: $i > $o,SV1003: $i,SV416: $i > $o] :
( ( ( ! [SY3860: $i] :
( ~ ( SV416 @ SY3860 )
| ( SV1003 = SY3860 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4879]) ).
thf(4912,plain,
! [SV996: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
| ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4880]) ).
thf(4913,plain,
! [SV997: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
| ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4881]) ).
thf(4914,plain,
! [SV998: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
| ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4882]) ).
thf(4915,plain,
! [SV999: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
| ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4883]) ).
thf(4916,plain,
! [SV991: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4884]) ).
thf(4917,plain,
! [SV141: $i > $o,SV416: $i > $o,SV991: $i] :
( ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4884]) ).
thf(4918,plain,
! [SV992: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4919,plain,
! [SV416: $i > $o,SV141: $i > $o,SV992: $i] :
( ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4885]) ).
thf(4920,plain,
! [SV442: $i,SV170: $i > $i > $o,SV993: $i,SV872: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV993 ) ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4886]) ).
thf(4921,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i,SV1009: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1009 @ SV442 )
| ~ ( SV170 @ SV1009 @ SV993 ) ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4887]) ).
thf(4922,plain,
! [SV442: $i,SV170: $i > $i > $o,SV985: $i,SV872: $i] :
( ( ( ~ ( ~ ( in @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV985 ) ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4888]) ).
thf(4923,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i,SV1008: $i] :
( ( ( ~ ( ~ ( in @ SV1008 @ SV442 )
| ~ ( SV170 @ SV1008 @ SV985 ) ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4889]) ).
thf(4924,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4890]) ).
thf(4925,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4926,plain,
! [SV849: $i,SV980: $i,SV45: $i] :
( ( ( ~ ! [SY3869: $i] :
( ~ ( in @ SY3869 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3869 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SY3869 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4891]) ).
thf(4927,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4892]) ).
thf(4928,plain,
! [SV849: $i,SV976: $i,SV45: $i] :
( ( ( ! [SY3863: $i] :
( ~ ( in @ SY3863 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3850: $i] :
( ~ ( in @ SY3850 @ SY3863 )
| ( in @ SY3850 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SY3863 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4893]) ).
thf(4929,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1007 )
= $false )
| ( ( ~ ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4894]) ).
thf(4930,plain,
! [SV921: $i,SV97: $i > $o,SV1006: $i,SV376: $i > $o] :
( ( ( ! [SY3861: $i] :
( ~ ( SV376 @ SY3861 )
| ( SV1006 = SY3861 ) ) )
= $false )
| ( ( SV376 @ SV1006 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4895]) ).
thf(4931,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4896]) ).
thf(4932,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4897]) ).
thf(4933,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4898]) ).
thf(4934,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4899]) ).
thf(4935,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4900]) ).
thf(4936,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4901]) ).
thf(4937,plain,
! [SV974: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4902]) ).
thf(4938,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1010 )
| ~ ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4903]) ).
thf(4939,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK145_SY3147 @ SV964 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4904]) ).
thf(4940,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3871: $i] :
( ~ ( SV416 @ SY3871 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3871 ) ) )
= $false )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4904]) ).
thf(4941,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK141_SY3147 @ SV964 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4905]) ).
thf(4942,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ! [SY3866: $i] :
( ~ ( SV416 @ SY3866 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3866 ) ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4906]) ).
thf(4943,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK146_SY2531 @ SV965 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4907]) ).
thf(4944,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3872: $i] :
( ~ ( SV141 @ SY3872 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3872 ) ) )
= $false )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4907]) ).
thf(4945,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK142_SY2531 @ SV965 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4908]) ).
thf(4946,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ! [SY3867: $i] :
( ~ ( SV141 @ SY3867 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3867 ) ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4909]) ).
thf(4947,plain,
! [SV1002: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
| ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4910]) ).
thf(4948,plain,
! [SV1003: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
| ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4911]) ).
thf(4949,plain,
! [SV996: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4912]) ).
thf(4950,plain,
! [SV141: $i > $o,SV416: $i > $o,SV996: $i] :
( ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4912]) ).
thf(4951,plain,
! [SV997: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4913]) ).
thf(4952,plain,
! [SV416: $i > $o,SV141: $i > $o,SV997: $i] :
( ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4913]) ).
thf(4953,plain,
! [SV998: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4914]) ).
thf(4954,plain,
! [SV141: $i > $o,SV416: $i > $o,SV998: $i] :
( ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4914]) ).
thf(4955,plain,
! [SV999: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4915]) ).
thf(4956,plain,
! [SV416: $i > $o,SV141: $i > $o,SV999: $i] :
( ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4915]) ).
thf(4957,plain,
! [SV991: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4916]) ).
thf(4958,plain,
! [SV991: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4917]) ).
thf(4959,plain,
! [SV992: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4918]) ).
thf(4960,plain,
! [SV992: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4919]) ).
thf(4961,plain,
! [SV442: $i,SV170: $i > $i > $o,SV993: $i,SV872: $i] :
( ( ( ~ ( ~ ( in @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV993 ) ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4920]) ).
thf(4962,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i,SV1009: $i] :
( ( ( ~ ( ~ ( in @ SV1009 @ SV442 )
| ~ ( SV170 @ SV1009 @ SV993 ) ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4921]) ).
thf(4963,plain,
! [SV442: $i,SV170: $i > $i > $o,SV985: $i,SV872: $i] :
( ( ( ~ ( in @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV985 ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4922]) ).
thf(4964,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV442 )
| ~ ( SV170 @ SV1008 @ SV985 ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4923]) ).
thf(4965,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( ~ ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4924]) ).
thf(4966,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4924]) ).
thf(4967,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4925]) ).
thf(4968,plain,
! [SV849: $i,SV980: $i,SV45: $i] :
( ( ( ! [SY3869: $i] :
( ~ ( in @ SY3869 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3858: $i] :
( ~ ( in @ SY3858 @ SY3869 )
| ( in @ SY3858 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SY3869 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4926]) ).
thf(4969,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
| ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4927]) ).
thf(4970,plain,
! [SV849: $i,SV976: $i,SV45: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV1011 )
| ( in @ SY3874 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4928]) ).
thf(4971,plain,
! [SV921: $i,SV97: $i > $o,SV1007: $i,SV376: $i > $o] :
( ( ( ! [SY3865: $i] :
( ~ ( SV376 @ SY3865 )
| ( SV1007 = SY3865 ) ) )
= $false )
| ( ( SV376 @ SV1007 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4929]) ).
thf(4972,plain,
! [SV1006: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK157_SY3861 @ SV921 @ SV97 @ SV1006 @ SV376 ) )
| ( SV1006
= ( sK157_SY3861 @ SV921 @ SV97 @ SV1006 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1006 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4930]) ).
thf(4973,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ~ ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4931]) ).
thf(4974,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4932]) ).
thf(4975,plain,
! [SV977: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4933]) ).
thf(4976,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1012 )
| ~ ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4934]) ).
thf(4977,plain,
! [SV978: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4935]) ).
thf(4978,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1013 )
| ~ ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4936]) ).
thf(4979,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1014 )
| ~ ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4937]) ).
thf(4980,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1010 )
| ~ ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4938]) ).
thf(4981,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK145_SY3147 @ SV964 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4939]) ).
thf(4982,plain,
! [SV141: $i > $o,SV964: $i,SV416: $i > $o] :
( ( ( ! [SY3871: $i] :
( ~ ( SV416 @ SY3871 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SY3871 ) ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4940]) ).
thf(4983,plain,
! [SV141: $i > $o,SV964: $i,SV1015: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1015 )
| ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1015 ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4942]) ).
thf(4984,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK146_SY2531 @ SV965 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4943]) ).
thf(4985,plain,
! [SV416: $i > $o,SV965: $i,SV141: $i > $o] :
( ( ( ! [SY3872: $i] :
( ~ ( SV141 @ SY3872 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SY3872 ) ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4944]) ).
thf(4986,plain,
! [SV416: $i > $o,SV965: $i,SV1016: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1016 )
| ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1016 ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4946]) ).
thf(4987,plain,
! [SV1002: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4947]) ).
thf(4988,plain,
! [SV141: $i > $o,SV416: $i > $o,SV1002: $i] :
( ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4947]) ).
thf(4989,plain,
! [SV1003: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(4990,plain,
! [SV416: $i > $o,SV141: $i > $o,SV1003: $i] :
( ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4948]) ).
thf(4991,plain,
! [SV996: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4949]) ).
thf(4992,plain,
! [SV996: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4950]) ).
thf(4993,plain,
! [SV997: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4951]) ).
thf(4994,plain,
! [SV997: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4952]) ).
thf(4995,plain,
! [SV998: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4953]) ).
thf(4996,plain,
! [SV998: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4954]) ).
thf(4997,plain,
! [SV999: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4955]) ).
thf(4998,plain,
! [SV999: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4956]) ).
thf(4999,plain,
! [SV991: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4957]) ).
thf(5000,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK158_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3878: $i] :
( ~ ( SV416 @ SY3878 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3878 ) ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4958]) ).
thf(5001,plain,
! [SV992: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4959]) ).
thf(5002,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK159_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3879: $i] :
( ~ ( SV141 @ SY3879 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3879 ) ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4960]) ).
thf(5003,plain,
! [SV442: $i,SV170: $i > $i > $o,SV993: $i,SV872: $i] :
( ( ( ~ ( in @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV442 )
| ~ ( SV170 @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV993 ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4961]) ).
thf(5004,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ SV442 )
| ~ ( SV170 @ SV1009 @ SV993 ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4962]) ).
thf(5005,plain,
! [SV442: $i,SV170: $i > $i > $o,SV985: $i,SV872: $i] :
( ( ( ~ ( in @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV442 ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4963]) ).
thf(5006,plain,
! [SV442: $i,SV985: $i,SV872: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV985 ) )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4963]) ).
thf(5007,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i,SV1008: $i] :
( ( ( ~ ( in @ SV1008 @ SV442 ) )
= $true )
| ( ( ~ ( SV170 @ SV1008 @ SV985 ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4964]) ).
thf(5008,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4965]) ).
thf(5009,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4966]) ).
thf(5010,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
| ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4967]) ).
thf(5011,plain,
! [SV849: $i,SV980: $i,SV45: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
| ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV1017 )
| ( in @ SY3880 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4968]) ).
thf(5012,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4969]) ).
thf(5013,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[4969]) ).
thf(5014,plain,
! [SV849: $i,SV976: $i,SV45: $i,SV1011: $i] :
( ( ( ~ ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV1011 )
| ( in @ SY3874 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[4970]) ).
thf(5015,plain,
! [SV1007: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK160_SY3865 @ SV921 @ SV97 @ SV1007 @ SV376 ) )
| ( SV1007
= ( sK160_SY3865 @ SV921 @ SV97 @ SV1007 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1007 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4971]) ).
thf(5016,plain,
! [SV1006: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK157_SY3861 @ SV921 @ SV97 @ SV1006 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1006 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4972]) ).
thf(5017,plain,
! [SV376: $i > $o,SV97: $i > $o,SV921: $i,SV1006: $i] :
( ( ( SV1006
= ( sK157_SY3861 @ SV921 @ SV97 @ SV1006 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1006 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[4972]) ).
thf(5018,plain,
! [SV983: $i,SV97: $i > $o,SV376: $i > $o] :
( ( ( ! [SY3073: $i] :
~ ~ ( ~ ( SV376 @ SY3073 )
| ~ ! [SY3074: $i] :
( ~ ( SV376 @ SY3074 )
| ( SY3073 = SY3074 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4973]) ).
thf(5019,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1018 )
| ~ ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4974]) ).
thf(5020,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1019 )
| ~ ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[4975]) ).
thf(5021,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1012 )
| ~ ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4976]) ).
thf(5022,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1020 )
| ~ ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4977]) ).
thf(5023,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1013 )
| ~ ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4978]) ).
thf(5024,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1014 )
| ~ ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4979]) ).
thf(5025,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1010 )
| ~ ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[4980]) ).
thf(5026,plain,
! [SV141: $i > $o,SV964: $i,SV1021: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1021 )
| ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1021 ) )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4982]) ).
thf(5027,plain,
! [SV141: $i > $o,SV964: $i,SV1015: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1015 ) )
= $true )
| ( ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1015 )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4983]) ).
thf(5028,plain,
! [SV416: $i > $o,SV965: $i,SV1022: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1022 )
| ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1022 ) )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[4985]) ).
thf(5029,plain,
! [SV416: $i > $o,SV965: $i,SV1016: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1016 ) )
= $true )
| ( ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1016 )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[4986]) ).
thf(5030,plain,
! [SV1002: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( ~ ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4987]) ).
thf(5031,plain,
! [SV1002: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4988]) ).
thf(5032,plain,
! [SV1003: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( ~ ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[4989]) ).
thf(5033,plain,
! [SV1003: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4990]) ).
thf(5034,plain,
! [SV996: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4991]) ).
thf(5035,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK161_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3884: $i] :
( ~ ( SV416 @ SY3884 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3884 ) ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4992]) ).
thf(5036,plain,
! [SV997: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[4993]) ).
thf(5037,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK162_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3885: $i] :
( ~ ( SV141 @ SY3885 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3885 ) ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4994]) ).
thf(5038,plain,
! [SV998: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4995]) ).
thf(5039,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK163_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3886: $i] :
( ~ ( SV416 @ SY3886 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3886 ) ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4996]) ).
thf(5040,plain,
! [SV999: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[4997]) ).
thf(5041,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK164_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3887: $i] :
( ~ ( SV141 @ SY3887 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3887 ) ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[4998]) ).
thf(5042,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK165_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3888: $i] :
( ~ ( SV416 @ SY3888 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3888 ) ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[4999]) ).
thf(5043,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK158_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3878: $i] :
( ~ ( SV416 @ SY3878 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3878 ) ) ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5000]) ).
thf(5044,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK166_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3889: $i] :
( ~ ( SV141 @ SY3889 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3889 ) ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5001]) ).
thf(5045,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK159_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3879: $i] :
( ~ ( SV141 @ SY3879 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3879 ) ) ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5002]) ).
thf(5046,plain,
! [SV442: $i,SV170: $i > $i > $o,SV993: $i,SV872: $i] :
( ( ( ~ ( in @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV442 ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5003]) ).
thf(5047,plain,
! [SV442: $i,SV993: $i,SV872: $i,SV170: $i > $i > $o] :
( ( ( ~ ( SV170 @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV993 ) )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5003]) ).
thf(5048,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i,SV1009: $i] :
( ( ( ~ ( in @ SV1009 @ SV442 ) )
= $true )
| ( ( ~ ( SV170 @ SV1009 @ SV993 ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5004]) ).
thf(5049,plain,
! [SV442: $i,SV170: $i > $i > $o,SV985: $i,SV872: $i] :
( ( ( in @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV442 )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5005]) ).
thf(5050,plain,
! [SV442: $i,SV985: $i,SV872: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ ( sK149_SY3838 @ SV872 @ SV985 @ SV170 @ SV442 ) @ SV985 )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5006]) ).
thf(5051,plain,
! [SV872: $i,SV985: $i,SV170: $i > $i > $o,SV442: $i,SV1008: $i] :
( ( ( in @ SV1008 @ SV442 )
= $false )
| ( ( ~ ( SV170 @ SV1008 @ SV985 ) )
= $true )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5007]) ).
thf(5052,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
| ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5008]) ).
thf(5053,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5009]) ).
thf(5054,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5009]) ).
thf(5055,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5010]) ).
thf(5056,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5010]) ).
thf(5057,plain,
! [SV849: $i,SV980: $i,SV45: $i,SV1017: $i] :
( ( ( ~ ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) ) )
= $true )
| ( ( ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV1017 )
| ( in @ SY3880 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5011]) ).
thf(5058,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5012]) ).
thf(5059,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5013]) ).
thf(5060,plain,
! [SV849: $i,SV976: $i,SV45: $i,SV1011: $i] :
( ( ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV1011 )
| ( in @ SY3874 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
| ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5014]) ).
thf(5061,plain,
! [SV1007: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK160_SY3865 @ SV921 @ SV97 @ SV1007 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1007 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5015]) ).
thf(5062,plain,
! [SV376: $i > $o,SV97: $i > $o,SV921: $i,SV1007: $i] :
( ( ( SV1007
= ( sK160_SY3865 @ SV921 @ SV97 @ SV1007 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1007 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5015]) ).
thf(5063,plain,
! [SV1006: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK157_SY3861 @ SV921 @ SV97 @ SV1006 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1006 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV921
= ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $false )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5016]) ).
thf(5064,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( ~ ~ ( ~ ( SV376 @ SV1023 )
| ~ ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5018]) ).
thf(5065,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1018 )
| ~ ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5019]) ).
thf(5066,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1019 )
| ~ ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5020]) ).
thf(5067,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1012 )
| ~ ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5021]) ).
thf(5068,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1020 )
| ~ ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5022]) ).
thf(5069,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1013 )
| ~ ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5023]) ).
thf(5070,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1014 )
| ~ ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5024]) ).
thf(5071,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1010 ) )
= $true )
| ( ( ~ ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5025]) ).
thf(5072,plain,
! [SV141: $i > $o,SV964: $i,SV1021: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1021 ) )
= $true )
| ( ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1021 )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5026]) ).
thf(5073,plain,
! [SV141: $i > $o,SV964: $i,SV1015: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1015 )
= $false )
| ( ( ( sK141_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1015 )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV964
= ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5027]) ).
thf(5074,plain,
! [SV416: $i > $o,SV965: $i,SV1022: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1022 ) )
= $true )
| ( ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1022 )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5028]) ).
thf(5075,plain,
! [SV416: $i > $o,SV965: $i,SV1016: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1016 )
= $false )
| ( ( ( sK142_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1016 )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV965
= ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $false )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5029]) ).
thf(5076,plain,
! [SV1002: $i,SV141: $i > $o,SV416: $i > $o] :
( ( ( ! [SY3147: $i] :
~ ~ ( ~ ( SV416 @ SY3147 )
| ~ ! [SY3148: $i] :
( ~ ( SV416 @ SY3148 )
| ( SY3147 = SY3148 ) ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5030]) ).
thf(5077,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3891: $i] :
( ~ ( SV416 @ SY3891 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3891 ) ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5031]) ).
thf(5078,plain,
! [SV1003: $i,SV416: $i > $o,SV141: $i > $o] :
( ( ( ! [SY2531: $i] :
~ ~ ( ~ ( SV141 @ SY2531 )
| ~ ! [SY2532: $i] :
( ~ ( SV141 @ SY2532 )
| ( SY2531 = SY2532 ) ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5032]) ).
thf(5079,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3892: $i] :
( ~ ( SV141 @ SY3892 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3892 ) ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5033]) ).
thf(5080,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK169_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3893: $i] :
( ~ ( SV416 @ SY3893 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3893 ) ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5034]) ).
thf(5081,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK161_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3884: $i] :
( ~ ( SV416 @ SY3884 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3884 ) ) ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5035]) ).
thf(5082,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK170_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3894: $i] :
( ~ ( SV141 @ SY3894 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3894 ) ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5036]) ).
thf(5083,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK162_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3885: $i] :
( ~ ( SV141 @ SY3885 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3885 ) ) ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5037]) ).
thf(5084,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK171_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3895: $i] :
( ~ ( SV416 @ SY3895 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3895 ) ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5038]) ).
thf(5085,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK163_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3886: $i] :
( ~ ( SV416 @ SY3886 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3886 ) ) ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5039]) ).
thf(5086,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK172_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3896: $i] :
( ~ ( SV141 @ SY3896 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3896 ) ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5040]) ).
thf(5087,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK164_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3887: $i] :
( ~ ( SV141 @ SY3887 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3887 ) ) ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5041]) ).
thf(5088,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK165_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3888: $i] :
( ~ ( SV416 @ SY3888 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3888 ) ) ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5042]) ).
thf(5089,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK158_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3878: $i] :
( ~ ( SV416 @ SY3878 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3878 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5043]) ).
thf(5090,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK166_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3889: $i] :
( ~ ( SV141 @ SY3889 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3889 ) ) ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5044]) ).
thf(5091,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK159_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3879: $i] :
( ~ ( SV141 @ SY3879 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3879 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5045]) ).
thf(5092,plain,
! [SV442: $i,SV170: $i > $i > $o,SV993: $i,SV872: $i] :
( ( ( in @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV442 )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5046]) ).
thf(5093,plain,
! [SV442: $i,SV993: $i,SV872: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ ( sK154_SY3845 @ SV872 @ SV993 @ SV170 @ SV442 ) @ SV993 )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5047]) ).
thf(5094,plain,
! [SV872: $i,SV993: $i,SV170: $i > $i > $o,SV442: $i,SV1009: $i] :
( ( ( in @ SV1009 @ SV442 )
= $false )
| ( ( ~ ( SV170 @ SV1009 @ SV993 ) )
= $true )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5048]) ).
thf(5095,plain,
! [SV872: $i,SV442: $i,SV985: $i,SV1008: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ SV1008 @ SV985 )
= $false )
| ( ( in @ SV1008 @ SV442 )
= $false )
| ( ( in @ SV985 @ ( sK110_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV872
= ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5051]) ).
thf(5096,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( ~ ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) ) )
= $false )
| ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5052]) ).
thf(5097,plain,
! [SV45: $i,SV958: $i,SV938: $i] :
( ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5052]) ).
thf(5098,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $false )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5053]) ).
thf(5099,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5055]) ).
thf(5100,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5056]) ).
thf(5101,plain,
! [SV849: $i,SV980: $i,SV45: $i,SV1017: $i] :
( ( ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV1017 )
| ( in @ SY3880 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
| ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5057]) ).
thf(5102,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5058]) ).
thf(5103,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5059]) ).
thf(5104,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1011: $i] :
( ( ( ! [SY3874: $i] :
( ~ ( in @ SY3874 @ SV1011 )
| ( in @ SY3874 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) ) )
= $true )
| ( ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 )
= $true )
| ( ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5060]) ).
thf(5105,plain,
! [SV1007: $i,SV97: $i > $o,SV921: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK160_SY3865 @ SV921 @ SV97 @ SV1007 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1007 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV921 )
= $false )
| ( ( SV97 @ ( sK115_SY3789 @ SV376 @ SV921 @ SV97 ) )
= $true )
| ( ( ( sK9_SY3069 @ SV376 @ SV97 )
= ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5061]) ).
thf(5106,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( ~ ( ~ ( SV376 @ SV1023 )
| ~ ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5064]) ).
thf(5107,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1018 )
| ~ ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5065]) ).
thf(5108,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1019 )
| ~ ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5066]) ).
thf(5109,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1012 ) )
= $true )
| ( ( ~ ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5067]) ).
thf(5110,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1020 )
| ~ ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5068]) ).
thf(5111,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1013 ) )
= $true )
| ( ( ~ ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5069]) ).
thf(5112,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1014 ) )
= $true )
| ( ( ~ ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5070]) ).
thf(5113,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1010 )
= $false )
| ( ( ~ ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5071]) ).
thf(5114,plain,
! [SV141: $i > $o,SV964: $i,SV1021: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1021 )
= $false )
| ( ( ( sK145_SY3147 @ SV964 @ SV141 @ SV416 )
= SV1021 )
= $true )
| ( ( SV141 @ SV964 )
= $false )
| ( ( SV141 @ ( sK132_SY3812 @ SV416 @ SV964 @ SV141 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5072]) ).
thf(5115,plain,
! [SV416: $i > $o,SV965: $i,SV1022: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1022 )
= $false )
| ( ( ( sK146_SY2531 @ SV965 @ SV416 @ SV141 )
= SV1022 )
= $true )
| ( ( SV416 @ SV965 )
= $false )
| ( ( SV416 @ ( sK133_SY3813 @ SV141 @ SV965 @ SV416 ) )
= $true )
| ( ( ( sK13_SY3143 @ SV416 @ SV141 )
= ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5074]) ).
thf(5116,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ~ ( ~ ( SV416 @ ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3897: $i] :
( ~ ( SV416 @ SY3897 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3897 ) ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5076]) ).
thf(5117,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3891: $i] :
( ~ ( SV416 @ SY3891 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3891 ) ) ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5077]) ).
thf(5118,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ~ ( ~ ( SV141 @ ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3898: $i] :
( ~ ( SV141 @ SY3898 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3898 ) ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5078]) ).
thf(5119,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3892: $i] :
( ~ ( SV141 @ SY3892 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3892 ) ) ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5079]) ).
thf(5120,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK169_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3893: $i] :
( ~ ( SV416 @ SY3893 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3893 ) ) ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5080]) ).
thf(5121,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK161_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3884: $i] :
( ~ ( SV416 @ SY3884 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3884 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5081]) ).
thf(5122,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK170_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3894: $i] :
( ~ ( SV141 @ SY3894 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3894 ) ) ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5082]) ).
thf(5123,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK162_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3885: $i] :
( ~ ( SV141 @ SY3885 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3885 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5083]) ).
thf(5124,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK171_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3895: $i] :
( ~ ( SV416 @ SY3895 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3895 ) ) ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5084]) ).
thf(5125,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK163_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3886: $i] :
( ~ ( SV416 @ SY3886 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3886 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5085]) ).
thf(5126,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK172_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3896: $i] :
( ~ ( SV141 @ SY3896 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3896 ) ) ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5086]) ).
thf(5127,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK164_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3887: $i] :
( ~ ( SV141 @ SY3887 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3887 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5087]) ).
thf(5128,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK165_SY3147 @ SV991 @ SV141 @ SV416 ) )
| ~ ! [SY3888: $i] :
( ~ ( SV416 @ SY3888 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3888 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5088]) ).
thf(5129,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK158_SY3147 @ SV991 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5089]) ).
thf(5130,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3878: $i] :
( ~ ( SV416 @ SY3878 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3878 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5089]) ).
thf(5131,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK166_SY2531 @ SV992 @ SV416 @ SV141 ) )
| ~ ! [SY3889: $i] :
( ~ ( SV141 @ SY3889 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3889 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5090]) ).
thf(5132,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK159_SY2531 @ SV992 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5091]) ).
thf(5133,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3879: $i] :
( ~ ( SV141 @ SY3879 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3879 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5091]) ).
thf(5134,plain,
! [SV872: $i,SV442: $i,SV993: $i,SV1009: $i,SV170: $i > $i > $o] :
( ( ( SV170 @ SV1009 @ SV993 )
= $false )
| ( ( in @ SV1009 @ SV442 )
= $false )
| ( ( in @ SV993 @ ( sK117_SY3204 @ SV872 @ SV170 @ SV442 ) )
= $true )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ SV872 )
= $false )
| ( ( SV170 @ ( sK15_SY3201 @ SV170 @ SV442 ) @ ( sK91_SY3749 @ SV872 @ SV442 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5094]) ).
thf(5135,plain,
! [SV45: $i,SV938: $i,SV958: $i] :
( ( ( in @ SV958 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( in @ SV938 @ ( sK137_SY3806 @ SV958 @ SV938 @ SV45 ) )
= $true )
| ( ( SV938 = SV958 )
= $true )
| ( ( in @ SV938 @ SV45 )
= $false )
| ( ( in @ SV958 @ SV45 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5096]) ).
thf(5136,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
| ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5099]) ).
thf(5137,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5100]) ).
thf(5138,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1017: $i] :
( ( ( ! [SY3880: $i] :
( ~ ( in @ SY3880 @ SV1017 )
| ( in @ SY3880 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) ) )
= $true )
| ( ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 )
= $true )
| ( ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5101]) ).
thf(5139,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ~ ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5140,plain,
! [SV976: $i,SV849: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5102]) ).
thf(5141,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( ! [SY3848: $i] :
~ ~ ( ~ ( in @ SY3848 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SY3848 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5103]) ).
thf(5142,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1011: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV1011 )
| ( in @ SV1024 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
= $true )
| ( ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 )
= $true )
| ( ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5104]) ).
thf(5143,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1023 )
| ~ ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5106]) ).
thf(5144,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1018 ) )
= $true )
| ( ( ~ ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5107]) ).
thf(5145,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1019 ) )
= $true )
| ( ( ~ ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5108]) ).
thf(5146,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1012 )
= $false )
| ( ( ~ ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5109]) ).
thf(5147,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1020 ) )
= $true )
| ( ( ~ ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5110]) ).
thf(5148,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1013 )
= $false )
| ( ( ~ ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5111]) ).
thf(5149,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1014 )
= $false )
| ( ( ~ ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5112]) ).
thf(5150,plain,
! [SV974: $i,SV97: $i > $o,SV1010: $i,SV376: $i > $o] :
( ( ( ! [SY3873: $i] :
( ~ ( SV376 @ SY3873 )
| ( SV1010 = SY3873 ) ) )
= $false )
| ( ( SV376 @ SV1010 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5113]) ).
thf(5151,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( ~ ( SV416 @ ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3897: $i] :
( ~ ( SV416 @ SY3897 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3897 ) ) ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5116]) ).
thf(5152,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3891: $i] :
( ~ ( SV416 @ SY3891 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3891 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5117]) ).
thf(5153,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( ~ ( SV141 @ ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3898: $i] :
( ~ ( SV141 @ SY3898 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3898 ) ) ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5118]) ).
thf(5154,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3892: $i] :
( ~ ( SV141 @ SY3892 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3892 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5119]) ).
thf(5155,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK169_SY3147 @ SV996 @ SV141 @ SV416 ) )
| ~ ! [SY3893: $i] :
( ~ ( SV416 @ SY3893 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3893 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5120]) ).
thf(5156,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK161_SY3147 @ SV996 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5121]) ).
thf(5157,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3884: $i] :
( ~ ( SV416 @ SY3884 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3884 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5121]) ).
thf(5158,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK170_SY2531 @ SV997 @ SV416 @ SV141 ) )
| ~ ! [SY3894: $i] :
( ~ ( SV141 @ SY3894 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3894 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5122]) ).
thf(5159,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK162_SY2531 @ SV997 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5123]) ).
thf(5160,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3885: $i] :
( ~ ( SV141 @ SY3885 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3885 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5123]) ).
thf(5161,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK171_SY3147 @ SV998 @ SV141 @ SV416 ) )
| ~ ! [SY3895: $i] :
( ~ ( SV416 @ SY3895 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3895 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5124]) ).
thf(5162,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK163_SY3147 @ SV998 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5125]) ).
thf(5163,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3886: $i] :
( ~ ( SV416 @ SY3886 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3886 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5125]) ).
thf(5164,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK172_SY2531 @ SV999 @ SV416 @ SV141 ) )
| ~ ! [SY3896: $i] :
( ~ ( SV141 @ SY3896 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3896 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5126]) ).
thf(5165,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK164_SY2531 @ SV999 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5166,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3887: $i] :
( ~ ( SV141 @ SY3887 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3887 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5127]) ).
thf(5167,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK165_SY3147 @ SV991 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5128]) ).
thf(5168,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3888: $i] :
( ~ ( SV416 @ SY3888 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3888 ) ) )
= $false )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5128]) ).
thf(5169,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK158_SY3147 @ SV991 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5129]) ).
thf(5170,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ! [SY3878: $i] :
( ~ ( SV416 @ SY3878 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3878 ) ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5130]) ).
thf(5171,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK166_SY2531 @ SV992 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5131]) ).
thf(5172,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3889: $i] :
( ~ ( SV141 @ SY3889 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3889 ) ) )
= $false )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5131]) ).
thf(5173,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK159_SY2531 @ SV992 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5132]) ).
thf(5174,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ! [SY3879: $i] :
( ~ ( SV141 @ SY3879 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3879 ) ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5133]) ).
thf(5175,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ~ ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5176,plain,
! [SV980: $i,SV849: $i,SV45: $i] :
( ( ( ~ ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5136]) ).
thf(5177,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( ! [SY3856: $i] :
~ ~ ( ~ ( in @ SY3856 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SY3856 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5137]) ).
thf(5178,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1017: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV1017 )
| ( in @ SV1025 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
= $true )
| ( ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 )
= $true )
| ( ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5138]) ).
thf(5179,plain,
! [SV45: $i,SV849: $i,SV976: $i] :
( ( ( in @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5139]) ).
thf(5180,plain,
! [SV976: $i,SV849: $i,SV45: $i] :
( ( ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV849 )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5140]) ).
thf(5181,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1026: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SV1026 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5141]) ).
thf(5182,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1011: $i,SV1024: $i] :
( ( ( ~ ( in @ SV1024 @ SV1011 ) )
= $true )
| ( ( in @ SV1024 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
= $true )
| ( ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 )
= $true )
| ( ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5142]) ).
thf(5183,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ SV1023 ) )
= $true )
| ( ( ~ ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5143]) ).
thf(5184,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1018 )
= $false )
| ( ( ~ ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5144]) ).
thf(5185,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1019 )
= $false )
| ( ( ~ ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5145]) ).
thf(5186,plain,
! [SV977: $i,SV97: $i > $o,SV1012: $i,SV376: $i > $o] :
( ( ( ! [SY3875: $i] :
( ~ ( SV376 @ SY3875 )
| ( SV1012 = SY3875 ) ) )
= $false )
| ( ( SV376 @ SV1012 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5146]) ).
thf(5187,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1020 )
= $false )
| ( ( ~ ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5147]) ).
thf(5188,plain,
! [SV978: $i,SV97: $i > $o,SV1013: $i,SV376: $i > $o] :
( ( ( ! [SY3876: $i] :
( ~ ( SV376 @ SY3876 )
| ( SV1013 = SY3876 ) ) )
= $false )
| ( ( SV376 @ SV1013 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5148]) ).
thf(5189,plain,
! [SV974: $i,SV97: $i > $o,SV1014: $i,SV376: $i > $o] :
( ( ( ! [SY3877: $i] :
( ~ ( SV376 @ SY3877 )
| ( SV1014 = SY3877 ) ) )
= $false )
| ( ( SV376 @ SV1014 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5149]) ).
thf(5190,plain,
! [SV1010: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK175_SY3873 @ SV974 @ SV97 @ SV1010 @ SV376 ) )
| ( SV1010
= ( sK175_SY3873 @ SV974 @ SV97 @ SV1010 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1010 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5150]) ).
thf(5191,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 ) )
| ~ ! [SY3897: $i] :
( ~ ( SV416 @ SY3897 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3897 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5151]) ).
thf(5192,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5152]) ).
thf(5193,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3891: $i] :
( ~ ( SV416 @ SY3891 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3891 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5152]) ).
thf(5194,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 ) )
| ~ ! [SY3898: $i] :
( ~ ( SV141 @ SY3898 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3898 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5153]) ).
thf(5195,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5154]) ).
thf(5196,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3892: $i] :
( ~ ( SV141 @ SY3892 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3892 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5154]) ).
thf(5197,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK169_SY3147 @ SV996 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5155]) ).
thf(5198,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3893: $i] :
( ~ ( SV416 @ SY3893 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3893 ) ) )
= $false )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5155]) ).
thf(5199,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK161_SY3147 @ SV996 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5156]) ).
thf(5200,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ! [SY3884: $i] :
( ~ ( SV416 @ SY3884 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3884 ) ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5157]) ).
thf(5201,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK170_SY2531 @ SV997 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5158]) ).
thf(5202,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3894: $i] :
( ~ ( SV141 @ SY3894 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3894 ) ) )
= $false )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5158]) ).
thf(5203,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK162_SY2531 @ SV997 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5159]) ).
thf(5204,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ! [SY3885: $i] :
( ~ ( SV141 @ SY3885 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3885 ) ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5160]) ).
thf(5205,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK171_SY3147 @ SV998 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5161]) ).
thf(5206,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3895: $i] :
( ~ ( SV416 @ SY3895 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3895 ) ) )
= $false )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5161]) ).
thf(5207,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK163_SY3147 @ SV998 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5162]) ).
thf(5208,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ! [SY3886: $i] :
( ~ ( SV416 @ SY3886 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3886 ) ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5163]) ).
thf(5209,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK172_SY2531 @ SV999 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5164]) ).
thf(5210,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3896: $i] :
( ~ ( SV141 @ SY3896 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3896 ) ) )
= $false )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5164]) ).
thf(5211,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK164_SY2531 @ SV999 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5165]) ).
thf(5212,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ! [SY3887: $i] :
( ~ ( SV141 @ SY3887 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3887 ) ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5166]) ).
thf(5213,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK165_SY3147 @ SV991 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5167]) ).
thf(5214,plain,
! [SV141: $i > $o,SV991: $i,SV416: $i > $o] :
( ( ( ! [SY3888: $i] :
( ~ ( SV416 @ SY3888 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SY3888 ) ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5168]) ).
thf(5215,plain,
! [SV141: $i > $o,SV991: $i,SV1027: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1027 )
| ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1027 ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5170]) ).
thf(5216,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK166_SY2531 @ SV992 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5171]) ).
thf(5217,plain,
! [SV416: $i > $o,SV992: $i,SV141: $i > $o] :
( ( ( ! [SY3889: $i] :
( ~ ( SV141 @ SY3889 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SY3889 ) ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5172]) ).
thf(5218,plain,
! [SV416: $i > $o,SV992: $i,SV1028: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1028 )
| ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1028 ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5174]) ).
thf(5219,plain,
! [SV45: $i,SV849: $i,SV980: $i] :
( ( ( in @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) @ ( sK2_SY2224 @ SV45 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5175]) ).
thf(5220,plain,
! [SV980: $i,SV849: $i,SV45: $i] :
( ( ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV849 )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5176]) ).
thf(5221,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1029: $i] :
( ( ( ~ ~ ( ~ ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SV1029 @ SV849 ) ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5177]) ).
thf(5222,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1017: $i,SV1025: $i] :
( ( ( ~ ( in @ SV1025 @ SV1017 ) )
= $true )
| ( ( in @ SV1025 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
= $true )
| ( ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 )
= $true )
| ( ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5178]) ).
thf(5223,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1026: $i] :
( ( ( ~ ( ~ ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SV1026 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5181]) ).
thf(5224,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1011: $i,SV1024: $i] :
( ( ( in @ SV1024 @ SV1011 )
= $false )
| ( ( in @ SV1024 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
= $true )
| ( ( in @ ( sK138_SY3847 @ SV45 @ SV849 @ SV976 ) @ SV1011 )
= $true )
| ( ( in @ SV1011 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5182]) ).
thf(5225,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( SV376 @ SV1023 )
= $false )
| ( ( ~ ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5183]) ).
thf(5226,plain,
! [SV983: $i,SV97: $i > $o,SV1018: $i,SV376: $i > $o] :
( ( ( ! [SY3881: $i] :
( ~ ( SV376 @ SY3881 )
| ( SV1018 = SY3881 ) ) )
= $false )
| ( ( SV376 @ SV1018 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5184]) ).
thf(5227,plain,
! [SV977: $i,SV97: $i > $o,SV1019: $i,SV376: $i > $o] :
( ( ( ! [SY3882: $i] :
( ~ ( SV376 @ SY3882 )
| ( SV1019 = SY3882 ) ) )
= $false )
| ( ( SV376 @ SV1019 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5185]) ).
thf(5228,plain,
! [SV1012: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK176_SY3875 @ SV977 @ SV97 @ SV1012 @ SV376 ) )
| ( SV1012
= ( sK176_SY3875 @ SV977 @ SV97 @ SV1012 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1012 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5186]) ).
thf(5229,plain,
! [SV978: $i,SV97: $i > $o,SV1020: $i,SV376: $i > $o] :
( ( ( ! [SY3883: $i] :
( ~ ( SV376 @ SY3883 )
| ( SV1020 = SY3883 ) ) )
= $false )
| ( ( SV376 @ SV1020 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5187]) ).
thf(5230,plain,
! [SV1013: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK177_SY3876 @ SV978 @ SV97 @ SV1013 @ SV376 ) )
| ( SV1013
= ( sK177_SY3876 @ SV978 @ SV97 @ SV1013 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1013 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5188]) ).
thf(5231,plain,
! [SV1014: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK178_SY3877 @ SV974 @ SV97 @ SV1014 @ SV376 ) )
| ( SV1014
= ( sK178_SY3877 @ SV974 @ SV97 @ SV1014 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1014 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5189]) ).
thf(5232,plain,
! [SV1010: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK175_SY3873 @ SV974 @ SV97 @ SV1010 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1010 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5190]) ).
thf(5233,plain,
! [SV376: $i > $o,SV97: $i > $o,SV974: $i,SV1010: $i] :
( ( ( SV1010
= ( sK175_SY3873 @ SV974 @ SV97 @ SV1010 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1010 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5190]) ).
thf(5234,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5235,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ~ ! [SY3897: $i] :
( ~ ( SV416 @ SY3897 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3897 ) ) )
= $false )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5191]) ).
thf(5236,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5192]) ).
thf(5237,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ! [SY3891: $i] :
( ~ ( SV416 @ SY3891 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3891 ) ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5193]) ).
thf(5238,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5194]) ).
thf(5239,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ~ ! [SY3898: $i] :
( ~ ( SV141 @ SY3898 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3898 ) ) )
= $false )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5194]) ).
thf(5240,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5195]) ).
thf(5241,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ! [SY3892: $i] :
( ~ ( SV141 @ SY3892 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3892 ) ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5196]) ).
thf(5242,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK169_SY3147 @ SV996 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5197]) ).
thf(5243,plain,
! [SV141: $i > $o,SV996: $i,SV416: $i > $o] :
( ( ( ! [SY3893: $i] :
( ~ ( SV416 @ SY3893 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SY3893 ) ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5198]) ).
thf(5244,plain,
! [SV141: $i > $o,SV996: $i,SV1030: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1030 )
| ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1030 ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5200]) ).
thf(5245,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK170_SY2531 @ SV997 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5201]) ).
thf(5246,plain,
! [SV416: $i > $o,SV997: $i,SV141: $i > $o] :
( ( ( ! [SY3894: $i] :
( ~ ( SV141 @ SY3894 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SY3894 ) ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5202]) ).
thf(5247,plain,
! [SV416: $i > $o,SV997: $i,SV1031: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1031 )
| ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1031 ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5204]) ).
thf(5248,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK171_SY3147 @ SV998 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5205]) ).
thf(5249,plain,
! [SV141: $i > $o,SV998: $i,SV416: $i > $o] :
( ( ( ! [SY3895: $i] :
( ~ ( SV416 @ SY3895 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SY3895 ) ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5206]) ).
thf(5250,plain,
! [SV141: $i > $o,SV998: $i,SV1032: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1032 )
| ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1032 ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5208]) ).
thf(5251,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK172_SY2531 @ SV999 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5209]) ).
thf(5252,plain,
! [SV416: $i > $o,SV999: $i,SV141: $i > $o] :
( ( ( ! [SY3896: $i] :
( ~ ( SV141 @ SY3896 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SY3896 ) ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5210]) ).
thf(5253,plain,
! [SV416: $i > $o,SV999: $i,SV1033: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1033 )
| ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1033 ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5212]) ).
thf(5254,plain,
! [SV141: $i > $o,SV991: $i,SV1034: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1034 )
| ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1034 ) )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5214]) ).
thf(5255,plain,
! [SV141: $i > $o,SV991: $i,SV1027: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1027 ) )
= $true )
| ( ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1027 )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5215]) ).
thf(5256,plain,
! [SV416: $i > $o,SV992: $i,SV1035: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1035 )
| ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1035 ) )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5217]) ).
thf(5257,plain,
! [SV416: $i > $o,SV992: $i,SV1028: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1028 ) )
= $true )
| ( ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1028 )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5218]) ).
thf(5258,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1029: $i] :
( ( ( ~ ( ~ ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SV1029 @ SV849 ) ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5221]) ).
thf(5259,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1017: $i,SV1025: $i] :
( ( ( in @ SV1025 @ SV1017 )
= $false )
| ( ( in @ SV1025 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
= $true )
| ( ( in @ ( sK143_SY3855 @ SV45 @ SV849 @ SV980 ) @ SV1017 )
= $true )
| ( ( in @ SV1017 @ ( sK2_SY2224 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5222]) ).
thf(5260,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1026: $i] :
( ( ( ~ ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
| ~ ( in @ SV1026 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5223]) ).
thf(5261,plain,
! [SV983: $i,SV97: $i > $o,SV1023: $i,SV376: $i > $o] :
( ( ( ! [SY3890: $i] :
( ~ ( SV376 @ SY3890 )
| ( SV1023 = SY3890 ) ) )
= $false )
| ( ( SV376 @ SV1023 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5225]) ).
thf(5262,plain,
! [SV1018: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK179_SY3881 @ SV983 @ SV97 @ SV1018 @ SV376 ) )
| ( SV1018
= ( sK179_SY3881 @ SV983 @ SV97 @ SV1018 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1018 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5226]) ).
thf(5263,plain,
! [SV1019: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK180_SY3882 @ SV977 @ SV97 @ SV1019 @ SV376 ) )
| ( SV1019
= ( sK180_SY3882 @ SV977 @ SV97 @ SV1019 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1019 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[5227]) ).
thf(5264,plain,
! [SV1012: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK176_SY3875 @ SV977 @ SV97 @ SV1012 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1012 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5228]) ).
thf(5265,plain,
! [SV376: $i > $o,SV97: $i > $o,SV977: $i,SV1012: $i] :
( ( ( SV1012
= ( sK176_SY3875 @ SV977 @ SV97 @ SV1012 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1012 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5228]) ).
thf(5266,plain,
! [SV1020: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK181_SY3883 @ SV978 @ SV97 @ SV1020 @ SV376 ) )
| ( SV1020
= ( sK181_SY3883 @ SV978 @ SV97 @ SV1020 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1020 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5229]) ).
thf(5267,plain,
! [SV1013: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK177_SY3876 @ SV978 @ SV97 @ SV1013 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1013 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5230]) ).
thf(5268,plain,
! [SV376: $i > $o,SV97: $i > $o,SV978: $i,SV1013: $i] :
( ( ( SV1013
= ( sK177_SY3876 @ SV978 @ SV97 @ SV1013 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1013 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5230]) ).
thf(5269,plain,
! [SV1014: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK178_SY3877 @ SV974 @ SV97 @ SV1014 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1014 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5231]) ).
thf(5270,plain,
! [SV376: $i > $o,SV97: $i > $o,SV974: $i,SV1014: $i] :
( ( ( SV1014
= ( sK178_SY3877 @ SV974 @ SV97 @ SV1014 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1014 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5231]) ).
thf(5271,plain,
! [SV1010: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK175_SY3873 @ SV974 @ SV97 @ SV1010 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1010 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV974
= ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5232]) ).
thf(5272,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( SV416 @ ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5234]) ).
thf(5273,plain,
! [SV141: $i > $o,SV1002: $i,SV416: $i > $o] :
( ( ( ! [SY3897: $i] :
( ~ ( SV416 @ SY3897 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SY3897 ) ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5235]) ).
thf(5274,plain,
! [SV141: $i > $o,SV1002: $i,SV1036: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1036 )
| ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1036 ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5237]) ).
thf(5275,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( SV141 @ ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5238]) ).
thf(5276,plain,
! [SV416: $i > $o,SV1003: $i,SV141: $i > $o] :
( ( ( ! [SY3898: $i] :
( ~ ( SV141 @ SY3898 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SY3898 ) ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5239]) ).
thf(5277,plain,
! [SV416: $i > $o,SV1003: $i,SV1037: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1037 )
| ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1037 ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5241]) ).
thf(5278,plain,
! [SV141: $i > $o,SV996: $i,SV1038: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1038 )
| ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1038 ) )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5243]) ).
thf(5279,plain,
! [SV141: $i > $o,SV996: $i,SV1030: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1030 ) )
= $true )
| ( ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1030 )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5244]) ).
thf(5280,plain,
! [SV416: $i > $o,SV997: $i,SV1039: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1039 )
| ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1039 ) )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[5246]) ).
thf(5281,plain,
! [SV416: $i > $o,SV997: $i,SV1031: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1031 ) )
= $true )
| ( ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1031 )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5247]) ).
thf(5282,plain,
! [SV141: $i > $o,SV998: $i,SV1040: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1040 )
| ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1040 ) )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5249]) ).
thf(5283,plain,
! [SV141: $i > $o,SV998: $i,SV1032: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1032 ) )
= $true )
| ( ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1032 )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5250]) ).
thf(5284,plain,
! [SV416: $i > $o,SV999: $i,SV1041: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1041 )
| ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1041 ) )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5252]) ).
thf(5285,plain,
! [SV416: $i > $o,SV999: $i,SV1033: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1033 ) )
= $true )
| ( ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1033 )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5253]) ).
thf(5286,plain,
! [SV141: $i > $o,SV991: $i,SV1034: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1034 ) )
= $true )
| ( ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1034 )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5254]) ).
thf(5287,plain,
! [SV141: $i > $o,SV991: $i,SV1027: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1027 )
= $false )
| ( ( ( sK158_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1027 )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV991
= ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5255]) ).
thf(5288,plain,
! [SV416: $i > $o,SV992: $i,SV1035: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1035 ) )
= $true )
| ( ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1035 )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5256]) ).
thf(5289,plain,
! [SV416: $i > $o,SV992: $i,SV1028: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1028 )
= $false )
| ( ( ( sK159_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1028 )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV992
= ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5257]) ).
thf(5290,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
| ~ ( in @ SV1029 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5258]) ).
thf(5291,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1026: $i] :
( ( ( ~ ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV1026 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5260]) ).
thf(5292,plain,
! [SV1023: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK182_SY3890 @ SV983 @ SV97 @ SV1023 @ SV376 ) )
| ( SV1023
= ( sK182_SY3890 @ SV983 @ SV97 @ SV1023 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1023 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[5261]) ).
thf(5293,plain,
! [SV1018: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK179_SY3881 @ SV983 @ SV97 @ SV1018 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1018 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5262]) ).
thf(5294,plain,
! [SV376: $i > $o,SV97: $i > $o,SV983: $i,SV1018: $i] :
( ( ( SV1018
= ( sK179_SY3881 @ SV983 @ SV97 @ SV1018 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1018 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5262]) ).
thf(5295,plain,
! [SV1019: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK180_SY3882 @ SV977 @ SV97 @ SV1019 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1019 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5263]) ).
thf(5296,plain,
! [SV376: $i > $o,SV97: $i > $o,SV977: $i,SV1019: $i] :
( ( ( SV1019
= ( sK180_SY3882 @ SV977 @ SV97 @ SV1019 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1019 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[5263]) ).
thf(5297,plain,
! [SV1012: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK176_SY3875 @ SV977 @ SV97 @ SV1012 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1012 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV977
= ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5264]) ).
thf(5298,plain,
! [SV1020: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK181_SY3883 @ SV978 @ SV97 @ SV1020 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1020 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5266]) ).
thf(5299,plain,
! [SV376: $i > $o,SV97: $i > $o,SV978: $i,SV1020: $i] :
( ( ( SV1020
= ( sK181_SY3883 @ SV978 @ SV97 @ SV1020 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1020 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5266]) ).
thf(5300,plain,
! [SV1013: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK177_SY3876 @ SV978 @ SV97 @ SV1013 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1013 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV978
= ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5267]) ).
thf(5301,plain,
! [SV1014: $i,SV97: $i > $o,SV974: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK178_SY3877 @ SV974 @ SV97 @ SV1014 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1014 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV974 )
= $false )
| ( ( SV97 @ ( sK136_SY3822 @ SV376 @ SV974 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5269]) ).
thf(5302,plain,
! [SV141: $i > $o,SV1002: $i,SV1042: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1042 )
| ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1042 ) )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5273]) ).
thf(5303,plain,
! [SV141: $i > $o,SV1002: $i,SV1036: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1036 ) )
= $true )
| ( ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1036 )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5274]) ).
thf(5304,plain,
! [SV416: $i > $o,SV1003: $i,SV1043: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1043 )
| ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1043 ) )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[5276]) ).
thf(5305,plain,
! [SV416: $i > $o,SV1003: $i,SV1037: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1037 ) )
= $true )
| ( ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1037 )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5277]) ).
thf(5306,plain,
! [SV141: $i > $o,SV996: $i,SV1038: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1038 ) )
= $true )
| ( ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1038 )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5278]) ).
thf(5307,plain,
! [SV141: $i > $o,SV996: $i,SV1030: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1030 )
= $false )
| ( ( ( sK161_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1030 )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV996
= ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5279]) ).
thf(5308,plain,
! [SV416: $i > $o,SV997: $i,SV1039: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1039 ) )
= $true )
| ( ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1039 )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5280]) ).
thf(5309,plain,
! [SV416: $i > $o,SV997: $i,SV1031: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1031 )
= $false )
| ( ( ( sK162_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1031 )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV997
= ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5281]) ).
thf(5310,plain,
! [SV141: $i > $o,SV998: $i,SV1040: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1040 ) )
= $true )
| ( ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1040 )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5282]) ).
thf(5311,plain,
! [SV141: $i > $o,SV998: $i,SV1032: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1032 )
= $false )
| ( ( ( sK163_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1032 )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV998
= ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5283]) ).
thf(5312,plain,
! [SV416: $i > $o,SV999: $i,SV1041: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1041 ) )
= $true )
| ( ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1041 )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5284]) ).
thf(5313,plain,
! [SV416: $i > $o,SV999: $i,SV1033: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1033 )
= $false )
| ( ( ( sK164_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1033 )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV999
= ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5285]) ).
thf(5314,plain,
! [SV141: $i > $o,SV991: $i,SV1034: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1034 )
= $false )
| ( ( ( sK165_SY3147 @ SV991 @ SV141 @ SV416 )
= SV1034 )
= $true )
| ( ( SV141 @ SV991 )
= $false )
| ( ( SV141 @ ( sK147_SY3843 @ SV416 @ SV991 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5286]) ).
thf(5315,plain,
! [SV416: $i > $o,SV992: $i,SV1035: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1035 )
= $false )
| ( ( ( sK166_SY2531 @ SV992 @ SV416 @ SV141 )
= SV1035 )
= $true )
| ( ( SV416 @ SV992 )
= $false )
| ( ( SV416 @ ( sK148_SY3844 @ SV141 @ SV992 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5288]) ).
thf(5316,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1029: $i] :
( ( ( ~ ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) ) )
= $true )
| ( ( ~ ( in @ SV1029 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[5290]) ).
thf(5317,plain,
! [SV45: $i,SV849: $i,SV976: $i,SV1026: $i] :
( ( ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV1026 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5291]) ).
thf(5318,plain,
! [SV1023: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( ~ ( SV376 @ ( sK182_SY3890 @ SV983 @ SV97 @ SV1023 @ SV376 ) ) )
= $false )
| ( ( SV376 @ SV1023 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5292]) ).
thf(5319,plain,
! [SV376: $i > $o,SV97: $i > $o,SV983: $i,SV1023: $i] :
( ( ( SV1023
= ( sK182_SY3890 @ SV983 @ SV97 @ SV1023 @ SV376 ) )
= $false )
| ( ( SV376 @ SV1023 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[5292]) ).
thf(5320,plain,
! [SV1018: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK179_SY3881 @ SV983 @ SV97 @ SV1018 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1018 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV983
= ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $false )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5293]) ).
thf(5321,plain,
! [SV1019: $i,SV97: $i > $o,SV977: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK180_SY3882 @ SV977 @ SV97 @ SV1019 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1019 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV977 )
= $false )
| ( ( SV97 @ ( sK139_SY3829 @ SV376 @ SV977 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[5295]) ).
thf(5322,plain,
! [SV1020: $i,SV97: $i > $o,SV978: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK181_SY3883 @ SV978 @ SV97 @ SV1020 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1020 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV978 )
= $false )
| ( ( SV97 @ ( sK140_SY3830 @ SV376 @ SV978 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $false )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5298]) ).
thf(5323,plain,
! [SV141: $i > $o,SV1002: $i,SV1042: $i,SV416: $i > $o] :
( ( ( ~ ( SV416 @ SV1042 ) )
= $true )
| ( ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1042 )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5302]) ).
thf(5324,plain,
! [SV141: $i > $o,SV1002: $i,SV1036: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1036 )
= $false )
| ( ( ( sK167_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1036 )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV1002
= ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5303]) ).
thf(5325,plain,
! [SV416: $i > $o,SV1003: $i,SV1043: $i,SV141: $i > $o] :
( ( ( ~ ( SV141 @ SV1043 ) )
= $true )
| ( ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1043 )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[5304]) ).
thf(5326,plain,
! [SV416: $i > $o,SV1003: $i,SV1037: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1037 )
= $false )
| ( ( ( sK168_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1037 )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV1003
= ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $false )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5305]) ).
thf(5327,plain,
! [SV141: $i > $o,SV996: $i,SV1038: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1038 )
= $false )
| ( ( ( sK169_SY3147 @ SV996 @ SV141 @ SV416 )
= SV1038 )
= $true )
| ( ( SV141 @ SV996 )
= $false )
| ( ( SV141 @ ( sK150_SY3851 @ SV416 @ SV996 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5306]) ).
thf(5328,plain,
! [SV416: $i > $o,SV997: $i,SV1039: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1039 )
= $false )
| ( ( ( sK170_SY2531 @ SV997 @ SV416 @ SV141 )
= SV1039 )
= $true )
| ( ( SV416 @ SV997 )
= $false )
| ( ( SV416 @ ( sK151_SY3852 @ SV141 @ SV997 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5308]) ).
thf(5329,plain,
! [SV141: $i > $o,SV998: $i,SV1040: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1040 )
= $false )
| ( ( ( sK171_SY3147 @ SV998 @ SV141 @ SV416 )
= SV1040 )
= $true )
| ( ( SV141 @ SV998 )
= $false )
| ( ( SV141 @ ( sK152_SY3853 @ SV416 @ SV998 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5310]) ).
thf(5330,plain,
! [SV416: $i > $o,SV999: $i,SV1041: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1041 )
= $false )
| ( ( ( sK172_SY2531 @ SV999 @ SV416 @ SV141 )
= SV1041 )
= $true )
| ( ( SV416 @ SV999 )
= $false )
| ( ( SV416 @ ( sK153_SY3854 @ SV141 @ SV999 @ SV416 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $false )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5312]) ).
thf(5331,plain,
! [SV45: $i,SV849: $i,SV980: $i,SV1029: $i] :
( ( ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
= $false )
| ( ( ~ ( in @ SV1029 @ SV849 ) )
= $true )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5316]) ).
thf(5332,plain,
! [SV45: $i,SV976: $i,SV849: $i,SV1026: $i] :
( ( ( in @ SV1026 @ SV849 )
= $false )
| ( ( in @ SV1026 @ ( sK131_SY3738 @ SV976 @ SV849 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV45 )
= $false )
| ( ( in @ SV976 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5317]) ).
thf(5333,plain,
! [SV1023: $i,SV97: $i > $o,SV983: $i,SV376: $i > $o] :
( ( ( SV376 @ ( sK182_SY3890 @ SV983 @ SV97 @ SV1023 @ SV376 ) )
= $true )
| ( ( SV376 @ SV1023 )
= $false )
| ( ( ( descr
@ ^ [SY2403: $i] : ( SV97 @ SY2403 ) )
= ( descr
@ ^ [SY3076: $i] : ( SV376 @ SY3076 ) ) )
= $true )
| ( ( SV97 @ SV983 )
= $false )
| ( ( SV97 @ ( sK144_SY3837 @ SV376 @ SV983 @ SV97 ) )
= $true )
| ( ( SV97 @ ( sK9_SY3069 @ SV376 @ SV97 ) )
= $true )
| ( ( SV376 @ ( sK22_SY3614 @ SV97 @ SV376 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[5318]) ).
thf(5334,plain,
! [SV141: $i > $o,SV1002: $i,SV1042: $i,SV416: $i > $o] :
( ( ( SV416 @ SV1042 )
= $false )
| ( ( ( sK173_SY3147 @ SV1002 @ SV141 @ SV416 )
= SV1042 )
= $true )
| ( ( SV141 @ SV1002 )
= $false )
| ( ( SV141 @ ( sK155_SY3859 @ SV416 @ SV1002 @ SV141 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5323]) ).
thf(5335,plain,
! [SV416: $i > $o,SV1003: $i,SV1043: $i,SV141: $i > $o] :
( ( ( SV141 @ SV1043 )
= $false )
| ( ( ( sK174_SY2531 @ SV1003 @ SV416 @ SV141 )
= SV1043 )
= $true )
| ( ( SV416 @ SV1003 )
= $false )
| ( ( SV416 @ ( sK156_SY3860 @ SV141 @ SV1003 @ SV416 ) )
= $true )
| ( ( SV141 @ ( sK13_SY3143 @ SV416 @ SV141 ) )
= $true )
| ( ( SV416 @ ( sK23_SY3631 @ SV141 @ SV416 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[5325]) ).
thf(5336,plain,
! [SV45: $i,SV980: $i,SV849: $i,SV1029: $i] :
( ( ( in @ SV1029 @ SV849 )
= $false )
| ( ( in @ SV1029 @ ( sK135_SY3738 @ SV980 @ SV849 @ SV45 ) )
= $false )
| ( ( in @ ( sK87_SY3736 @ SV45 @ SV849 ) @ SV849 )
= $true )
| ( ( in @ SV980 @ SV849 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[5331]) ).
thf(5337,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[534,5336,5335,5334,5333,5332,5330,5329,5328,5327,5326,5324,5322,5321,5320,5319,5315,5314,5313,5311,5309,5307,5301,5300,5299,5297,5296,5294,5289,5287,5275,5272,5271,5270,5268,5265,5259,5251,5248,5245,5242,5240,5236,5233,5224,5220,5219,5216,5213,5211,5207,5203,5199,5180,5179,5173,5169,5135,5134,5115,5114,5105,5098,5097,5095,5093,5092,5075,5073,5063,5062,5054,5050,5049,5017,4984,4981,4945,4941,4860,4832,4829,4828,4804,4803,4798,4797,4796,4794,4793,4792,4791,4789,4788,4787,4782,4757,4756,4755,4754,4752,4751,4750,4748,4745,4743,4742,4738,4736,4735,4733,4732,4730,4729,4723,4722,4709,4702,4701,4695,4694,4691,4689,4686,4684,4680,4677,4672,4669,4666,4663,4662,4644,4636,4634,4633,4632,4631,4630,4628,4622,4621,4613,4610,4609,4607,4603,4602,4600,4597,4595,4580,4567,4557,4556,4554,4553,4551,4550,4548,4539,4538,4530,4526,4525,4523,4513,4502,4497,4495,4484,4481,4480,4479,4478,4476,4467,4465,4462,4459,4448,4447,4428,4418,4408,4397,4394,4391,4390,4388,4387,4386,4381,4374,4370,4345,4328,4319,4318,4302,4301,4300,4298,4295,4293,4276,4275,4274,4273,4272,4271,4253,4252,4251,4249,4232,4228,4225,4223,4214,4213,4197,4195,4182,4173,4170,4167,4155,4153,4152,4144,4142,4131,4130,4129,4120,4118,4116,4115,4113,4112,4111,4108,4107,4094,4093,4091,4075,4074,4069,4068,4052,4051,4048,4047,4046,4045,4042,4041,4040,4039,4036,4035,4029,4013,3985,3981,3980,3979,3978,3976,3974,3970,3960,3959,3946,3940,3933,3915,3911,3908,3904,3901,3897,3894,3893,3892,3885,3881,3880,3879,3876,3870,3866,3859,3846,3842,3839,3838,3836,3830,3829,3828,3826,3825,3823,3822,3816,3803,3802,3795,3786,3740,3739,3737,3736,3734,3733,3728,3727,3717,3716,3714,3713,3703,3702,3697,3693,3689,3688,3676,3668,3666,3665,3663,3660,3654,3651,3648,3645,3643,3640,3638,3622,3610,3607,3604,3600,3568,3565,3562,3552,3548,3545,3543,3541,3540,3538,3534,3524,3519,3511,3499,3481,3480,3471,3470,3469,3463,3462,3446,3445,3444,3443,3442,3441,3435,3419,3418,3417,3378,3376,3372,3371,3352,3349,3348,3347,3344,3343,3342,3313,3312,3310,3309,3308,3305,3304,3295,3292,3290,3289,3287,3286,3284,3279,3272,3271,3270,3269,3243,3242,3241,3230,3226,3219,3190,3189,3187,3180,3172,3152,3144,3125,3121,3116,3082,3081,3080,3030,3006,3000,2991,2987,2973,2967,2965,2964,2963,2961,2958,2953,2952,2950,2949,2944,2930,2929,2928,2924,2912,2908,2893,2884,2883,2882,2852,2849,2838,2837,2836,2830,2824,2822,2818,2817,2816,2801,2798,2784,2783,2778,2773,2757,2756,2744,2743,2734,2717,2716,2709,2708,2702,2698,2696,2694,2681,2679,2673,2666,2659,2653,2644,2640,2627,2618,2607,2582,2581,2576,2569,2559,2553,2552,2544,2541,2535,2525,2514,2491,2489,2481,2467,2465,2440,2429,2398,2383,2349,2348,2334,2325,2317,2315,2304,2296,2268,2264,2258,2253,2226,2214,2209,2201,2199,2196,2183,2155,2154,2145,2141,2140,2131,2123,2112,2110,2096,2063,2052,2051,2050,2048,2047,2024,2023,2011,2007,2002,2001,2000,1999,1982,1981,1974,1960,1958,1953,1949,1941,1928,1927,1924,1910,1897,1882,1864,1859,1846,1845,1844,1836,1827,1800,1787,1779,1745,1675,1652,1634,1633,1632,1621,1614,1593,1576,1502,1501,1500,1487,1486,1485,1197,1196,1195,1194,1193,1192,1191,1190,1189,1188,1187,1186,1185,1183,1182,1181,1180,1179,1178,1177,1176,1173,900,899,898,895,894,892,877,876,875,600,576,538]) ).
thf(5338,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[5337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU784^1 : 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
% 0.07/0.19 % Computer : n002.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:37:12 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 155.17/26.24 ..
% 155.17/26.24
% 155.17/26.24 No.of.Axioms: 0
% 155.17/26.24
% 155.17/26.24 Length.of.Defs: 72832
% 155.17/26.24
% 155.17/26.24 Contains.Choice.Funs: true
% 155.17/26.24 .........................................................................................................................................................................................................................................
% 155.17/26.24
% 155.17/26.24 ********************************
% 155.17/26.24 * All subproblems solved! *
% 155.17/26.24 ********************************
% 155.17/26.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:300,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5337,loop_count:0,foatp_calls:1,translation:fof_full)
% 155.17/26.24
% 155.17/26.24 %**** Beginning of derivation protocol ****
% 155.17/26.24 % SZS output start CNFRefutation
% See solution above
% 155.17/26.27
% 155.17/26.27 %**** End of derivation protocol ****
% 155.17/26.27 %**** no. of clauses in derivation: 5338 ****
% 155.17/26.27 %**** clause counter: 5337 ****
% 155.17/26.27
% 155.17/26.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:300,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:5337,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------